{"as_of":"2026-08-14T13:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:404e83aedc199017fe0ff539ae66d86475362dd0359a4d0388f64dd6942ba407","coverage":[{"denominator":111,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T11:11:43.583739Z","state":"measured"},{"denominator":104,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":104,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:30:27.395309Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-15T20:16:34.363965Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.23125","snapshot_observed_at":"2026-08-10T23:30:27.395309Z","title":"Path integral analysis of Schrödinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2412.20431","last_updated":"2025-08-01T08:19:01Z","snapshot_observed_at":"2026-08-13T19:50:02.055896Z","submitted_at":"2024-12-29T10:47:54Z","title":"False vacuum decay of excited states in finite-time instanton calculus","version":2},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:27.395309Z"},"links":{"cited_paper":"/paper/2507.23125","citing_paper":"/paper/2412.20431"},"observation_digest":"sha256:a2a1b3cb40f66d0301ac5e9a233604b16273777941f3cbb7aa37d2b150a8689f","observation_id":"2699ca69-5502-4d72-8c92-2e9bd753174c","resolution":{"observed_at":"2026-08-10T23:30:27.395309Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"cited_work":{"arxiv_id":"2507.23125","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.23125","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Garbrecht and N","venue":null,"work_id":"941d0f64-6bfc-4472-8f77-3877406e3b63","year":null},"citing_paper":{"arxiv_id":"2602.20576","last_updated":"2026-05-07T04:31:45Z","snapshot_observed_at":"2026-07-06T22:46:49.536946Z","submitted_at":"2026-02-24T05:58:59Z","title":"Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-15T20:13:35.392048Z"},"links":{"cited_paper":"/paper/2507.23125","citing_paper":"/paper/2602.20576"},"observation_digest":"sha256:ebc87fd3a9278de9901c2c08f7467c57b8169efb435e269197c9d48ca01e2216","observation_id":"072127e0-75ae-4c95-89f8-9d81a1b85d29","resolution":{"observed_at":"2026-05-15T20:16:34.368001Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"cited_work":{"arxiv_id":"2507.23125","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.23125","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Garbrecht and N","venue":null,"work_id":"941d0f64-6bfc-4472-8f77-3877406e3b63","year":null},"citing_paper":{"arxiv_id":"2604.05878","last_updated":"2026-05-12T04:48:34Z","snapshot_observed_at":"2026-07-06T22:54:30.567988Z","submitted_at":"2026-04-07T13:39:17Z","title":"Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-10T19:31:50.995501Z"},"links":{"cited_paper":"/paper/2507.23125","citing_paper":"/paper/2604.05878"},"observation_digest":"sha256:52ce9b34ebd75d0503d1127a41045909bf4ec59c3d87a63950ffa0d120e01427","observation_id":"a82add50-2d62-4628-84cb-22891ab8b516","resolution":{"observed_at":"2026-05-10T22:50:50.455835Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"cited_work":{"arxiv_id":"2507.23125","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.23125","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Garbrecht and N","venue":null,"work_id":"941d0f64-6bfc-4472-8f77-3877406e3b63","year":null},"citing_paper":{"arxiv_id":"2604.05878","last_updated":"2026-05-12T04:48:34Z","snapshot_observed_at":"2026-07-06T22:54:30.567988Z","submitted_at":"2026-04-07T13:39:17Z","title":"Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-13T07:52:12.455546Z"},"links":{"cited_paper":"/paper/2507.23125","citing_paper":"/paper/2604.05878"},"observation_digest":"sha256:b4ae869a3791abe383b3e00c1b038fff52dd45ca476412401c55b4e7e21f0479","observation_id":"fb1a8bb7-bb27-4ffa-ad86-eab64fd6cea3","resolution":{"observed_at":"2026-05-13T07:52:31.321120Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.23125/citation-record","integrity":"/paper/2507.23125/integrity","json":"/paper/2507.23125/citation-record.json","paper":"/paper/2507.23125"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:41.959849Z","title":"Zur Quantentheorie des Atomkernes","venue":null,"work_id":null,"year":1928},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:41.959849Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:d36ed413b014095d29df7aeda5c3d1526a9a12f0f97f33b46f12e9e7ab9378f3","observation_id":"aed97975-b190-46b7-9b94-325f7f56e294","resolution":{"observed_at":"2026-08-06T11:11:41.959849Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.037220Z","title":"On Certain Approximate Solutions of Linear Differential Equations of the Second Order","venue":null,"work_id":null,"year":1925},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.037220Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:586f4e7285d479701facdd3ad26f3119d759f7d71d8964dffefbb741f4f18333","observation_id":"07469847-4737-47c2-8d07-927a14ff7b14","resolution":{"observed_at":"2026-08-06T11:11:42.037220Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.192065Z","title":"Quantum Mechanics and Radioactive Disintegra- tion","venue":null,"work_id":null,"year":1929},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.192065Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:607f7d8ef9689a3668e03db99084c5b6d6334f7394b2c0ab20cf27ef710a24e5","observation_id":"0659b0a7-0096-40bb-980a-aaaa4a2269f2","resolution":{"observed_at":"2026-08-06T11:11:42.192065Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.344010Z","title":"Semiclassical approximations in wave mechanics","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.344010Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:654d477076b726a5ed6875544290e2cba7390a875ebf3943bc7a0b398019bf63","observation_id":"0c79b5fe-ca52-478d-8fbc-51aa4f624d54","resolution":{"observed_at":"2026-08-06T11:11:42.344010Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.502988Z","title":"Coupled Anharmonic Oscillators. I. Equal-Mass Case","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.502988Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:b53e6b96a3ca5890fefefad624e27da63e8e79b938a3124ceb13ee2be374ce7a","observation_id":"5582b931-532a-4e28-beb3-5ee4deb27d23","resolution":{"observed_at":"2026-08-06T11:11:42.502988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.610024Z","title":"WKB Wave Function for Systems with Many Degrees of Freedom: A Unified View of Solitons and Instantons","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.610024Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:21cb1c22aeb17043e0390d1fb22944ab0d43bdeca295d02cce1ea453d2127ed4","observation_id":"021cc0d7-3a1c-4496-a93a-06c8bac20322","resolution":{"observed_at":"2026-08-06T11:11:42.610024Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.687943Z","title":"Vacuum tunneling and fluctuations around a most probable escape path","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.687943Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:353b4a52a18670837a17658d58490e03a6ad81022b7d6cf7999a27ade69fa856","observation_id":"5a78b2b5-596a-44ee-8086-a77dde4c84f0","resolution":{"observed_at":"2026-08-06T11:11:42.687943Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.809121Z","title":"Theory of the condensation point","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.809121Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:00519ccb61d6d2a8b2a731b2c5c93488ad928e3b3ebe7656c958425816866446","observation_id":"8b4ab1bf-f43c-4d7a-8afc-6e600d7b1e6f","resolution":{"observed_at":"2026-08-06T11:11:42.809121Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.881169Z","title":"Statistical theory of the decay of metastable states","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.881169Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:570a394a78acff11f7846b16e247dfee781da3ec42ec4d5a321b00931d063809","observation_id":"d5767729-d7b7-491e-b9f0-cbc833eaf00b","resolution":{"observed_at":"2026-08-06T11:11:42.881169Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:42.991226Z","title":"Integration in functional spaces and it applications in quantum physics","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:42.991226Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:c2b1d8395f492a83dd6627c396517ea26c83d0ddedfee21011436de130f24a09","observation_id":"9bab3d8a-f6b4-4fd9-99c1-81d7df1cf10e","resolution":{"observed_at":"2026-08-06T11:11:42.991226Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.025523Z","title":"Nonperturbative methods and extended-hadron models in field theory. I. Semiclassical functional methods","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.025523Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:05aa68890bda4d0a5ab5b437dacaf294e7539b2dea5297c697c5b78ac538ab71","observation_id":"3bb952d0-4326-4967-9c92-436f54393e87","resolution":{"observed_at":"2026-08-06T11:11:43.025523Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.096216Z","title":"Pseudoparticle solutions of the Yang-Mills equations","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.096216Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:45feac8e5f7a8fc8b10a6b2a21bd37dea61a413df74edf72b30aec3b52e722e8","observation_id":"5bb2ee0e-7f30-4026-b986-4f5576781174","resolution":{"observed_at":"2026-08-06T11:11:43.096216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.173126Z","title":"Symmetry Breaking through Bell-Jackiw Anomalies","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.173126Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:0092c63edc5569290f5f8934be9e59cc66b055cebd58aa8bf8206b2d31b91bfc","observation_id":"0df31774-785d-4f2a-a711-d0406239b908","resolution":{"observed_at":"2026-08-06T11:11:43.173126Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.177519Z","title":"Bubbles in metastable vacuum","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.177519Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:f84c2efc5b2151741d6f942c86949cfe33a1926651e843d29867e1505ccf0859","observation_id":"982c09ef-5af5-43ac-82fd-30a01a03634b","resolution":{"observed_at":"2026-08-06T11:11:43.177519Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.182423Z","title":"Pseudoparticle contributions to the energy spectrum of a one-dimensional system","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.182423Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:663611ed60b149595453ef7800bcf1eddf57e7241a95e6ff097ab3adba16a5b9","observation_id":"5499efb6-bb78-492c-bd87-90fbf78812c0","resolution":{"observed_at":"2026-08-06T11:11:43.182423Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.187039Z","title":"The fate of the false vacuum. I. Semiclassical theory","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.187039Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:c611222312426013b8c56184f2c8af526ca7674560eb73e85d9be3d7c0d18ac0","observation_id":"90fd7957-2216-4c3c-9b9e-f21023402fcb","resolution":{"observed_at":"2026-08-06T11:11:43.187039Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.191717Z","title":"The fate of the false vacuum. II. First quantum corrections","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.191717Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:57627d6b1c39c143cbd1996fdfa254008411842c8a3060f4ae76161a1961e850","observation_id":"7501b2a2-6603-48f0-b619-0b92038e4cbb","resolution":{"observed_at":"2026-08-06T11:11:43.191717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.195819Z","title":"Electroweak Higgs Potentials and Vacuum Stability","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.195819Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:2c059c3e2ce9409be0c427a08cfcbcabdc5fa89b88efbf00013e08342ebc6931","observation_id":"7c39c2be-a7fb-4653-a7da-d6197d14d221","resolution":{"observed_at":"2026-08-06T11:11:43.195819Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-ph/9504241","last_updated":"1995-04-06T09:58:03Z","snapshot_observed_at":"2026-07-07T04:19:37.649953Z","submitted_at":"1995-04-06T09:58:03Z","title":"IMPROVED METASTABILITY BOUNDS ON THE STANDARD MODEL HIGGS MASS","version":1},"cited_work":{"arxiv_id":"hep-ph/9504241","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-ph/9504241","snapshot_observed_at":"2026-08-06T11:11:44.659811Z","title":"IMPROVED METASTABILITY BOUNDS ON THE STANDARD MODEL HIGGS MASS","venue":"hep-ph","work_id":"90ee10a2-a99a-4091-b170-98bd90cf36d6","year":1995},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.200432Z"},"links":{"cited_paper":"/paper/hep-ph/9504241","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:3a74c236d256a0acb3c3148f83f311ddd31855b3972a5cb43b5c5c80722888fd","observation_id":"8660b6c4-c0fb-462a-b8fe-ef775945d75b","resolution":{"observed_at":"2026-08-06T11:11:44.664830Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-ph/0104016","last_updated":"2001-05-31T13:49:39Z","snapshot_observed_at":"2026-07-07T03:52:01.546825Z","submitted_at":"2001-04-02T12:33:22Z","title":"On the metastability of the Standard Model vacuum","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-ph/0104016","snapshot_observed_at":"2026-08-06T11:11:43.205683Z","title":"On the metastability of the Standard Model vacuum","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.205683Z"},"links":{"cited_paper":"/paper/hep-ph/0104016","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:d01fdf590283cab06493740c547e79c9ac3a2b7505d7009915c2e60e1ea2206f","observation_id":"f48e0d95-663f-4ed3-bab1-75c4e274d6a9","resolution":{"observed_at":"2026-08-06T11:11:43.205683Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1307.3536","last_updated":"2014-09-22T14:12:25Z","snapshot_observed_at":"2026-08-13T03:56:06.885492Z","submitted_at":"2013-07-12T18:34:05Z","title":"Investigating the near-criticality of the Higgs boson","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1307.3536","snapshot_observed_at":"2026-08-06T11:11:43.210138Z","title":"Investigating the near-criticality of the Higgs boson","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.210138Z"},"links":{"cited_paper":"/paper/1307.3536","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:153810ee67f7ae8d1eca4299e619672b39fcf6c8cba5f9c8901f51bf52103ca8","observation_id":"70043d8c-4170-4389-b2c5-eda510173e2d","resolution":{"observed_at":"2026-08-06T11:11:43.210138Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1604.06090","last_updated":"2017-08-31T16:25:43Z","snapshot_observed_at":"2026-07-06T04:53:33.721115Z","submitted_at":"2016-04-20T20:00:00Z","title":"Precision decay rate calculations in quantum field theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1604.06090","snapshot_observed_at":"2026-08-06T11:11:43.214841Z","title":"Precisiondecayrate calcula- tions in quantum field theory","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.214841Z"},"links":{"cited_paper":"/paper/1604.06090","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:d22384998ce86490dec6274c766868cc420e9d34ed9b3c11ecb28d96ca3acc7a","observation_id":"3a723e1d-986c-47ec-839f-d8b07bab88a5","resolution":{"observed_at":"2026-08-06T11:11:43.214841Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.08124","last_updated":"2018-05-02T20:13:30Z","snapshot_observed_at":"2026-08-12T14:06:12.625363Z","submitted_at":"2017-07-25T18:00:04Z","title":"Scale Invariant Instantons and the Complete Lifetime of the Standard Model","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.08124","snapshot_observed_at":"2026-08-06T11:11:43.219397Z","title":"Scale-invariant instantons and the complete lifetime of the standard model","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.219397Z"},"links":{"cited_paper":"/paper/1707.08124","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:4d2d881431554ee1d54d6dc142b3abff13639d7ba3b132dc3e9f7ca95312de37","observation_id":"513bf93a-19f7-417d-9865-a9ed65aecbc7","resolution":{"observed_at":"2026-08-06T11:11:43.219397Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.224254Z","title":"Vanishing homologies and then variable saddlepoint method","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.224254Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:b5dadbb49dfa6bcb3627e460bd3616fcc346a96a3dc11995b0e45481fa0c9312","observation_id":"f6e58be5-1939-43f0-861b-b12a6c41a998","resolution":{"observed_at":"2026-08-06T11:11:43.224254Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.228751Z","title":"Global asymptotics for multiple integrals with boundaries","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.228751Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:f8bd506d12c35a91597f9d90efe74ffd6e2fdd900f9f85046388c0cb91ecdafd","observation_id":"c8ef1df9-2428-4ef2-8362-5a7b8ceaca7c","resolution":{"observed_at":"2026-08-06T11:11:43.228751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1001.2933","last_updated":"2010-08-28T04:23:48Z","snapshot_observed_at":"2026-08-06T06:26:01.233312Z","submitted_at":"2010-01-18T17:02:17Z","title":"Analytic Continuation Of Chern-Simons Theory","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1001.2933","snapshot_observed_at":"2026-08-06T11:11:43.233074Z","title":"Analytic Continuation Of Chern-Simons Theory","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.233074Z"},"links":{"cited_paper":"/paper/1001.2933","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:de5ccda4fd71d2ac7461e505072b96de06190dc8883e5a1cb06d486fbae7275f","observation_id":"3276eb4d-244a-44dc-ba69-1ac8346d039d","resolution":{"observed_at":"2026-08-06T11:11:43.233074Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1406.2386","last_updated":"2014-09-18T22:00:30Z","snapshot_observed_at":"2026-07-06T03:45:54.716117Z","submitted_at":"2014-06-09T23:26:54Z","title":"Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1406.2386","snapshot_observed_at":"2026-08-06T11:11:43.237351Z","title":"Real-time Feynman path integral with Picard-Lefschetz theory and its applications to quantum tunneling","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.237351Z"},"links":{"cited_paper":"/paper/1406.2386","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:0c7400eb83d926706702d0b6ca70016b589c0d08fb7003f2e2323ea7379767e0","observation_id":"7fd927a5-24b7-4c71-bdae-31a4551f2ad2","resolution":{"observed_at":"2026-08-06T11:11:43.237351Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1510.03435","last_updated":"2015-10-12T20:12:54Z","snapshot_observed_at":"2026-08-13T04:43:26.901049Z","submitted_at":"2015-10-12T20:12:54Z","title":"Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1510.03435","snapshot_observed_at":"2026-08-06T11:11:43.242241Z","title":"Toward Picard-Lefschetz theory of path integrals, complex saddles and resurgence","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.242241Z"},"links":{"cited_paper":"/paper/1510.03435","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:9ede1205485af8ad16a39a21015ced3fcb26bbc75cc63512e141727ea5dfb488","observation_id":"24b666d8-c5f1-4974-8494-0623207d4901","resolution":{"observed_at":"2026-08-06T11:11:43.242241Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.04236","last_updated":"2019-12-15T10:10:29Z","snapshot_observed_at":"2026-08-10T13:07:19.486951Z","submitted_at":"2019-05-10T16:05:49Z","title":"Functional methods for false vacuum decay in real time","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.04236","snapshot_observed_at":"2026-08-06T11:11:43.246656Z","title":"Functional methods for false vacuum decay in real time","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.246656Z"},"links":{"cited_paper":"/paper/1905.04236","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:8eac8c63c2264f63039ac0c7ca7c5a124f855f3c45b157f2331a45fb78f05f52","observation_id":"c41dd0e1-4c1e-44ea-882e-aa5789a31f52","resolution":{"observed_at":"2026-08-06T11:11:43.246656Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1011.0121","last_updated":"2011-08-06T14:01:33Z","snapshot_observed_at":"2026-07-06T02:18:28.603864Z","submitted_at":"2010-10-31T02:49:03Z","title":"Quantum tunneling as a classical anomaly","version":2},"cited_work":{"arxiv_id":"1011.0121","doi":null,"metadata_source":"pith","pith_arxiv_id":"1011.0121","snapshot_observed_at":"2026-08-06T11:11:44.484154Z","title":"Quantum tunneling as a classical anomaly","venue":"hep-th","work_id":"f2bc9cd9-d8c2-414a-acb9-84f27a740d4e","year":2010},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.251375Z"},"links":{"cited_paper":"/paper/1011.0121","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:701b5c6ff7408cf731ad9631fff688cf5362224fa46a69b70f369aa78e400b7c","observation_id":"0be0ff37-642d-434c-8e12-e0b29ecd3039","resolution":{"observed_at":"2026-08-06T11:11:44.489508Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1312.1772","last_updated":"2014-04-30T15:29:03Z","snapshot_observed_at":"2026-07-06T03:30:08.960400Z","submitted_at":"2013-12-06T05:47:46Z","title":"On Quantum Tunneling in Real Time","version":4},"cited_work":{"arxiv_id":"1312.1772","doi":null,"metadata_source":"pith","pith_arxiv_id":"1312.1772","snapshot_observed_at":"2026-08-06T11:11:44.461789Z","title":"On Quantum Tunneling in Real Time","venue":"quant-ph","work_id":"f7fb9b24-e07e-4b37-9649-8b92c472b785","year":2013},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.256379Z"},"links":{"cited_paper":"/paper/1312.1772","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:66a89c77204cb550129b19ea1ddb400b3b31a6e33d7456998c3755668766ceb0","observation_id":"ab01a991-713c-4df7-ba65-702cc2c8174a","resolution":{"observed_at":"2026-08-06T11:11:44.466613Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.0012","last_updated":"2014-08-19T17:06:34Z","snapshot_observed_at":"2026-07-06T03:50:38.885516Z","submitted_at":"2014-07-31T20:00:35Z","title":"Real-Time Feynman Path Integral Realization of Instantons","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1408.0012","snapshot_observed_at":"2026-08-06T11:11:43.260920Z","title":"Real-Time Feynman Path Integral Realization of Instantons","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.260920Z"},"links":{"cited_paper":"/paper/1408.0012","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:fd973d1d82997abb955ad4fc4cf6d8d3e00497fe6497210c59e64222b6d8771a","observation_id":"f815def6-17ab-4f01-93b4-79384a091559","resolution":{"observed_at":"2026-08-06T11:11:43.260920Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1605.02751","last_updated":"2016-09-15T11:28:40Z","snapshot_observed_at":"2026-07-06T04:55:39.926609Z","submitted_at":"2016-05-09T20:03:54Z","title":"Quantum tunneling from paths in complex time","version":2},"cited_work":{"arxiv_id":"1605.02751","doi":null,"metadata_source":"pith","pith_arxiv_id":"1605.02751","snapshot_observed_at":"2026-08-06T11:11:44.417618Z","title":"Quantum tunneling from paths in complex time","venue":"hep-th","work_id":"03a37c73-88a9-4f0e-b1cd-d4c15b4c5f12","year":2016},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.265649Z"},"links":{"cited_paper":"/paper/1605.02751","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:c58679607c1e934bb0679f3826d8e288ea56ff7ecc14ba4aeb809b4ecf6f71b6","observation_id":"55e154b7-6b26-4859-995a-933db55bf62a","resolution":{"observed_at":"2026-08-06T11:11:44.423982Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1602.01102","last_updated":"2016-02-02T21:00:10Z","snapshot_observed_at":"2026-07-06T04:44:55.350506Z","submitted_at":"2016-02-02T21:00:10Z","title":"A direct approach to quantum tunneling","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1602.01102","snapshot_observed_at":"2026-08-06T11:11:43.270086Z","title":"Direct Approach to Quantum Tunneling","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.270086Z"},"links":{"cited_paper":"/paper/1602.01102","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:ba06368e5385c78d0684d7b4ee768cd657c68d1b0485c2c8c19e0d1f4a48f7b6","observation_id":"c0372669-4259-43d7-a8f7-31d1a459a122","resolution":{"observed_at":"2026-08-06T11:11:43.270086Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.02488","last_updated":"2019-12-10T08:39:16Z","snapshot_observed_at":"2026-08-14T07:30:27.870037Z","submitted_at":"2019-09-05T15:40:43Z","title":"Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles","version":2},"cited_work":{"arxiv_id":"1909.02488","doi":null,"metadata_source":"pith","pith_arxiv_id":"1909.02488","snapshot_observed_at":"2026-08-06T11:11:44.356421Z","title":"Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles","venue":"hep-th","work_id":"3a869c34-a37f-4235-bc7e-464e24b1bf03","year":2019},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.274420Z"},"links":{"cited_paper":"/paper/1909.02488","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:ba8e412242e1fc0262adc422a235cdd97bf0f8c8fb34a966a51436f2cb2ea160","observation_id":"d8593fe3-2594-495b-aa88-30a286d5e9f9","resolution":{"observed_at":"2026-08-06T11:11:44.362143Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.06069","last_updated":"2019-06-20T15:47:17Z","snapshot_observed_at":"2026-07-06T06:45:05.493758Z","submitted_at":"2018-06-15T18:00:02Z","title":"A New Semiclassical Picture of Vacuum Decay","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.06069","snapshot_observed_at":"2026-08-06T11:11:43.278751Z","title":"New Semiclassical Picture of Vacuum Decay","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.278751Z"},"links":{"cited_paper":"/paper/1806.06069","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:59e6178ef395e539aa3adc4d8bd6559e6dd97390ddfede20033c87b438d06df2","observation_id":"718143a6-6cf7-4ce1-acd7-c8448a51f1ed","resolution":{"observed_at":"2026-08-06T11:11:43.278751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1904.08565","last_updated":"2019-08-13T21:15:59Z","snapshot_observed_at":"2026-08-14T03:25:36.710950Z","submitted_at":"2019-04-18T01:58:08Z","title":"Vacuum Decay in Real Time and Imaginary Time Formalisms","version":2},"cited_work":{"arxiv_id":"1904.08565","doi":null,"metadata_source":"pith","pith_arxiv_id":"1904.08565","snapshot_observed_at":"2026-08-06T11:11:44.311870Z","title":"Vacuum Decay in Real Time and Imaginary Time Formalisms","venue":"hep-th","work_id":"49a58dec-c0b3-4219-a4ff-e9662bb12d28","year":2019},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.284407Z"},"links":{"cited_paper":"/paper/1904.08565","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:85ffd2a22e74dce1600cb7589c32d18391438dc0d6751c40552c30f382f6b5a1","observation_id":"1622461b-1e4d-4e23-9721-3b50597e2b71","resolution":{"observed_at":"2026-08-06T11:11:44.317752Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2102.09767","last_updated":"2021-10-15T10:37:52Z","snapshot_observed_at":"2026-08-13T20:12:16.720886Z","submitted_at":"2021-02-19T07:00:01Z","title":"Lorentzian path integral for quantum tunneling and WKB approximation for wave-function","version":4},"cited_work":{"arxiv_id":"2102.09767","doi":null,"metadata_source":"pith","pith_arxiv_id":"2102.09767","snapshot_observed_at":"2026-08-06T11:11:44.287676Z","title":"Lorentzian path integral for quantum tunneling and WKB approximation for wave-function","venue":"gr-qc","work_id":"aa2df396-4d24-4431-b47f-5987086b211e","year":2021},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.289088Z"},"links":{"cited_paper":"/paper/2102.09767","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:f340785b5fddb00d546ddd5e8b750c5d81e9bbe4bc9cfeed4bb727da1afad532","observation_id":"695e18d8-74c9-4a0d-b6dc-def1d1deeed3","resolution":{"observed_at":"2026-08-06T11:11:44.293611Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11199","last_updated":"2023-08-02T05:07:29Z","snapshot_observed_at":"2026-08-13T13:17:35.668060Z","submitted_at":"2023-07-20T19:23:33Z","title":"A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations","version":2},"cited_work":{"arxiv_id":"2307.11199","doi":null,"metadata_source":"pith","pith_arxiv_id":"2307.11199","snapshot_observed_at":"2026-08-06T11:11:44.261102Z","title":"A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations","venue":"hep-th","work_id":"06259dfc-c5b4-42ee-8cdb-7323f3279084","year":2023},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.293543Z"},"links":{"cited_paper":"/paper/2307.11199","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:d5616c1325b50b064f9f9129596190307e7ff86f6c01ca678c6a72e92e769b0c","observation_id":"329f5151-08c6-4190-a0fc-f4cecebba229","resolution":{"observed_at":"2026-08-06T11:11:44.266356Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.07585","last_updated":"2023-09-14T10:35:39Z","snapshot_observed_at":"2026-08-13T10:13:49.435011Z","submitted_at":"2023-09-14T10:35:39Z","title":"Unraveling the bounce: a real time perspective on tunneling","version":1},"cited_work":{"arxiv_id":"2309.07585","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.07585","snapshot_observed_at":"2026-08-06T11:11:44.231684Z","title":"Unraveling the bounce: a real time perspective on tunneling","venue":"quant-ph","work_id":"fc5434d6-cd09-4c2a-94e0-035e7a4f5f7d","year":2023},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.297855Z"},"links":{"cited_paper":"/paper/2309.07585","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:00e40b6be1728f3b80ca0cd7ffa4d97466af778c9fc59cbe37561fd76b6039c4","observation_id":"b5bbc903-447a-458a-8415-a814ad05518f","resolution":{"observed_at":"2026-08-06T11:11:44.240124Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.19865","last_updated":"2025-04-22T23:49:13Z","snapshot_observed_at":"2026-08-13T05:37:18.034636Z","submitted_at":"2023-10-30T18:00:00Z","title":"Finite-Temperature Instantons from First Principles","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.19865","snapshot_observed_at":"2026-08-06T11:11:43.302373Z","title":"Finite-temperature instantons from first principles","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.302373Z"},"links":{"cited_paper":"/paper/2310.19865","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:1b9de8dbb1c9ad04dd54a52beb9dbd057ee0667a49295e905d98413a602a9d81","observation_id":"d7642bc9-8565-4d62-a1e2-9fa2c63ebaf2","resolution":{"observed_at":"2026-08-06T11:11:43.302373Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.00099","last_updated":"2025-07-29T17:59:59Z","snapshot_observed_at":"2026-08-13T04:29:49.696931Z","submitted_at":"2024-01-31T19:00:00Z","title":"Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.00099","snapshot_observed_at":"2026-08-06T11:11:43.306946Z","title":"Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.306946Z"},"links":{"cited_paper":"/paper/2402.00099","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:79355607b84ddce6084ec0b1c36049ab400cdd33274bb82d95d586a66c0bb707","observation_id":"c1846eba-4b32-40f3-9eab-1ae50778c452","resolution":{"observed_at":"2026-08-06T11:11:43.306946Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.02820","last_updated":"2024-11-05T19:24:41Z","snapshot_observed_at":"2026-08-12T22:51:25.125059Z","submitted_at":"2024-09-04T15:38:27Z","title":"Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem","version":2},"cited_work":{"arxiv_id":"2409.02820","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.02820","snapshot_observed_at":"2026-08-06T11:11:44.160973Z","title":"Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem","venue":"physics.chem-ph","work_id":"325037bd-dc66-4c73-b46b-1365e3316a16","year":2024},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.311530Z"},"links":{"cited_paper":"/paper/2409.02820","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:44c1f282258e44245d5b26fb15dbdb8a1e7d8244e66cfcb7ee735ad92b303e58","observation_id":"d3eeda2e-c60e-49c0-8b22-bdd6768dc855","resolution":{"observed_at":"2026-08-06T11:11:44.167480Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.12420","last_updated":"2023-09-21T18:43:24Z","snapshot_observed_at":"2026-08-13T10:08:05.422520Z","submitted_at":"2023-09-21T18:43:24Z","title":"Complex classical paths in quantum reflections and tunneling","version":1},"cited_work":{"arxiv_id":"2309.12420","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.12420","snapshot_observed_at":"2026-08-06T11:11:44.132919Z","title":"Complex classical paths in quantum reflections and tunneling","venue":"quant-ph","work_id":"a2ed9283-e7f7-4305-95ca-c96165d30ed7","year":2023},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.316267Z"},"links":{"cited_paper":"/paper/2309.12420","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:af759d42e017cd99d21cee2f840b13249c8520f3841d5d86a965f2727e830ae0","observation_id":"edf94ed7-1b99-4d6c-bb56-01fe136d534c","resolution":{"observed_at":"2026-08-06T11:11:44.139736Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20431","last_updated":"2025-08-01T08:19:01Z","snapshot_observed_at":"2026-08-13T19:50:02.055896Z","submitted_at":"2024-12-29T10:47:54Z","title":"False vacuum decay of excited states in finite-time instanton calculus","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.20431","snapshot_observed_at":"2026-08-06T11:11:43.320892Z","title":"False vacuum decay of excited states in finite-time instanton calculus","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.320892Z"},"links":{"cited_paper":"/paper/2412.20431","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:a3203a746ba1fda3982146fa491942acaade48072d5b94f4624e1bc8fcbb25a0","observation_id":"2c9579f5-f5ce-48b5-bc2e-5c9a65c7c55e","resolution":{"observed_at":"2026-08-06T11:11:43.320892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/9809072","last_updated":"1998-09-24T02:27:05Z","snapshot_observed_at":"2026-08-03T10:33:16.705390Z","submitted_at":"1998-09-24T02:27:05Z","title":"PT-Symmetric Quantum Mechanics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/9809072","snapshot_observed_at":"2026-08-06T11:11:43.325300Z","title":"PT -symmetric quantum mechanics","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.325300Z"},"links":{"cited_paper":"/paper/quant-ph/9809072","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:1f8b3f4960b7a8beed9f93343c6ea2c8af91ebe5352db03aa42160b468a00501","observation_id":"5d409bcd-4a0e-4068-bd1e-fd3232234254","resolution":{"observed_at":"2026-08-06T11:11:43.325300Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0208076","last_updated":"2002-10-30T13:52:44Z","snapshot_observed_at":"2026-07-07T07:10:39.202749Z","submitted_at":"2002-08-12T16:57:54Z","title":"Complex Extension of Quantum Mechanics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0208076","snapshot_observed_at":"2026-08-06T11:11:43.330284Z","title":"Complex extension of quantum mechanics","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.330284Z"},"links":{"cited_paper":"/paper/quant-ph/0208076","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:a6c9098537c12cb0199647f9148087bee360c428ee9f8ca19dfacbfc5aefd63e","observation_id":"4cf63f5f-ed66-415b-8317-3c1dff9581f3","resolution":{"observed_at":"2026-08-06T11:11:43.330284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0703096","last_updated":"2007-03-09T13:31:04Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2007-03-09T13:31:04Z","title":"Making Sense of Non-Hermitian Hamiltonians","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0703096","snapshot_observed_at":"2026-08-06T11:11:43.334857Z","title":"Making sense of non-Hermitian Hamiltonians","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.334857Z"},"links":{"cited_paper":"/paper/hep-th/0703096","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:b33f96a58604dec56c0dddd44b783bca655397e739e9df2a75146a190256b9ed","observation_id":"3204a6d6-a685-4ed7-96fe-520fc1f3d894","resolution":{"observed_at":"2026-08-06T11:11:43.334857Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0703066","last_updated":"2007-07-12T13:15:07Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2007-03-07T19:57:23Z","title":"The ODE/IM Correspondence","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0703066","snapshot_observed_at":"2026-08-06T11:11:43.339772Z","title":"The ODE/IM Correspondence","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.339772Z"},"links":{"cited_paper":"/paper/hep-th/0703066","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:28d71d7fb2c66d116de07c4fd7407f8791295ce566a8809f85c22f09baa290ec","observation_id":"37dd453f-4ab8-4549-bf94-2b21d9feecfd","resolution":{"observed_at":"2026-08-06T11:11:43.339772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.344303Z","title":"Contribution to the Decay Theory of a Quasi-Stationary State","venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.344303Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:05568ad2242519a79ee180f6de641fc961f5a6a1ec05e07f429c57cfc6d2816b","observation_id":"003109ee-444a-4b3c-83b2-2cefab247bf8","resolution":{"observed_at":"2026-08-06T11:11:43.344303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.348717Z","title":"Wie gut gilt das Exponentialgesetz beimα-Zerfall?","venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.348717Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:14e5db276be51790878b3bd1f7aef5058d4102b0b8b8a91d7691affa95b0c79d","observation_id":"db2b2679-9b17-4ee9-a892-4e166fd0f9e4","resolution":{"observed_at":"2026-08-06T11:11:43.348717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.353075Z","title":"The exponential decay law of unstable systems","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.353075Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:64bb9009a18932edce014a8a1867da0448dc4f9f97b31b4192648d30f9a3ffce","observation_id":"3b565a67-452f-4706-89e1-19e99afd0964","resolution":{"observed_at":"2026-08-06T11:11:43.353075Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.357729Z","title":"Time evolution of unstable quantum states and a resolution of Zeno’s paradox","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.357729Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:3934ecaf7ae3e80a08fe80ba3503fbe385ea24f7496c97b7847fff5108f079de","observation_id":"c81ae5fb-78f5-4cda-83b0-d6bc2b8ae040","resolution":{"observed_at":"2026-08-06T11:11:43.357729Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.361844Z","title":"Decay theory of unstable quantum systems","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.361844Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:5d04669933cf5b7377c54777d4b471816dd84bbb30a11574db56cdc55436c377","observation_id":"a62e98a9-a4eb-463e-878a-6719b964ee06","resolution":{"observed_at":"2026-08-06T11:11:43.361844Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.366045Z","title":"Nonexponential decay law","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.366045Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:9ae8bbcb75cf7d6d0bae04eb8ce0e67ed8da94e692ef67fd2bf3f3e96d7317ca","observation_id":"2f928ca3-9cf3-44c0-a7a6-c5e2ee2c5617","resolution":{"observed_at":"2026-08-06T11:11:43.366045Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.370242Z","title":"On the Derivation of the Dispersion Formula for Nuclear Reactions","venue":null,"work_id":null,"year":1939},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.370242Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:54e18cf779abc5f6507a49c637b05b422b75a94766006ac31b3f096129038217","observation_id":"2e7981a3-7146-4083-b90a-21c5c2b9142a","resolution":{"observed_at":"2026-08-06T11:11:43.370242Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.374621Z","title":"Introduction to Spectral Theory: With Applications to Schrödinger Operators","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.374621Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:bf2b405722952014b46a41be80563aa181db24c2030edb05aca02bf0a5fc6572","observation_id":"7ce9e76c-900e-4e99-94d4-fd0f849d3702","resolution":{"observed_at":"2026-08-06T11:11:43.374621Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0201091","last_updated":"2002-06-11T09:40:09Z","snapshot_observed_at":"2026-07-07T07:07:14.349502Z","submitted_at":"2002-01-21T10:27:38Z","title":"A Pedestrian Introduction to Gamow Vectors","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0201091","snapshot_observed_at":"2026-08-06T11:11:43.379803Z","title":"A pedestrian introduction to Gamow vectors","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.379803Z"},"links":{"cited_paper":"/paper/quant-ph/0201091","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:b75f67217b7817a975079c6968b4beb19ab4c4965df3724ee316a73fd4a69833","observation_id":"b5ae9427-6f71-4e91-a378-95ceb3a831d4","resolution":{"observed_at":"2026-08-06T11:11:43.379803Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0705.1388","last_updated":"2007-08-06T05:08:14Z","snapshot_observed_at":"2026-08-09T20:28:22.391221Z","submitted_at":"2007-05-10T04:05:24Z","title":"Some properties of the resonant state in quantum mechanics and its computation","version":2},"cited_work":{"arxiv_id":"0705.1388","doi":null,"metadata_source":"pith","pith_arxiv_id":"0705.1388","snapshot_observed_at":"2026-08-06T11:11:43.953747Z","title":"Some properties of the resonant state in quantum mechanics and its computation","venue":"quant-ph","work_id":"998cb01c-63c6-445a-87dd-e939493b4f41","year":2007},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.384535Z"},"links":{"cited_paper":"/paper/0705.1388","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:2e49f43d5c01a55ccb40080f5a9328806f9fe26ec4715e696754987b93182275","observation_id":"897ea0ab-7b3f-45c4-b169-de0ea0758cf6","resolution":{"observed_at":"2026-08-06T11:11:43.959167Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.389356Z","title":"Algebraic Analysis of Singular Perturbation Theory","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.389356Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:78d9480e69d058e19ab5a9d8457d9a017909552a24aa659a9b3734b08f6034c1","observation_id":"95f621d3-eca7-407f-abaa-b3379f28a0ff","resolution":{"observed_at":"2026-08-06T11:11:43.389356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.393809Z","title":"Global theory of a second order linear ordinary differential equation with a polynomial coefficient","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.393809Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:6b95c9bb5d7d9efc6b79be4fd1d18cc56f2b372d149326ce572552891e4480a8","observation_id":"6b8ee50e-170f-4dbf-91d6-3dc103e061e6","resolution":{"observed_at":"2026-08-06T11:11:43.393809Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:43.398976Z","title":"Asymptotic Analysis: Linear Ordinary Differential Equations","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.398976Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:733872c365576b5baf9dff44abb971e94a251e792f7807ff23fad7502abebab2","observation_id":"be5e90d9-cff4-4006-a662-25fc54dbd8ce","resolution":{"observed_at":"2026-08-06T11:11:43.398976Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1005.1696","last_updated":"2010-08-23T12:59:51Z","snapshot_observed_at":"2026-07-06T02:10:07.809178Z","submitted_at":"2010-05-11T00:25:58Z","title":"Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families","version":2},"cited_work":{"arxiv_id":"1005.1696","doi":null,"metadata_source":"pith","pith_arxiv_id":"1005.1696","snapshot_observed_at":"2026-08-06T11:11:43.931785Z","title":"Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families","venue":"math-ph","work_id":"e88db6c2-f62a-4cc7-ad49-8da4681a8605","year":2010},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.403508Z"},"links":{"cited_paper":"/paper/1005.1696","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:5f512138c8481e74254cedc6ef83485e6409f8e3f86eedaeb6d1b7109ee9d0b4","observation_id":"babbcf5d-0ab7-49f7-891c-82db9a0544a5","resolution":{"observed_at":"2026-08-06T11:11:43.936843Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.296674Z","title":"Anharmonic Oscillator","venue":null,"work_id":"2f184f84-68c9-422d-a39a-68f8b30e5f30","year":1969},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.408734Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:b7b69da195f6568a1fad035f06c1816c889d811a06eb8b2cee78e97a78d59061","observation_id":"74a2ee8e-08d4-456b-9323-f7d9376b5226","resolution":{"observed_at":"2026-08-06T11:11:45.303171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.275242Z","title":"Analytic continuation of eigenvalue problems","venue":null,"work_id":"0c86c929-144e-4a75-bf2d-d338db685e4b","year":1993},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.413306Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:cdf3ed6564aa2ed5b13cf4e236f2f0d2180cfba0d88eda5a1f6badc1875c307b","observation_id":"7bbdfa3a-5d49-4920-b6e2-45469cdf5305","resolution":{"observed_at":"2026-08-06T11:11:45.281014Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math-ph/9902016","last_updated":"1999-02-10T15:48:15Z","snapshot_observed_at":"2026-08-14T03:40:59.281348Z","submitted_at":"1999-02-10T15:48:15Z","title":"An exact solution method for 1D polynomial Schr\\\"odinger equations","version":1},"cited_work":{"arxiv_id":"math-ph/9902016","doi":null,"metadata_source":"pith","pith_arxiv_id":"math-ph/9902016","snapshot_observed_at":"2026-08-06T11:11:43.910890Z","title":"An exact solution method for 1D polynomial Schr\\\"odinger equations","venue":"math-ph","work_id":"960b1b36-0ce0-43fb-a5a9-333a384c5036","year":1999},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.417783Z"},"links":{"cited_paper":"/paper/math-ph/9902016","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:2f11d7ce70deccc3d233f91b5073ab4768a68568fd1699ac80785b088b949c1c","observation_id":"cfc303f3-6122-4602-9b46-4a54039cf670","resolution":{"observed_at":"2026-08-06T11:11:43.915581Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math-ph/0007006","last_updated":"2000-07-05T07:42:34Z","snapshot_observed_at":"2026-07-07T06:12:30.674409Z","submitted_at":"2000-07-05T07:42:34Z","title":"On the eigenproblems of PT-symmetric oscillators","version":1},"cited_work":{"arxiv_id":"math-ph/0007006","doi":null,"metadata_source":"pith","pith_arxiv_id":"math-ph/0007006","snapshot_observed_at":"2026-08-06T11:11:43.889389Z","title":"On the eigenproblems of PT-symmetric oscillators","venue":"math-ph","work_id":"5ccb3cac-fe21-45d3-b78d-cdec8335887e","year":2000},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.422274Z"},"links":{"cited_paper":"/paper/math-ph/0007006","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:2b2e1c24c636b9db3a75811a4cecdc32d21646984b7fc73494139bf17f97f55a","observation_id":"9c8531f0-5e39-421c-834e-0842aaeea634","resolution":{"observed_at":"2026-08-06T11:11:43.894471Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0407018","last_updated":"2005-01-03T08:31:33Z","snapshot_observed_at":"2026-08-14T06:24:12.393229Z","submitted_at":"2004-07-01T16:30:21Z","title":"Eigenvalues of PT-symmetric oscillators with polynomial potentials","version":3},"cited_work":{"arxiv_id":"math/0407018","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0407018","snapshot_observed_at":"2026-08-06T11:11:43.867043Z","title":"Eigenvalues of PT-symmetric oscillators with polynomial potentials","venue":"math.SP","work_id":"cb734906-b902-4725-9b88-786f62d58033","year":2004},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.426840Z"},"links":{"cited_paper":"/paper/math/0407018","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:1f363124e8d470e41f41c36899bc81c8d81682329c538993d4708ac069afd1a6","observation_id":"a0c93d14-f1bb-4a7e-9d55-16035f996231","resolution":{"observed_at":"2026-08-06T11:11:43.872439Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.253244Z","title":"A class of analytic perturbations for one-body Schrödinger Hamiltonians","venue":null,"work_id":"318ca178-b8e3-43b5-b4d7-29047bd94133","year":1971},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.431333Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:f064b477249625507411996a8ea40c20cda854f6676811b6bfd1cd4e2d3e2f75","observation_id":"1fc9acfc-5839-49c5-9cbf-d2404746bc0f","resolution":{"observed_at":"2026-08-06T11:11:45.259918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.234664Z","title":"Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions","venue":null,"work_id":"bd9429e1-446a-433b-ba9a-c781a5f7acc7","year":1971},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.435778Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:f4b6883d2bb50eb12b404f5cc23eefccef6e0a170c821a587fc3e5da53ca5cac","observation_id":"f39ceb80-0b81-4862-82c3-422067264224","resolution":{"observed_at":"2026-08-06T11:11:45.240363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.210904Z","title":"Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory","venue":null,"work_id":"c2f2d264-3134-4fbe-9ac8-3dac4b148bd8","year":1973},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.440252Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:3d5da3881699f898e6287cb1c32894733e76a0f59b62c797ef6b418c204c58a6","observation_id":"204e29ae-a74f-4350-8488-b23cd82d0973","resolution":{"observed_at":"2026-08-06T11:11:45.220863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.192838Z","title":"Resonance calculations for arbitrary potentials","venue":null,"work_id":"e79672ed-fe90-4ef9-b167-f3ffb68ea85e","year":1978},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.446610Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:95610313a34d65628d70e5c8a353376801b0ba448c388589d11c5f6e05bf56d4","observation_id":"ae7cef84-a827-4d95-a880-83a7110feddb","resolution":{"observed_at":"2026-08-06T11:11:45.197760Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.174494Z","title":"Complex Coordinates in the Theory of Atomic and Molecular Structure and Dynamics","venue":null,"work_id":"1a848235-088e-4e1f-a012-b09f2533a5d4","year":1982},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.452101Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:1b753d7e216af6b817db0395e69ba05fd76af81c879b40ed9810da903de0b034","observation_id":"6170d82b-ac0f-4f3b-9432-7eeaff91b04f","resolution":{"observed_at":"2026-08-06T11:11:45.180624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.151060Z","title":"Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling","venue":null,"work_id":"f267fa35-cf1a-4a4c-8c69-ce1289ebee73","year":1998},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.460177Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:aa3571f6e7963f677ae76e70b9e8aa0f862f4fea7041e89c82ec44a55707bda0","observation_id":"f8c44223-3c01-4b90-8a21-a531b0617d05","resolution":{"observed_at":"2026-08-06T11:11:45.159198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.129956Z","title":"Advanced Topics in Quantum Mechanics","venue":null,"work_id":"76916ddc-2ac5-4b1f-90de-6c9e0da77ec9","year":2021},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.464820Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:204c6e8ed22d527e10843676bd52bce190f98d098dd0ed9c77f0c6acf0390870","observation_id":"9b20f17c-3b12-4a56-b393-b55ab5cba95e","resolution":{"observed_at":"2026-08-06T11:11:45.135669Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0410012","last_updated":"2005-02-18T13:51:52Z","snapshot_observed_at":"2026-07-07T07:17:19.238694Z","submitted_at":"2004-10-01T12:58:05Z","title":"Pseudo-Hermitian Description of PT-Symmetric Systems Defined on a Complex Contour","version":3},"cited_work":{"arxiv_id":"quant-ph/0410012","doi":null,"metadata_source":"pith","pith_arxiv_id":"quant-ph/0410012","snapshot_observed_at":"2026-08-06T11:11:43.842530Z","title":"Pseudo-Hermitian Description of PT-Symmetric Systems Defined on a Complex Contour","venue":"quant-ph","work_id":"cb647f62-68ab-433d-a0e7-5298dd488206","year":2004},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.469893Z"},"links":{"cited_paper":"/paper/quant-ph/0410012","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:11bd01a033813887f85e4d736ee2d75a50cfdb001108876634a8e82517c7a617","observation_id":"16031141-3a34-42e0-ba30-3f441487ac30","resolution":{"observed_at":"2026-08-06T11:11:43.848537Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0810.5643","last_updated":"2011-02-07T14:39:41Z","snapshot_observed_at":"2026-08-13T18:42:58.687527Z","submitted_at":"2008-10-31T09:25:57Z","title":"Pseudo-Hermitian Representation of Quantum Mechanics","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0810.5643","snapshot_observed_at":"2026-08-06T11:11:43.474445Z","title":"Pseudo-Hermitian Representation of Quantum Mechanics","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.474445Z"},"links":{"cited_paper":"/paper/0810.5643","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:f4750e6a9724ba41282c514ad521cb3ff8baf07db9b84aeed2e1c8abf39b35ea","observation_id":"adc0f22d-96d3-48cf-88c2-41c6e05726d6","resolution":{"observed_at":"2026-08-06T11:11:43.474445Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.111733Z","title":"Boundary Value and Expansion Problems of Ordinary Linear Differential Equations","venue":null,"work_id":"3b0a308f-3b8d-42c0-bca0-47ac6396bb09","year":1908},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.480617Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:74dbfd0ffca353274edfdf41b19d71b5947e5536f069abcd1142ef644cd95270","observation_id":"7868ba21-8a09-4182-b4ab-55e2620d1242","resolution":{"observed_at":"2026-08-06T11:11:45.117525Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.094051Z","title":"Biorthogonal Systems of Functions","venue":null,"work_id":"face065b-5a73-46c3-81c1-d34ea7adf880","year":1911},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.488622Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:e05fd110dd3b75c1f5f38ac57185daed955d7a594ef4ca7e9765afb17a2f709d","observation_id":"f4535f38-6a14-41cd-9380-9203ca645f5a","resolution":{"observed_at":"2026-08-06T11:11:45.099572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.075811Z","title":"Biorthogonal systems and bases in Hilbert space","venue":null,"work_id":"77e96139-9837-44f0-8dde-7323e874e216","year":1951},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.493845Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:fde51a7cddc1f9154ed0d7b24834eedda4f65247245f09858509863e79fca609","observation_id":"33d11dd0-7c4e-4206-b132-978ae37907d4","resolution":{"observed_at":"2026-08-06T11:11:45.081829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.057044Z","title":"Non-Hermitian Hamiltonians, Decaying States, and Perturbation Theory","venue":null,"work_id":"f9b03f97-155f-4b6d-96c9-11492d4aecb2","year":1972},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.498404Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:39e7901884d146aff2f42ff0c6d3da059e6d0c596524d826b8592aef55d4fe91","observation_id":"01080b4a-3123-48b8-baeb-00a856dc8b94","resolution":{"observed_at":"2026-08-06T11:11:45.062814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1308.2609","last_updated":"2013-11-26T17:40:15Z","snapshot_observed_at":"2026-07-06T03:20:30.934369Z","submitted_at":"2013-08-12T16:11:48Z","title":"Biorthogonal Quantum Mechanics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1308.2609","snapshot_observed_at":"2026-08-06T11:11:43.502574Z","title":"Biorthogonal quantum mechanics","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.502574Z"},"links":{"cited_paper":"/paper/1308.2609","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:6ceeab4a470424be8f15c27927376eb26a4f6ece9026af62d98f105b8b731196","observation_id":"fbfcbf9b-3980-462e-a98b-6465d8cfe7ae","resolution":{"observed_at":"2026-08-06T11:11:43.502574Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0411143","last_updated":"2004-11-07T08:37:59Z","snapshot_observed_at":"2026-08-11T07:46:51.503808Z","submitted_at":"2004-11-07T08:37:59Z","title":"Schr\\\"odinger type eigenvalue problems with polynomial potentials: Asymptotics of eigenvalues","version":1},"cited_work":{"arxiv_id":"math/0411143","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0411143","snapshot_observed_at":"2026-08-06T11:11:43.780630Z","title":"Schr\\\"odinger type eigenvalue problems with polynomial potentials: Asymptotics of eigenvalues","venue":"math.SP","work_id":"cd3a417e-ae15-414f-afb4-715fbfc25c49","year":2004},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.507092Z"},"links":{"cited_paper":"/paper/math/0411143","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:17989b6feea4971fb295b01a8252d59abb45817b7ca4d41c7002d01463716bfd","observation_id":"a927e1c0-767a-493a-9157-7f65facfd545","resolution":{"observed_at":"2026-08-06T11:11:43.785601Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.039850Z","title":"Functional Integration and Semiclassical Expansions","venue":null,"work_id":"e68da446-cdee-4d05-8f0c-548a0fb0cd64","year":1982},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.511662Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:c09437d5eae46c2cb6800073eaaec1c8a0d7b8ce1cda7ebed71322f710b27c17","observation_id":"d18d87ff-dd84-4547-b5de-1281a6870566","resolution":{"observed_at":"2026-08-06T11:11:45.045156Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.023042Z","title":"On the Product of Semi-Groups of Operators","venue":null,"work_id":"77a6adc8-50b1-4ff2-8661-ccde16eea5e4","year":1959},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.516264Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:c3a7abbae6a35aacff9211b8b89f00f87a2d94b3c81e1b73e23315f8f0ef7049","observation_id":"fbc5ef0a-6482-42ae-8f47-2b44acf7ad3f","resolution":{"observed_at":"2026-08-06T11:11:45.027904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:45.006507Z","title":"Generalized Trotter’s formula and systematic approximants of expo- nential operators and inner derivations with applications to many-body problems","venue":null,"work_id":"58df7f6b-7aab-402e-a133-cb2cad791890","year":1976},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.521025Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:79093471f449842d0dc7834a1614c72bfe84f5838bbc4ba388a1d8b2689b635a","observation_id":"77f52242-a920-4296-a3b3-c4e91d1b158a","resolution":{"observed_at":"2026-08-06T11:11:45.011720Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.989816Z","title":"Lagrangian for Diffusion in Curved Phase Space","venue":null,"work_id":"a355cd47-5403-4236-8367-921b8d74be07","year":1977},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.525645Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:e08512864f9a71e5f7097fc2db218e45031c3ac74b85aa8ef5da0705fafd5e6d","observation_id":"ff563a6f-c69a-42fb-92a0-e9ed4e6dcb94","resolution":{"observed_at":"2026-08-06T11:11:44.995069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.973861Z","title":"Path integral formulation of general diffusion processes","venue":null,"work_id":"fc3f71b2-c0e2-4edf-ae3b-ef83783fe691","year":1977},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.529767Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:7e3d18ad4fa5d451f839aa8bd95801d798f3d39f7d7c015b81bcd7f6140ec1e6","observation_id":"1e7e58f4-4505-4477-bb0c-566eb9197886","resolution":{"observed_at":"2026-08-06T11:11:44.978781Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.958475Z","title":"Point Transformations in Quantum Mechanics","venue":null,"work_id":"20f81b7b-2f8d-4196-a839-356606872d3e","year":1952},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.534573Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:a26c66cda67ab79321fe14fbbe4c8baa4e1c9f762c4425337103cd92ff7d50b0","observation_id":"7fbbdf85-2ae8-4828-8c51-1e15477e6f02","resolution":{"observed_at":"2026-08-06T11:11:44.963578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.943436Z","title":"Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles","venue":null,"work_id":"69ada175-f35c-448d-b23b-da64be121e1f","year":1957},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.539081Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:bb82f685ba1748ccd70b2a3df0b8085e3c1cccdea3b65a8151eaa5b6810f401b","observation_id":"25044af4-6135-43ae-929b-919cbc2a7083","resolution":{"observed_at":"2026-08-06T11:11:44.948316Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.928279Z","title":"On Stochastic Differential Equations","venue":null,"work_id":"8d2b193b-517c-4b36-8d6b-64e434873324","year":1951},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.543970Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:7152bbd202fd3858505da19fe457c0f6054a4262599279a1fb205fd905552250","observation_id":"1caea252-6c41-48eb-b6f6-8af03547138b","resolution":{"observed_at":"2026-08-06T11:11:44.933527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.906393Z","title":"A New Representation for Stochastic Integrals and Equations","venue":null,"work_id":"3593831f-1ff3-4e06-b8a0-a2e9cde32aa4","year":1966},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.548197Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:261ad1f48c2979666c77abf22296ad780c34b22073134e63605180a5b8ba76d0","observation_id":"d6047cd3-6af2-4570-b8d8-d8da8d663fa2","resolution":{"observed_at":"2026-08-06T11:11:44.912188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.889079Z","title":"Path Integrals in Curved Spaces","venue":null,"work_id":"029bb103-f9f9-4e8b-a67c-d90866b732c8","year":1971},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.552534Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:730e11b15f2dbece84e8a7209e61d0d2bdb2ae2baf4d8d2bc4c3fb2c0a043d33","observation_id":"6d4f5136-12a7-4c44-84b0-2466a1ec2ace","resolution":{"observed_at":"2026-08-06T11:11:44.894644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.873222Z","title":"Point canonical transformations in the path integral","venue":null,"work_id":"dfed337b-807c-4704-a052-a50f455cd854","year":1976},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.556717Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:4bb8ba5c003c55ab08b06bb16025901123f2e42ac952e2d33b27e06edbfa7cac","observation_id":"397740e1-7485-436f-9047-b76624ee89dd","resolution":{"observed_at":"2026-08-06T11:11:44.878226Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.856704Z","title":"Canonical and covariant path integrals","venue":null,"work_id":"de8b1b27-8a83-4281-9e1a-3c0576628698","year":1978},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.560972Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:0ad6b78fbe8e765ac25cb5423daa3fae5965c5e36c3b9ae6473c4772127f2515","observation_id":"4ac77699-3780-4d95-baf6-b24536104366","resolution":{"observed_at":"2026-08-06T11:11:44.861759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.841596Z","title":"Operator ordering schemes and covariant path integrals of quantum and stochastic processes in Curved space","venue":null,"work_id":"e7d68dff-d93f-476b-b596-3d2ca0990449","year":1978},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.565200Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:7f9461f038f5a863581bbf472f35e2ba177a54fc140d1cd0b3854c8fa32d3312","observation_id":"cf906093-cea0-4cd7-8b45-4ea6759351f8","resolution":{"observed_at":"2026-08-06T11:11:44.846462Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.826732Z","title":"Functional integrals and the Fokker-Planck equation","venue":null,"work_id":"ad9fe7f8-26c1-479b-99e2-f52593128835","year":1979},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.569472Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:fe019857fbfc47aa24306de65c0e915684231cea0d18394d64a135f2aa8a0385","observation_id":"08bceab9-cd84-41e8-a18c-cbae13f81821","resolution":{"observed_at":"2026-08-06T11:11:44.831649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.09470","last_updated":"2023-04-04T21:21:09Z","snapshot_observed_at":"2026-08-13T13:40:28.978267Z","submitted_at":"2022-11-17T11:27:32Z","title":"Path integrals and stochastic calculus","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.09470","snapshot_observed_at":"2026-08-06T11:11:43.573886Z","title":"Path integrals and stochastic calculus","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.573886Z"},"links":{"cited_paper":"/paper/2211.09470","citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:fbd2f165fe7db7c1c754a37ad2d3867f9bd128d116c6bc549df310475103913b","observation_id":"27bd9b27-a830-49e8-9a96-f6c9afdb8d23","resolution":{"observed_at":"2026-08-06T11:11:43.573886Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.810425Z","title":"Techniques and Applications of Path Integration","venue":null,"work_id":"695784a1-8126-4be7-a934-939f097f2850","year":2005},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.579068Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:205a1786ac0dcc4b2424755e948e1f07e611df6506c04a663f37b825242f184a","observation_id":"c1d6b4d1-3db9-4fea-85a7-fa7d2361bbb6","resolution":{"observed_at":"2026-08-06T11:11:44.815804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:11:44.789081Z","title":"Complex time and the Gaussian approximation","venue":null,"work_id":"784a1897-649e-441b-8324-f4f4e028a284","year":1981},"citing_paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:43.583739Z"},"links":{"citing_paper":"/paper/2507.23125"},"observation_digest":"sha256:5d20265577564aaf542d7bd0d42e1a727959f7984a0f238f310ff7f3b0e14b8f","observation_id":"23814e66-f251-436b-8649-6230ae9b7026","resolution":{"observed_at":"2026-08-06T11:11:44.799360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.23125","last_updated":"2025-07-30T22:05:02Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-13T03:57:55.552002Z","submitted_at":"2025-07-30T22:05:02Z","title":"Path integral analysis of Schr\\\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":53,"verified_exact":18,"verified_fuzzy":29},"total_outbound_references":111},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 100 of 111 outbound references and 4 inbound Pith citation observations for arXiv:2507.23125."}