{"as_of":"2026-08-21T01:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4e8e74f248899fdfbb8a33926145ed7b2e426fc2e69c17e0ce4b42518b67d58a","coverage":[{"denominator":74,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":74,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-19T04:52:47.512140Z","state":"measured"},{"denominator":75,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":75,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T17:48:30.578739Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.13011","snapshot_observed_at":"2026-08-02T17:48:30.578739Z","title":"Ihssen and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.21151","last_updated":"2026-07-27T12:20:59Z","snapshot_observed_at":"2026-08-16T09:18:36.040117Z","submitted_at":"2026-03-22T10:03:22Z","title":"Solving Functional Renormalization Group Equations with Neural Networks","version":2},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-02T17:48:30.578739Z"},"links":{"cited_paper":"/paper/2507.13011","citing_paper":"/paper/2603.21151"},"observation_digest":"sha256:843a8865356b8776a7c03ba95b7e1319767c01c3a06da20d95499019624b7e72","observation_id":"bb8f0c39-fe98-4a6b-b6c9-3fa63a674e00","resolution":{"observed_at":"2026-08-02T17:48:30.578739Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.13011/citation-record","integrity":"/paper/2507.13011/integrity","json":"/paper/2507.13011/citation-record.json","paper":"/paper/2507.13011"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"First we remark that the relation (25) translates into a similar one for the effec- tive action Γϕ[ϕ, JO]","venue":null,"work_id":"2b36f0a0-263e-45f1-a9cc-1c45db0a5a16","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:b732fe3b217fd4f48be859fce8431251f3c3fcb7b81724a8742e393ec1982eeb","observation_id":"3293891e-1b94-47e3-a52f-7bd7bfe36c40","resolution":{"observed_at":"2026-05-19T04:52:59.639420Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d0bce6b9-0788-4f39-b5ef-023ee394973a","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:84487696be5dbf46eef21ff0994536df44e24ca4f0330afdf3831ccb6d36e28a","observation_id":"c6fc6e9d-0ba2-480b-aa39-41d48663de40","resolution":{"observed_at":"2026-05-19T04:52:59.628220Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"This choice was already alluded to at the end of Section III B 1","venue":null,"work_id":"99b03e0d-321e-4673-965e-f71541ef3549","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:9759c1cb9da9fcafde037239819e56d7531c54aabcfcb61830f04e2d2cc3a303","observation_id":"07f11794-77fc-4540-9811-d511490b7da2","resolution":{"observed_at":"2026-05-19T04:52:59.619916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"The restrictions mirror those on ˙ϕ, which were put forward in [1, 4]","venue":null,"work_id":"6ecad1d4-8178-4e0e-adec-1da0beff1f1b","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:e8a8ac1a8631ed6edf9da5aafc6a0048f5f379d3a3dbecef788f3776a2a59f03","observation_id":"dc53d248-ff4a-4c25-b5da-9ad7357d34dd","resolution":{"observed_at":"2026-05-19T04:52:59.611834Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"Rij ϕ Gil δϕO nj δϕl # . (48) With (30) and (48), the integrability condition (47) reads ∂t⟨ ˆOn⟩ + ∂t ϕO nm δΓϕ δϕm − ∂t","venue":null,"work_id":"c1470ec3-8136-43ad-96e0-040aa789543c","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:3448e06c4a8653cae027dd60640adc1231bbe1efddbe3e27b41e939e3313b72b","observation_id":"ddb878dd-a668-4fae-86c3-ed504ea73319","resolution":{"observed_at":"2026-05-19T04:52:59.624351Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"This may be seen as the analogue of a classical target action","venue":null,"work_id":"057ec58b-5d25-4471-b697-72bd23ca5dc5","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:f875fdc1802f0b4b4879bcaea6af47ae60e9176647b7fd347c8bc38e6f59b4b7","observation_id":"fddc7e0b-9948-41db-a101-e0db38aa6408","resolution":{"observed_at":"2026-05-19T04:52:59.607666Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"(A1) Then, the generalised flow equation provides a linear ODE for ˙ϕ(ϕ), see (60c)","venue":null,"work_id":"6b5f36d4-42ac-43be-822f-2477e792ee34","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:886d1a8d3d790941887a77e0bb04100090d7642feb1d0899f2845021edb833f2","observation_id":"8abe96db-105d-4397-963c-98db8ed2e244","resolution":{"observed_at":"2026-05-19T04:52:59.631696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"As discussed in Sec- tion IV B we may use different splits of the operator O2, such as (69) or (73)","venue":null,"work_id":"3aeab6f2-e28a-4459-8cd3-40dcb6b7a8f9","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:e7900c3ac6c6ce7e8d6227d3e7183d920f32c5e10d9ffde4fddb5b24c69ee793","observation_id":"39c0a881-232a-4424-900b-addc7dce014b","resolution":{"observed_at":"2026-05-19T04:52:59.615840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"(A8) Then we have to resort to the generalised operator flow (30) as (A8) induces a JO-dependence for ˙ϕ(ϕ, JO)","venue":null,"work_id":"147df28c-f4f6-4335-9c66-afdc0f1c1928","year":null},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:5ba1efdd9c75b8a723d31052f763a11e69424e1ffbd30d43e7368cdf3ce82265","observation_id":"8ad1d2bc-140f-4575-87bf-f5319421abea","resolution":{"observed_at":"2026-05-19T04:52:59.589484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.13679","last_updated":"2025-08-28T10:21:55Z","snapshot_observed_at":"2026-08-16T13:16:47.558263Z","submitted_at":"2024-09-20T17:41:43Z","title":"Physics-informed renormalisation group flows","version":3},"cited_work":{"arxiv_id":"2409.13679","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.13679","snapshot_observed_at":"2026-07-10T06:26:51.370619Z","title":"Ihssen and J","venue":"hep-th","work_id":"3607679c-2ea4-4eab-a59b-d4d309c9bafe","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2409.13679","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:bff7b23e8d4a207f4037d56101bbb0e6c92498784d666d7f517214b1023caf5b","observation_id":"9fb41d17-06af-4f04-bcbc-6e4885d3627b","resolution":{"observed_at":"2026-05-19T04:52:59.329148Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0512261","last_updated":"2006-02-23T19:17:40Z","snapshot_observed_at":"2026-08-14T15:50:27.721784Z","submitted_at":"2005-12-20T20:59:48Z","title":"Aspects of the Functional Renormalisation Group","version":2},"cited_work":{"arxiv_id":"hep-th/0512261","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/0512261","snapshot_observed_at":"2026-07-11T00:07:45.564694Z","title":"Aspects of the Functional Renormalisation Group","venue":"hep-th","work_id":"18523d10-1c04-4ab0-96bf-aeda94677482","year":2005},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-th/0512261","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1d8b39df5520b2b4826b46a0da0e5b44b476bf631317ce63b5f5dfd880d36828","observation_id":"ab86b56e-da94-4fc5-971b-3411fa34b60a","resolution":{"observed_at":"2026-05-19T04:52:59.244466Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1710.05815","last_updated":"2017-10-16T16:27:50Z","snapshot_observed_at":"2026-08-14T20:23:21.262980Z","submitted_at":"2017-10-16T16:27:50Z","title":"Exact evolution equation for the effective potential","version":1},"cited_work":{"arxiv_id":"1710.05815","doi":null,"metadata_source":"pith","pith_arxiv_id":"1710.05815","snapshot_observed_at":"2026-07-11T00:07:44.847267Z","title":"Exact evolution equation for the effective potential","venue":"hep-th","work_id":"7842548c-e95a-45bf-bca9-26dc8435c397","year":2017},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1710.05815","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1bddf102648bd084992aec1a049989d0fe199643d3319422fbba607b891c481f","observation_id":"74a683d7-c874-4e1a-ab48-188f2d6c79a3","resolution":{"observed_at":"2026-05-19T04:52:59.308260Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.22638","last_updated":"2025-03-28T17:28:41Z","snapshot_observed_at":"2026-08-18T11:48:00.267371Z","submitted_at":"2025-03-28T17:28:41Z","title":"Physics-informed gauge theories","version":1},"cited_work":{"arxiv_id":"2503.22638","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.22638","snapshot_observed_at":"2026-07-11T00:07:45.877824Z","title":"Ihssen and J","venue":"hep-th","work_id":"d9f94089-fa25-44c6-83f9-d4fda5aa13ff","year":2025},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2503.22638","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:ba4bf1bff74058f65d8b37d039d882857149cdf4ce58b76f52b625bc2c2a281c","observation_id":"477a571a-7996-4a93-aceb-f95d94c65ba7","resolution":{"observed_at":"2026-05-19T04:52:59.248588Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2504.03437","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Bonanno, F","venue":null,"work_id":"2af3abb1-df4d-47cc-84fc-b96e24c9f792","year":2025},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:ea1272614317facccc98cec8aac3cba00877343e843c2298b6aa3489a82fe638","observation_id":"a17479e0-eb46-4160-8c95-84a51abb1da4","resolution":{"observed_at":"2026-05-19T04:52:59.312776Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.02118","last_updated":"2022-03-07T22:47:27Z","snapshot_observed_at":"2026-08-20T14:17:58.616731Z","submitted_at":"2021-12-03T19:01:53Z","title":"Relational observables in Asymptotically safe gravity","version":2},"cited_work":{"arxiv_id":"2112.02118","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.02118","snapshot_observed_at":"2026-07-11T00:07:45.072295Z","title":"Baldazzi, K","venue":"hep-th","work_id":"28bc3623-2d4d-4a42-8c86-2c53b811d1fc","year":2021},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2112.02118","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:c44f8664f7f58d2ab9d26b19b404142d70b748d814fda0eff89d4efea9a9f905","observation_id":"b1a763d2-478b-44b6-8a38-d7baff711317","resolution":{"observed_at":"2026-05-19T04:52:59.378702Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.04679","last_updated":"2024-10-20T16:47:51Z","snapshot_observed_at":"2026-08-16T14:20:42.029997Z","submitted_at":"2024-02-07T09:09:21Z","title":"Field transformations in functional integral, effective action and functional flow equations","version":3},"cited_work":{"arxiv_id":"2402.04679","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.04679","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Wetterich, Nucl","venue":null,"work_id":"485a880f-384d-4587-8ce5-fb7ca2c1dfc1","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2402.04679","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:f8f6e3a7f528e1140c950a120448ad7897330f2a723cb2e28f9d3f2bc039e0de","observation_id":"27ddd9fc-c9b5-4b0f-805d-51f2e8f64094","resolution":{"observed_at":"2026-05-19T04:52:59.354486Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"ph/9604227","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Wetterich, Z","venue":null,"work_id":"341371da-370a-4b39-bb4d-8afd9838dc46","year":1996},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:a5cbb94da66795713d952593c3e9e7972e767b901890a1525e07ccbeab5cb7f6","observation_id":"2c630039-c5bd-4024-9e68-77484930a5e4","resolution":{"observed_at":"2026-05-19T04:52:59.231664Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0107221","last_updated":"2001-11-15T15:06:07Z","snapshot_observed_at":"2026-07-07T04:40:46.926153Z","submitted_at":"2001-07-25T15:09:08Z","title":"Renormalization Flow of Bound States","version":2},"cited_work":{"arxiv_id":"hep-th/0107221","doi":"10.1103/physrevd.65.065001","metadata_source":"pith","pith_arxiv_id":"hep-th/0107221","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Renormalization Flow of Bound States","venue":"hep-th","work_id":"32498174-5c27-48b3-a0f3-986b6dd3f6da","year":2001},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-th/0107221","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:6db80ad68310357704dbb56331bcbc4da8ba1ced09141a132c51036cfddc7466","observation_id":"68a9a687-7d31-43c8-8129-c9770dd4db4b","resolution":{"observed_at":"2026-05-19T04:52:59.294455Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0209183","last_updated":"2003-10-24T12:26:32Z","snapshot_observed_at":"2026-07-07T04:44:44.299883Z","submitted_at":"2002-09-23T12:46:50Z","title":"Universality of spontaneous chiral symmetry breaking in gauge theories","version":2},"cited_work":{"arxiv_id":"hep-th/0209183","doi":"10.1103/physrevd.69.025001","metadata_source":"pith","pith_arxiv_id":"hep-th/0209183","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Universality of spontaneous chiral symmetry breaking in gauge theories","venue":"hep-th","work_id":"c60654da-5516-4fc1-9145-4c3fc5a86bec","year":2002},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-th/0209183","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:0f94a5f2e600d8d09fada22f232edff02ad0fede755d5c529c2ede8cd34c576a","observation_id":"3d4ce310-85e5-4cc4-ab65-0fc69cbf17b6","resolution":{"observed_at":"2026-05-19T04:52:59.345656Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0905.0915","last_updated":"2009-10-06T15:08:24Z","snapshot_observed_at":"2026-08-15T05:49:01.254135Z","submitted_at":"2009-05-06T20:19:01Z","title":"Exact flow equation for composite operators","version":2},"cited_work":{"arxiv_id":"0905.0915","doi":"10.1016/j.physletb.2009.09.014","metadata_source":"pith","pith_arxiv_id":"0905.0915","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Exact flow equation for composite operators","venue":"hep-th","work_id":"2ba302c4-4c9c-4455-a714-552e9de81b0a","year":2009},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/0905.0915","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:05ac41e358c2d2f4d00b5d0ca0a389e2f3e5f8177d8e68f5b91cf9d86130d7b2","observation_id":"b1bd4788-a230-463e-abb3-23b1298e015f","resolution":{"observed_at":"2026-05-19T04:52:59.349824Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.02991","last_updated":"2019-09-06T16:10:34Z","snapshot_observed_at":"2026-08-16T23:19:07.717387Z","submitted_at":"2019-09-06T16:10:34Z","title":"The QCD phase structure at finite temperature and density","version":1},"cited_work":{"arxiv_id":"1909.02991","doi":"10.1103/physrevd.101.054032","metadata_source":"pith","pith_arxiv_id":"1909.02991","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"QCD phase structure at finite temperature and density","venue":"hep-ph","work_id":"51e85d15-8557-46d2-9959-0b6bf24ff469","year":2019},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1909.02991","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:2942c38ed62073f657c34771f06a89016138da51aa1c80b39314bf00c0e8b50e","observation_id":"892d97ee-9517-419e-a9f3-f0d11d7d82bd","resolution":{"observed_at":"2026-05-19T04:52:59.189784Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.08413","last_updated":"2024-08-15T20:40:49Z","snapshot_observed_at":"2026-08-16T13:26:09.591489Z","submitted_at":"2024-08-15T20:40:49Z","title":"Towards quantitative precision in functional QCD I","version":1},"cited_work":{"arxiv_id":"2408.08413","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.08413","snapshot_observed_at":"2026-07-09T13:36:19.505685Z","title":"Ihssen, J","venue":"hep-ph","work_id":"fa5bac5c-592d-4203-90e0-1926ddc29db5","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2408.08413","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:d69ac389d995a7f7dfe7996f07ea477fefa35106c0b191f1656f22795a003f46","observation_id":"13eeb2a2-2d49-48b8-b0bc-ec98050863ea","resolution":{"observed_at":"2026-05-19T04:52:59.302808Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"Lamprecht, Diploma thesis Heidelberg University (2007)","venue":null,"work_id":"1b8f79c2-e093-42de-ac53-5cd0228d9970","year":2007},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:a8d0c61f68edbbccb8def1c414bf574e53d2aa012d15acd3737ddeadb418e644","observation_id":"96fda44b-b9dd-4096-a617-4777dd98349f","resolution":{"observed_at":"2026-05-19T04:52:59.599586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.10373","last_updated":"2018-09-21T14:52:00Z","snapshot_observed_at":"2026-08-14T18:58:40.524753Z","submitted_at":"2018-06-27T09:44:48Z","title":"Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations","version":2},"cited_work":{"arxiv_id":"1806.10373","doi":null,"metadata_source":"pith","pith_arxiv_id":"1806.10373","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations","venue":"cond-mat.quant-gas","work_id":"436dcacd-332e-44df-9176-7223ae4335e4","year":2018},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1806.10373","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:613192cc04bcb952d4f876548cadd8e8ac9fc10e07baa7d980a754ee4c4af64b","observation_id":"db950616-aede-446c-925d-14da3049b7a7","resolution":{"observed_at":"2026-05-19T04:52:59.264181Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.07135","last_updated":"2019-11-13T22:04:18Z","snapshot_observed_at":"2026-08-14T17:14:18.726700Z","submitted_at":"2019-02-19T16:46:25Z","title":"Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action","version":3},"cited_work":{"arxiv_id":"1902.07135","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.07135","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Isaule, M","venue":null,"work_id":"01baad7a-d7b7-457f-a464-08aab89e7814","year":2020},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1902.07135","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:aed27a2a919a2b37a6a712c055ba37bacf64de1083cc83102f14f345afbb41d1","observation_id":"d0665702-30b7-4ace-a359-12370de2b304","resolution":{"observed_at":"2026-05-19T04:52:59.221093Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.10057","last_updated":"2022-08-10T12:51:19Z","snapshot_observed_at":"2026-08-16T16:44:29.495077Z","submitted_at":"2022-07-20T17:38:40Z","title":"Functional flows for complex effective actions","version":2},"cited_work":{"arxiv_id":"2207.10057","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2207.10057","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ihssen and J","venue":null,"work_id":"f3771b6f-c5ac-451f-add7-bd632b7c95e9","year":2023},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2207.10057","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:a03851978aa7042235cfaabcb6e01049cc8778610741414c4e9ceee3945ce674","observation_id":"8caa7b6d-62de-4c38-8358-00cae0c98274","resolution":{"observed_at":"2026-05-19T04:52:59.323551Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"mat/0607289","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Salmhofer, Annalen Phys","venue":null,"work_id":"115bf036-7b9c-4eed-ba50-ce3457f7a81b","year":2007},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:a3b7b1cdf1f7ccd411a1b27e2627024db457d2783c3908dafd1a194e04cfef8f","observation_id":"c06dbf26-828d-4314-9bec-0816ee26d37a","resolution":{"observed_at":"2026-05-19T04:52:59.269582Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"0bc3f65c-392b-4afd-9fb9-7705d8666df8","year":2098},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:86beabc474efe0646412d0c0eb73d1b3981dfc63dd94df10a14be3b75289558e","observation_id":"3fc0df51-c78d-4d4b-b935-7c333ac6fce0","resolution":{"observed_at":"2026-05-19T04:52:59.603082Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2105.11482","last_updated":"2022-05-11T14:43:32Z","snapshot_observed_at":"2026-08-18T11:37:38.859631Z","submitted_at":"2021-05-24T18:11:09Z","title":"Essential renormalisation group","version":3},"cited_work":{"arxiv_id":"2105.11482","doi":null,"metadata_source":"pith","pith_arxiv_id":"2105.11482","snapshot_observed_at":"2026-07-11T00:07:44.791018Z","title":"Baldazzi, R","venue":"hep-th","work_id":"79bc9e20-f2d7-457b-a928-034767c0ddf5","year":2021},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2105.11482","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1016d8c011ca744217f3f60ac3b42e3e4dcf149881f7a3000b42dd6bc74e8995","observation_id":"61446f8e-925a-4590-9063-25c21b028465","resolution":{"observed_at":"2026-05-19T04:52:59.280159Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2107.00671","last_updated":"2021-08-10T15:50:39Z","snapshot_observed_at":"2026-08-20T21:11:30.306490Z","submitted_at":"2021-07-01T18:00:22Z","title":"Essential Quantum Einstein Gravity","version":2},"cited_work":{"arxiv_id":"2107.00671","doi":null,"metadata_source":"pith","pith_arxiv_id":"2107.00671","snapshot_observed_at":"2026-07-11T00:07:44.500385Z","title":"Baldazzi and K","venue":"hep-th","work_id":"c449951b-6a89-411b-9fab-9dabb31b78e4","year":2021},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2107.00671","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:470b16a8658d8deea600763e8127aacef6b108dbd833f751a06b11143b068d66","observation_id":"600abe3a-f610-4b3b-981b-09ba9e48ac96","resolution":{"observed_at":"2026-05-19T04:52:59.296719Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.08564","last_updated":"2023-10-19T09:59:04Z","snapshot_observed_at":"2026-08-18T08:38:45.931492Z","submitted_at":"2022-04-18T21:18:49Z","title":"Safe essential scalar-tensor theories","version":2},"cited_work":{"arxiv_id":"2204.08564","doi":null,"metadata_source":"pith","pith_arxiv_id":"2204.08564","snapshot_observed_at":"2026-07-11T00:07:44.147428Z","title":"Knorr, (2022), arXiv:2204.08564 [hep-th]","venue":"hep-th","work_id":"ec830af7-2829-4a18-bfb6-d406e1765b34","year":2022},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2204.08564","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:515689190d0ff0ba4f1bfa52ef53cd5b8ce0408636648f9d4e4c6013ce7dd0f1","observation_id":"0bd44de1-5626-480a-ac05-583a671e9b1c","resolution":{"observed_at":"2026-05-19T04:52:59.359069Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.03831","last_updated":"2023-12-06T19:00:02Z","snapshot_observed_at":"2026-08-20T16:16:46.699750Z","submitted_at":"2023-12-06T19:00:02Z","title":"Robustness of the derivative expansion in Asymptotic Safety","version":1},"cited_work":{"arxiv_id":"2312.03831","doi":null,"metadata_source":"pith","pith_arxiv_id":"2312.03831","snapshot_observed_at":"2026-07-11T00:07:45.626553Z","title":"Baldazzi, K","venue":"hep-th","work_id":"96c76bb5-40d2-46f9-a3bb-6a44e9b5fa11","year":2023},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2312.03831","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:8e056eb9bdc008a37cc0215f562a8d19d8f81cfc75a1a721aad198365301e031","observation_id":"01a99028-5105-4a8e-857a-55002370398e","resolution":{"observed_at":"2026-05-19T04:52:59.286418Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2506.03601","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ohta and M","venue":null,"work_id":"d82d0ca9-384a-401d-9449-2cad568fac41","year":2025},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:b65479224253cc5f6dd44cdc0080c89d5ff149e39e8d754e3f8bd9f96c3a1d00","observation_id":"e818c03b-bfd4-4a99-a3a4-25882a672ae8","resolution":{"observed_at":"2026-05-19T04:52:59.137191Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1603.07250","last_updated":"2016-03-23T15:57:41Z","snapshot_observed_at":"2026-08-14T22:04:46.622856Z","submitted_at":"2016-03-23T15:57:41Z","title":"A note on scaling arguments in the effective average action formalism","version":1},"cited_work":{"arxiv_id":"1603.07250","doi":null,"metadata_source":"pith","pith_arxiv_id":"1603.07250","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A note on scaling arguments in the effective average action formalism","venue":"hep-th","work_id":"2045bcc9-618d-453d-bbef-e4382ff466ec","year":2016},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1603.07250","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:5690a5fb85d6bcc2d6bc01dbd8f00d3f59c56c14d3510cd530421ff869706ce5","observation_id":"9f907db8-5644-4c2c-b46d-d00d7a92eeb0","resolution":{"observed_at":"2026-05-19T04:52:59.211230Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1510.03830","last_updated":"2015-10-13T19:25:50Z","snapshot_observed_at":"2026-08-14T22:28:01.861347Z","submitted_at":"2015-10-13T19:25:50Z","title":"Confinement order parameters and fluctuations","version":1},"cited_work":{"arxiv_id":"1510.03830","doi":null,"metadata_source":"pith","pith_arxiv_id":"1510.03830","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Confinement order parameters and fluctuations","venue":"hep-ph","work_id":"d466949e-29b5-4744-8142-ad62ee02e71e","year":2015},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1510.03830","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1197edfec5b7ebc8bb3b60daf548969fffb8c1f950594cceec4797a36a5cd94a","observation_id":"2cd762b0-a881-45a1-b25e-2406d5a53e5e","resolution":{"observed_at":"2026-05-19T04:52:59.087767Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.11816","last_updated":"2019-04-13T08:30:12Z","snapshot_observed_at":"2026-08-14T18:08:12.504752Z","submitted_at":"2018-10-28T14:11:38Z","title":"Geometric operators in the asymptotic safety scenario for quantum gravity","version":2},"cited_work":{"arxiv_id":"1810.11816","doi":null,"metadata_source":"pith","pith_arxiv_id":"1810.11816","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Geometric operators in the asymptotic safety scenario for quantum gravity","venue":"gr-qc","work_id":"660a8097-18a7-4f5d-a475-07461ee436de","year":2018},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1810.11816","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:b241b12e918f6ae209b5c59303cf9c1e2b1f4e89116e8738708a0ba8bce0c874","observation_id":"c172ba2f-5ba1-42c9-ac6b-9e98ffa23a39","resolution":{"observed_at":"2026-05-19T04:52:59.092854Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"Becker and C","venue":null,"work_id":"3761789b-3025-41ba-aa96-d295835eb5aa","year":2019},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:4e5246a42c43b4fcb7c2f66bdebc99aa5725d0d960872dda75682306e0832c24","observation_id":"1663b50b-f2a0-4616-8e92-fe93b10cef82","resolution":{"observed_at":"2026-05-19T04:52:59.635502Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.00256","last_updated":"2020-05-06T16:01:39Z","snapshot_observed_at":"2026-08-15T08:37:33.229089Z","submitted_at":"2020-02-01T19:03:21Z","title":"On the scaling of composite operators in Asymptotic Safety","version":2},"cited_work":{"arxiv_id":"2002.00256","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.00256","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Houthoff, A","venue":null,"work_id":"67b96df6-18d9-45cf-9e46-40c8643ec6c9","year":2002},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2002.00256","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:05b2d2405e1efa155627155c41b74200df6b1814e327957472e402dc2249c917","observation_id":"153b49d3-86a3-4595-8cec-412cede5bb4a","resolution":{"observed_at":"2026-05-19T04:52:59.083039Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.03199","last_updated":"2024-05-28T15:09:46Z","snapshot_observed_at":"2026-08-16T14:12:32.909021Z","submitted_at":"2024-03-05T18:37:37Z","title":"Operator Learning Renormalization Group","version":2},"cited_work":{"arxiv_id":"2403.03199","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2403.03199","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ca5a7938-1430-4fba-aa72-3b974785cf3f","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2403.03199","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:b616984b7f5de07bb0c82797bf3aad93b4a0b539c54bf457ff1ecfe9958cb867","observation_id":"e14e1309-7509-45d1-928f-ae71f99ca9a8","resolution":{"observed_at":"2026-05-19T04:52:59.077287Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1512.03598","last_updated":"2015-12-11T11:04:14Z","snapshot_observed_at":"2026-08-14T22:18:59.648632Z","submitted_at":"2015-12-11T11:04:14Z","title":"Physics and the choice of regulators in functional renormalisation group flows","version":1},"cited_work":{"arxiv_id":"1512.03598","doi":null,"metadata_source":"pith","pith_arxiv_id":"1512.03598","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Physics and the choice of regulators in functional renormalisation group flows","venue":"hep-th","work_id":"0b804d01-b802-4ac7-a3fe-de31539e2ba1","year":2015},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1512.03598","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:0a1b4fd8e487abc0f2f41de4c82af96d34f13e8c826411423a2f1bee8b719fff","observation_id":"ee15e075-0d52-44fe-9e93-5f6612fdbc2d","resolution":{"observed_at":"2026-05-19T04:52:59.373828Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9607188","last_updated":"1996-07-24T07:18:29Z","snapshot_observed_at":"2026-07-07T05:11:19.588712Z","submitted_at":"1996-07-24T07:18:29Z","title":"On the construction of renormalized gauge theories using renormalization group techniques","version":1},"cited_work":{"arxiv_id":"hep-th/9607188","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/9607188","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the construction of renormalized gauge theories using renormalization group techniques","venue":"hep-th","work_id":"589b7f3f-0542-49d4-a8bd-8fc5e2607ca9","year":1996},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-th/9607188","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:ac87349f90cddbb81a0eaad808ca2c8861ef95e20589c134c813394967f1398a","observation_id":"95dd0bdc-e48a-4dc7-95d6-bb2f58b9cdcf","resolution":{"observed_at":"2026-05-19T04:52:59.290241Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0909.0327","last_updated":"2009-09-02T08:08:22Z","snapshot_observed_at":"2026-08-15T05:40:04.803679Z","submitted_at":"2009-09-02T08:08:22Z","title":"Realization of symmetry in the ERG approach to quantum field theory","version":1},"cited_work":{"arxiv_id":"0909.0327","doi":"10.1143/ptps.181.1","metadata_source":"pith","pith_arxiv_id":"0909.0327","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Realization of symmetry in the ERG approach to quantum field theory","venue":"hep-th","work_id":"d6c34e7d-5240-4bf1-a8e7-53ea9aeaf689","year":2009},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/0909.0327","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:bc452220a290f366ec09f9103a39352b5b9509ab4241d316354ecd7bb8cde528","observation_id":"c7150087-0a26-448b-90eb-5efc215d1888","resolution":{"observed_at":"2026-05-19T04:52:59.115189Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.00816","last_updated":"2023-11-25T15:14:07Z","snapshot_observed_at":"2026-08-16T15:36:31.728696Z","submitted_at":"2023-05-01T13:32:48Z","title":"Flowing fields and optimal RG-flows","version":2},"cited_work":{"arxiv_id":"2305.00816","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2305.00816","snapshot_observed_at":"2026-06-29T11:13:20.966309Z","title":"Ihssen and J","venue":null,"work_id":"b4286b90-5a51-4e7c-a026-4d3f7644a346","year":2023},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2305.00816","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:b74485d5fcc69ab84809197ad5b3584b5e6427f2a143a4c502f4b318965ca85b","observation_id":"954cce49-a573-4da6-af7f-9fd74ae8ca12","resolution":{"observed_at":"2026-05-19T04:52:59.270497Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"Ihssen, D","venue":null,"work_id":"b042eb09-1eb9-4f86-bf1b-9bd604083e6c","year":2025},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:4512a24e30542c52f85122d17eecdaa13890c332db10f2bdb593c17919d03bb7","observation_id":"d18ddb7a-411c-46e0-a087-5f07458503ad","resolution":{"observed_at":"2026-05-19T04:52:59.596163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.17851","last_updated":"2025-08-22T16:34:06Z","snapshot_observed_at":"2026-08-18T11:38:13.001672Z","submitted_at":"2025-04-24T18:00:10Z","title":"Equivalence of effective actions","version":3},"cited_work":{"arxiv_id":"2504.17851","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.17851","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Falls, (2025), arXiv:2504.17851 [hep-th]","venue":null,"work_id":"60179461-0daa-4f0c-b7fa-54bd47ad346a","year":2025},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2504.17851","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:e846d0c5bf6bcde8fdfbfb4f5de25d472d19f1fb51a90490f66437e38c808cca","observation_id":"ea52f5dd-db69-49de-876a-9943ea460637","resolution":{"observed_at":"2026-05-19T04:52:59.239032Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.14388","last_updated":"2025-02-20T09:23:13Z","snapshot_observed_at":"2026-08-20T22:02:02.921399Z","submitted_at":"2025-02-20T09:23:13Z","title":"Four-quark scatterings in QCD III","version":1},"cited_work":{"arxiv_id":"2502.14388","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.14388","snapshot_observed_at":"2026-07-09T13:36:19.430477Z","title":"Four-quark scatterings in QCD III","venue":"hep-ph","work_id":"b2972ff7-3c24-4bb5-bee5-2124cd19d36f","year":2025},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2502.14388","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:0392513995426ca7f186f0fbdf48aadaabf37625da0e1b931bd8bad110f627e2","observation_id":"d58a3eee-303d-41dc-a4de-2d23877f0849","resolution":{"observed_at":"2026-05-19T04:52:59.274218Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0202188","last_updated":"2002-07-16T12:56:58Z","snapshot_observed_at":"2026-07-07T04:42:45.412439Z","submitted_at":"2002-02-27T18:06:42Z","title":"Completeness and consistency of renormalisation group flows","version":2},"cited_work":{"arxiv_id":"hep-th/0202188","doi":"10.1103/physrevd.66.025030","metadata_source":"pith","pith_arxiv_id":"hep-th/0202188","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Completeness and consistency of renormalisation group flows","venue":"hep-th","work_id":"5de7622e-74fc-45ca-9f80-2544f85026eb","year":2002},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-th/0202188","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1ceba3c28537dace0d81728bd9cddb1fd8aa00ac506cb70b722c329bb22cbf62","observation_id":"bda3dcea-8136-4f36-88bb-fc5aa7f9916a","resolution":{"observed_at":"2026-05-19T04:52:59.393849Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-05-22T14:23:24.176899+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-22T14:23:24.176899+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0111191","last_updated":"2002-02-27T17:08:16Z","snapshot_observed_at":"2026-07-07T04:41:51.051630Z","submitted_at":"2001-11-21T18:04:37Z","title":"Perturbation theory and renormalisation group equations","version":3},"cited_work":{"arxiv_id":"hep-th/0111191","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/0111191","snapshot_observed_at":"2026-07-11T00:07:45.683974Z","title":"Perturbation theory and renormalisation group equations","venue":"hep-th","work_id":"e3e69ae3-416f-46d8-8a79-c0b063589e32","year":2001},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-th/0111191","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:e797777daf444a3d46761fd778d4ba3ea3d82127f1d5c9801da90c27403394c9","observation_id":"4ef02b09-6d56-4b07-bb51-e656dba76262","resolution":{"observed_at":"2026-05-19T04:52:59.368329Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0208216","last_updated":"2002-09-17T13:53:03Z","snapshot_observed_at":"2026-07-07T04:44:32.271313Z","submitted_at":"2002-08-29T15:59:42Z","title":"Wilsonian flows and background fields","version":2},"cited_work":{"arxiv_id":"hep-th/0208216","doi":"10.1016/s0370-2693(02)02693-x","metadata_source":"pith","pith_arxiv_id":"hep-th/0208216","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Wilsonian flows and background fields","venue":"hep-th","work_id":"2c3da7ea-9051-4240-8374-2a2b4ac7f5a7","year":2002},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-th/0208216","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:94ceb226b6391721cc02b236fe9e13a3066b29d49bc4914b069eb9a39b2771a1","observation_id":"832e8f6c-5c6b-4520-aead-6a7e6dffd82d","resolution":{"observed_at":"2026-05-19T04:52:59.222147Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-05-22T14:23:23.723835+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-22T14:23:23.723835+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.04853","last_updated":"2021-05-07T08:46:33Z","snapshot_observed_at":"2026-08-18T11:35:52.406301Z","submitted_at":"2020-06-08T18:17:41Z","title":"The nonperturbative functional renormalization group and its applications","version":3},"cited_work":{"arxiv_id":"2006.04853","doi":null,"metadata_source":"pith","pith_arxiv_id":"2006.04853","snapshot_observed_at":"2026-07-08T11:14:55.097123Z","title":"Dupuis, L","venue":"cond-mat.stat-mech","work_id":"6f057d29-f970-4f18-b37b-88482270fd00","year":2020},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2006.04853","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:e3927d968a87b28e7e24d41307e3b154fba2c857315a33b8418f3af9d9d53067","observation_id":"ca5eac3a-eec1-4e27-8d67-fc0bc8334f24","resolution":{"observed_at":"2026-05-19T04:52:59.098706Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":"Reuter and C","venue":null,"work_id":"f782c00f-26d5-49de-adeb-1989cee36710","year":1994},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:63a3a7407777752a73ed4fd349b8b8415680ddbb370a06f61dc1dcff2b0cc968","observation_id":"8ec0c174-f15f-471f-a9a2-e57a9bb4d3e6","resolution":{"observed_at":"2026-05-19T04:52:59.592531Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"th/9605030","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T07:19:39.330135Z","title":"Reuter, Phys","venue":null,"work_id":"6a082206-8e07-4397-8127-3a67116afdf4","year":1998},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:d14faff52098697127d4d56dd7d00896ca7efef4aac1c9133a69bda9a20b9d00","observation_id":"a6851166-fa12-477e-b00d-bae03e533757","resolution":{"observed_at":"2026-05-19T04:52:59.323098Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"nucl-th/9903003","last_updated":"1999-03-01T16:40:35Z","snapshot_observed_at":"2026-07-31T21:43:41.560740Z","submitted_at":"1999-03-01T16:40:35Z","title":"Renormalization Group Flow and Equation of State of Quarks and Mesons","version":1},"cited_work":{"arxiv_id":"nucl-th/9903003","doi":null,"metadata_source":"pith","pith_arxiv_id":"nucl-th/9903003","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Renormalization Group Flow and Equation of State of Quarks and Mesons","venue":"nucl-th","work_id":"3b4289c2-1421-422d-ad02-bf52c7ee18e6","year":1999},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/nucl-th/9903003","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:a188a6db143ed2039777e2781a7cc2f5a52e74c4b1ddd767c42a0b06f00a33bf","observation_id":"f844a466-3cb5-4e54-91c7-b7293e213e4c","resolution":{"observed_at":"2026-05-19T04:52:59.299037Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"th/0202167","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Zappala, Phys","venue":null,"work_id":"b7fff99a-181e-4a9e-881c-12907b37730a","year":2002},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:8e4cab603f50523ac6af9c87cd50b258bed83b33d4fd6eec33b016f2fc9250c5","observation_id":"c0acbfb9-2284-4d39-99d2-4a667a8b6f11","resolution":{"observed_at":"2026-05-19T04:52:59.312982Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-ph/0603256","last_updated":"2006-07-07T14:25:50Z","snapshot_observed_at":"2026-07-07T04:10:32.906579Z","submitted_at":"2006-03-30T14:01:47Z","title":"Susceptibilities near the QCD (tri)critical point","version":3},"cited_work":{"arxiv_id":"hep-ph/0603256","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-ph/0603256","snapshot_observed_at":"2026-07-03T02:17:34.546355Z","title":"Susceptibilities near the QCD (tri)critical point","venue":"hep-ph","work_id":"16cd1124-f0d4-4700-9fa6-483f08bf3aea","year":2006},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/hep-ph/0603256","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:84126e1278c5282d31fd366a8102c598a363b56f398a75f7d1c523479695b984","observation_id":"79a8e26c-4a87-4e49-96e2-071fa0e46802","resolution":{"observed_at":"2026-05-19T04:52:59.383399Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1502.07396","last_updated":"2015-04-27T14:35:46Z","snapshot_observed_at":"2026-08-14T22:58:37.070018Z","submitted_at":"2015-02-25T23:04:27Z","title":"Background independent exact renormalization group for conformally reduced gravity","version":3},"cited_work":{"arxiv_id":"1502.07396","doi":null,"metadata_source":"pith","pith_arxiv_id":"1502.07396","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Background independent exact renormalization group for conformally reduced gravity","venue":"hep-th","work_id":"0e22bade-f8d1-495b-ba23-f495ec2b289c","year":2015},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1502.07396","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:0a5761d8ec8829f342c54e8dfd3c9dc16b0f66ee1ad302c362c619d626ce6e87","observation_id":"a17485d6-e820-4d5c-8e58-b50e0745ce72","resolution":{"observed_at":"2026-05-19T04:52:59.334993Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1603.04772","last_updated":"2016-03-15T17:37:16Z","snapshot_observed_at":"2026-08-14T22:05:55.978004Z","submitted_at":"2016-03-15T17:37:16Z","title":"Background independence in a background dependent renormalization group","version":1},"cited_work":{"arxiv_id":"1603.04772","doi":null,"metadata_source":"pith","pith_arxiv_id":"1603.04772","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Background independence in a background dependent renormalization group","venue":"hep-th","work_id":"3b8e4f9b-eec7-4d83-9dce-ffb0caf0665d","year":2016},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1603.04772","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1a2d6d07a2c05200249ecbfbe8615264c666cbd628683f7c89a4ecc0f3aec74a","observation_id":"aa5d9cae-5259-4b5c-b4db-a015a1386eb2","resolution":{"observed_at":"2026-05-19T04:52:59.303760Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1710.02494","last_updated":"2018-07-17T16:07:38Z","snapshot_observed_at":"2026-08-14T20:26:09.363046Z","submitted_at":"2017-10-06T16:53:49Z","title":"Gauge-invariant fields and flow equations for Yang-Mills theories","version":2},"cited_work":{"arxiv_id":"1710.02494","doi":null,"metadata_source":"pith","pith_arxiv_id":"1710.02494","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Gauge-invariant fields and flow equations for Yang-Mills theories","venue":"hep-th","work_id":"d2b52fb6-6702-49bb-b229-353b1dc8b111","year":2017},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1710.02494","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1626875c300f64d20edf1950030a74e26591f633479eb1f51b79f22efb652ce1","observation_id":"fd3fa97f-7211-437d-9092-833efc768212","resolution":{"observed_at":"2026-05-19T04:52:59.233279Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.04409","last_updated":"2018-05-29T07:47:11Z","snapshot_observed_at":"2026-08-14T19:26:42.762654Z","submitted_at":"2018-04-12T10:20:30Z","title":"Renormalized Functional Renormalization Group","version":2},"cited_work":{"arxiv_id":"1804.04409","doi":null,"metadata_source":"pith","pith_arxiv_id":"1804.04409","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Renormalized Functional Renormalization Group","venue":"hep-th","work_id":"aa1fd8ec-1450-421b-97b8-ba0db7982582","year":2018},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1804.04409","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:2d632daa77dd9f9097a51a93101ccaf59c2287cdd2447b500eda141326f274bf","observation_id":"33f1040a-c60c-42af-b9a7-c2e2ab8c8bbb","resolution":{"observed_at":"2026-05-19T04:52:59.404397Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1912.08135","last_updated":"2020-01-30T16:00:02Z","snapshot_observed_at":"2026-08-18T04:15:10.796969Z","submitted_at":"2019-12-17T16:58:01Z","title":"On Exact Proper Time Wilsonian RG Flows","version":2},"cited_work":{"arxiv_id":"1912.08135","doi":null,"metadata_source":"pith","pith_arxiv_id":"1912.08135","snapshot_observed_at":"2026-07-11T00:07:45.059464Z","title":"Bonanno, S","venue":"hep-th","work_id":"ba2c45a1-29d1-4e1b-89bd-457a64f508b1","year":2019},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1912.08135","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:980f200bb28d8c439f12d53d59bb443e08a73ab83bf698ea9d7f1875f05f4aaf","observation_id":"45488089-9098-4ae6-9b04-5458cec99aae","resolution":{"observed_at":"2026-05-19T04:52:59.275711Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2004.11409","last_updated":"2020-08-12T08:37:57Z","snapshot_observed_at":"2026-08-08T11:28:21.610163Z","submitted_at":"2020-04-23T18:08:11Z","title":"Background independent exact renormalisation","version":2},"cited_work":{"arxiv_id":"2004.11409","doi":null,"metadata_source":"pith","pith_arxiv_id":"2004.11409","snapshot_observed_at":"2026-07-11T00:07:45.485905Z","title":"Falls, Eur","venue":"hep-th","work_id":"4379641c-b75d-4c9a-9d72-657c3437b86a","year":2020},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2004.11409","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:0143c29f1c5303721c781c1a8aac84427a3cd3ad90cf1574e51ba3cf7f3fd42f","observation_id":"6887fc2a-04f0-421c-8a2a-6e331ededfad","resolution":{"observed_at":"2026-05-19T04:52:59.409849Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2210.00492","last_updated":"2023-03-22T16:54:01Z","snapshot_observed_at":"2026-08-18T22:52:22.664540Z","submitted_at":"2022-10-02T11:42:11Z","title":"Properties of a proposed background independent exact renormalization group","version":3},"cited_work":{"arxiv_id":"2210.00492","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2210.00492","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Mandric and T","venue":null,"work_id":"e4c60922-f071-4767-a4b4-70bb056fd2a4","year":2023},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2210.00492","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:dce7027b419608f740461b8b0db8182cc6b8551ed0b64d0ffa81c96471b31a31","observation_id":"ba519c53-66fc-481d-9cbf-a68e2d26d4b1","resolution":{"observed_at":"2026-05-19T04:52:59.120280Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.17523","last_updated":"2025-04-08T13:18:36Z","snapshot_observed_at":"2026-08-18T17:24:52.222208Z","submitted_at":"2024-03-26T09:25:25Z","title":"Simplified functional flow equation","version":3},"cited_work":{"arxiv_id":"2403.17523","doi":null,"metadata_source":"pith","pith_arxiv_id":"2403.17523","snapshot_observed_at":"2026-07-11T00:07:45.484706Z","title":"Wetterich, Phys","venue":"hep-th","work_id":"f78cfc30-7293-40a0-8833-d33e92ee2b76","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2403.17523","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:a99f3ea33b6a9e846f8325a44a4fb939def87f7b3f994e95d611426923ed7829","observation_id":"6b4ec298-68ea-403e-aa4e-c6f5f075687e","resolution":{"observed_at":"2026-05-19T04:52:59.363224Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.03625","last_updated":"2024-08-07T08:35:19Z","snapshot_observed_at":"2026-08-16T13:28:01.933627Z","submitted_at":"2024-08-07T08:35:19Z","title":"Background dependent cutoff for Wilson actions","version":1},"cited_work":{"arxiv_id":"2408.03625","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2408.03625","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Pagani and H","venue":null,"work_id":"8a9e92c9-0a97-45cf-9ee2-efe9ee7bdb73","year":2025},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2408.03625","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:3b158c2b82f389d35827ca9caced7edef56250deab77481f145c31535edf5840","observation_id":"3e3e9efb-80ba-4ea7-82cd-45234b4414a5","resolution":{"observed_at":"2026-05-19T04:52:59.208764Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.09503","last_updated":"2022-11-15T19:02:20Z","snapshot_observed_at":"2026-08-17T08:51:56.396790Z","submitted_at":"2019-03-22T13:35:45Z","title":"Resolving phase transitions with Discontinuous Galerkin methods","version":4},"cited_work":{"arxiv_id":"1903.09503","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1903.09503","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Grossi and N","venue":null,"work_id":"3bc04a92-356b-4df9-a958-ad3ccae97ef8","year":2023},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/1903.09503","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:8b8c63de70f0326660bc1169659e37a8227ece693e0e55a4a6051607710d2596","observation_id":"1c1ada2b-85bb-4af5-8fac-a9c27f8a4260","resolution":{"observed_at":"2026-05-19T04:52:59.317988Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2102.01602","last_updated":"2021-02-02T16:54:29Z","snapshot_observed_at":"2026-08-18T01:37:14.401797Z","submitted_at":"2021-02-02T16:54:29Z","title":"Shocks and quark-meson scatterings at large density","version":1},"cited_work":{"arxiv_id":"2102.01602","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2102.01602","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Grossi, F","venue":null,"work_id":"6eb8ee86-8141-4792-bb8f-4e9bf7a14c64","year":2021},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2102.01602","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:3bda5e5dd27ac778eadcd8bd9565156b2d7a1e5b4579549fb55fd5a688819aba","observation_id":"dc2f047d-988a-471a-baf9-ce7ef692048e","resolution":{"observed_at":"2026-05-19T04:52:59.171542Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.10085","last_updated":"2022-09-15T16:35:35Z","snapshot_observed_at":"2026-08-16T18:01:35.802026Z","submitted_at":"2021-08-23T11:33:26Z","title":"Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows","version":2},"cited_work":{"arxiv_id":"2108.10085","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2108.10085","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Koenigstein, M","venue":null,"work_id":"c624e3ce-fa66-4941-b5ef-05de14124e1b","year":2022},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2108.10085","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1177da8cf81d3bd00b0130433219bd3b4b0bd251ab4a04d6674c1156f821e2d8","observation_id":"db0095f3-7267-4410-af57-e1bd6b553dec","resolution":{"observed_at":"2026-05-19T04:52:59.242931Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.04037","last_updated":"2022-09-15T16:51:22Z","snapshot_observed_at":"2026-08-17T17:25:03.493253Z","submitted_at":"2021-08-09T13:42:12Z","title":"Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\\rightarrow\\infty$ limit in $O(N)$-type models","version":2},"cited_work":{"arxiv_id":"2108.04037","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2108.04037","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"367428a5-8394-41f9-82d7-4d38aac86f31","year":2022},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2108.04037","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:6142edcc0dac567433af264fcc1f301036696ec12be4c8af7f80d60db13b8cbe","observation_id":"177fbdb5-b0a6-4b8d-a627-d2f1904c43bb","resolution":{"observed_at":"2026-05-19T04:52:59.399344Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.02504","last_updated":"2022-09-15T16:14:50Z","snapshot_observed_at":"2026-08-19T13:42:16.852875Z","submitted_at":"2021-08-05T10:23:47Z","title":"Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model","version":2},"cited_work":{"arxiv_id":"2108.02504","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2108.02504","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Koenigstein, M","venue":null,"work_id":"b69b75f2-d8ba-4387-ad25-bb33fabbb037","year":2022},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2108.02504","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:df4daffa0252d9bccb8017f62f9fbfaef87b032f06c410785b0acf0689dfe682","observation_id":"fe6fa74a-267d-4057-9d70-fb6f9c860b27","resolution":{"observed_at":"2026-05-19T04:52:59.226480Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2207.12266","last_updated":"2022-08-16T09:57:04Z","snapshot_observed_at":"2026-08-19T17:41:08.535051Z","submitted_at":"2022-07-25T15:38:13Z","title":"Local Discontinuous Galerkin for the Functional Renormalisation Group","version":2},"cited_work":{"arxiv_id":"2207.12266","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2207.12266","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ihssen, J","venue":null,"work_id":"315cad46-dd13-4590-a15d-f52999e78c5e","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2207.12266","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:f93d27cf5585ccb82a07647a22329fc598acb70f3a53dd7ab65b04165c9c9bf4","observation_id":"e2eb4970-fb1e-4a1a-babc-11a88c626693","resolution":{"observed_at":"2026-05-19T04:52:59.340525Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.04736","last_updated":"2023-02-09T16:16:05Z","snapshot_observed_at":"2026-08-19T13:42:20.996080Z","submitted_at":"2023-02-09T16:16:05Z","title":"Numerical RG-time integration of the effective potential: Analysis and Benchmark","version":1},"cited_work":{"arxiv_id":"2302.04736","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2302.04736","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ihssen, F","venue":null,"work_id":"15d314de-1d35-4332-9189-cbe921f5d88a","year":2023},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2302.04736","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:8e25a3dd99b850336d380e83ba6a1b0ee147f26a1f1a74acc4dea7649264b239","observation_id":"dab68d2c-1def-45e9-b768-9b2fbd26b5f7","resolution":{"observed_at":"2026-05-19T04:52:59.285391Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.13043","last_updated":"2024-12-17T16:08:06Z","snapshot_observed_at":"2026-08-18T14:01:40.327279Z","submitted_at":"2024-12-17T16:08:06Z","title":"DiFfRG: A Discretisation Framework for functional Renormalisation Group flows","version":1},"cited_work":{"arxiv_id":"2412.13043","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.13043","snapshot_observed_at":"2026-06-29T11:13:20.976436Z","title":null,"venue":null,"work_id":"ac55decb-af1a-4ae2-9f59-7cdb77c02aa2","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2412.13043","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:1cc051a92b8fbe569aa0c150e1049963f9160ee70510ad2eb9f2c894a115117a","observation_id":"7b485e71-9348-46a8-8ca1-a5fc468602d2","resolution":{"observed_at":"2026-05-19T04:52:59.318329Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16053","last_updated":"2024-12-20T16:53:43Z","snapshot_observed_at":"2026-08-18T05:44:24.507724Z","submitted_at":"2024-12-20T16:53:43Z","title":"Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space","version":1},"cited_work":{"arxiv_id":"2412.16053","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.16053","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Zorbach, A","venue":null,"work_id":"ce305b3d-7d13-4e8e-9aa1-4dae2283bcf9","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"cited_paper":"/paper/2412.16053","citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:34a46e1c68d69f1b010f89bfec3d6733f1aeb4308526c20760d2f38df2e61d03","observation_id":"4e921bf4-2167-4688-ae35-5763f8cd829f","resolution":{"observed_at":"2026-05-19T04:52:59.388993Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"496cf957-b8e7-4eeb-8f77-5e1dd1fe0fd1","year":2024},"citing_paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables","version":2},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-05-19T04:52:47.512140Z"},"links":{"citing_paper":"/paper/2507.13011"},"observation_digest":"sha256:eaa4c12c597d000eb214a634863f32540d9f03e8f2b1056d3e2d28c767b10314","observation_id":"e21b1e5a-545d-4714-966c-c19a209cdc52","resolution":{"observed_at":"2026-05-19T04:52:59.585414Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.13011","last_updated":"2026-04-10T09:19:38Z","latest_version":2,"primary_category":"hep-th","snapshot_observed_at":"2026-08-12T21:54:37.403131Z","submitted_at":"2025-07-17T11:31:50Z","title":"Physics-informed operator flows and observables"},"reference_resolution":{"displayed":74,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":3,"verified_exact":58,"verified_fuzzy":12},"total_outbound_references":74},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 74 of 74 outbound references and 1 inbound Pith citation observation for arXiv:2507.13011."}