{"as_of":"2026-08-20T19:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:31b8cbd353276907e56e6fce054960f20b159ad2ac3f515241ad5593321c8156","coverage":[{"denominator":46,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":46,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T18:06:24.802524Z","state":"measured"},{"denominator":49,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":49,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-07T20:34:32.470620Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"pith","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-05T02:28:24.338817Z","source":"pith"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"cited_work":{"arxiv_id":"2512.06939","doi":"10.48550/arxiv.2512.06939","metadata_source":"pith","pith_arxiv_id":"2512.06939","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Numerical","venue":"math.AG","work_id":"ac56f47a-a801-413a-917e-163a5ed8c060","year":2025},"citing_paper":{"arxiv_id":"2605.15970","last_updated":"2026-05-15T14:00:47Z","snapshot_observed_at":"2026-08-15T07:38:22.057493Z","submitted_at":"2026-05-15T14:00:47Z","title":"Copositive Matrices with Ordered Off-Diagonal Entries","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-05-20T17:20:29.589792Z"},"links":{"cited_paper":"/paper/2512.06939","citing_paper":"/paper/2605.15970"},"observation_digest":"sha256:af9f814e921cc4523607a38fac89af0f9a12de1d01fb927528d8f309a611909f","observation_id":"54b532f3-05a0-4f1f-a3e4-86b4cb849cbd","resolution":{"observed_at":"2026-06-19T17:11:31.466213Z","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":"2026-05-24T04:54:20.250868+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-24T04:54:20.250868+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":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"cited_work":{"arxiv_id":"2512.06939","doi":"10.48550/arxiv.2512.06939","metadata_source":"pith","pith_arxiv_id":"2512.06939","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Numerical","venue":"math.AG","work_id":"ac56f47a-a801-413a-917e-163a5ed8c060","year":2025},"citing_paper":{"arxiv_id":"2606.18440","last_updated":"2026-06-16T19:41:33Z","snapshot_observed_at":"2026-08-20T00:24:38.056999Z","submitted_at":"2026-06-16T19:41:33Z","title":"Algebraic Networks and Architectural Degenerations","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-26T22:13:06.697566Z"},"links":{"cited_paper":"/paper/2512.06939","citing_paper":"/paper/2606.18440"},"observation_digest":"sha256:1cbac8a8498ddf95e38c1ad9510c3ef38b9200e7c3165a17cc28ffdb8e633206","observation_id":"f544a6e7-edbc-4cf1-81b4-6ed89ff1c156","resolution":{"observed_at":"2026-07-03T23:29:02.711160Z","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":"2026-05-24T04:54:20.250868+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-24T04:54:20.250868+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":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"cited_work":{"arxiv_id":"2512.06939","doi":"10.48550/arxiv.2512.06939","metadata_source":"pith","pith_arxiv_id":"2512.06939","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Numerical","venue":"math.AG","work_id":"ac56f47a-a801-413a-917e-163a5ed8c060","year":2025},"citing_paper":{"arxiv_id":"2607.05269","last_updated":"2026-07-06T16:19:20Z","snapshot_observed_at":"2026-08-05T23:37:13.894888Z","submitted_at":"2026-07-06T16:19:20Z","title":"Excitation spectra and rank tomography of linear matrix product tangent spaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-07T20:34:32.470620Z"},"links":{"cited_paper":"/paper/2512.06939","citing_paper":"/paper/2607.05269"},"observation_digest":"sha256:3dad8f2451aa46e5325da1289f8c907d6a5ebf1427bc23b9c36c34da9e69150a","observation_id":"3ad5ed4a-bdfc-4727-8ec3-a1b667c3d97d","resolution":{"observed_at":"2026-07-07T20:44:09.122312Z","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":"2026-05-24T04:54:20.250868+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-24T04:54:20.250868+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2512.06939/citation-record","integrity":"/paper/2512.06939/integrity","json":"/paper/2512.06939/citation-record.json","paper":"/paper/2512.06939"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:20.874178Z","title":"Bezanson, A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:20.874178Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:780452098f67d67f88eb06dacacbfd08588850f3e72059d93061a122534c4598","observation_id":"851e9885-ef80-47cf-97ee-ec345a8135a3","resolution":{"observed_at":"2026-08-03T18:06:20.874178Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:20.961075Z","title":"Borovik.Flat degenerations and polynomial system solving in physics and chemistry","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:20.961075Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:466afb36ef59d9b26e375f3857a17460c37b549c2923cb1632c536e6a8c42f30","observation_id":"6c5d6d34-4ff5-4ffd-b69d-dff9ba38c803","resolution":{"observed_at":"2026-08-03T18:06:20.961075Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:21.103526Z","title":"Borovik and P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:21.103526Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:f28770899ee1a5214d31a37fc055effc707430f45d98954a761c3a1721696dc1","observation_id":"eb5d5acb-17d8-434e-91ba-4f8339d98296","resolution":{"observed_at":"2026-08-03T18:06:21.103526Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:21.269001Z","title":"Borovik, H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:21.269001Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:e5d70d8d19cbb7b64be9333b1cbea8039549593cb981b1f04fed52490598b741","observation_id":"143cbd6f-113a-4e85-bbd8-2413fb39000b","resolution":{"observed_at":"2026-08-03T18:06:21.269001Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:21.379528Z","title":"Breiding, B","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:21.379528Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:454d3870f56305b690cfd89970dfea86c9ce7e39e1598ae5cc6915560f9af140","observation_id":"1e9fa4d0-33fd-4de9-b80f-b07a39b4674e","resolution":{"observed_at":"2026-08-03T18:06:21.379528Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:21.552720Z","title":"Breiding and S","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:21.552720Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:527371cd0ba427bcab121c858bfc48afb3f0a42701530388b5c316a209cd7492","observation_id":"fda0d244-d257-41db-90e1-418450742584","resolution":{"observed_at":"2026-08-03T18:06:21.552720Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:21.710741Z","title":"Buczy´ nska, J","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:21.710741Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:bd475d46a5c17627a104d2ca073434c83c884aa02394e4346c391a09b39c32b1","observation_id":"40d84ada-e9cc-4eb8-af41-40d5bff8b726","resolution":{"observed_at":"2026-08-03T18:06:21.710741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:21.815976Z","title":"Draisma, E","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:21.815976Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:3c1b6a84e0ff11113d36e42f94fa856a77d3a4026007697a2ae224f5964fb1d6","observation_id":"1d20a6ad-1228-4489-a0c9-55fb7ed13a2f","resolution":{"observed_at":"2026-08-03T18:06:21.815976Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:21.920954Z","title":"Drineas, M","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:21.920954Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:7f800e2b38252f04b1f1bef1c79d64b915eaeb16f442a3c63536869f04c9044a","observation_id":"05507d1d-3040-45b2-ae12-7eca769bcc05","resolution":{"observed_at":"2026-08-03T18:06:21.920954Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.034537Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.034537Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:649312bdc975dfb979c89aabb03f68b2b7706336cac1b2a73a13e8ae6aaa4de3","observation_id":"91ccd67e-b87b-48ab-a627-8da285d00c7f","resolution":{"observed_at":"2026-08-03T18:06:22.034537Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.178612Z","title":"Eisenbud and J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.178612Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:fcba37d9e2e83917ac66decdb31c5e3dcb980514a33cf50b48a845e68c012394","observation_id":"5b0824a5-8c6b-4174-b966-011155a828b4","resolution":{"observed_at":"2026-08-03T18:06:22.178612Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.285599Z","title":"Falc´ o, W","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.285599Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:6d4c7f71616107048fde5723dd1d6a20f84abf1fbbeb54c591e282640a0ba5ec","observation_id":"8db16563-adaa-4249-a42d-78597f07ebf6","resolution":{"observed_at":"2026-08-03T18:06:22.285599Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.416865Z","title":"Faulstich and M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.416865Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:6866eb6984be1cb1760b691729542151844f2eb8e3afc4bf00dd7057ded1bba4","observation_id":"c04b91d6-f84a-4ba4-aa4e-eeafd516b83f","resolution":{"observed_at":"2026-08-03T18:06:22.416865Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.531814Z","title":"Faulstich, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.531814Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:5167749ceef4be43b78d837000acd95402777bafd14d26329b529961ee4c356d","observation_id":"8441b9ee-7b95-4464-a5b9-0b10e8958335","resolution":{"observed_at":"2026-08-03T18:06:22.531814Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.669299Z","title":"Fulton.Intersection theory, volume 2 ofErgebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas]","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.669299Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:ce9cafdd285fdd34f1b38ea9809a8bb267d64b8588b0daebca4bd56954f47650","observation_id":"d1a670a0-2f11-45be-8d03-ca36ca5cf7f6","resolution":{"observed_at":"2026-08-03T18:06:22.669299Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.782774Z","title":"Garstka, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.782774Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:e2fbe07c33a4a821b4a83edfd7d7b91fb176ecefafc233f982896a4f0d1136f4","observation_id":"d1344d94-ad4d-4fba-80d3-633ee8b0883d","resolution":{"observed_at":"2026-08-03T18:06:22.782774Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.897659Z","title":"Grasedyck","venue":null,"work_id":null,"year":2029},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.897659Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:26792fbc8c228e84747e7f91f8db0fa954d297eeb6a1b591daf4a9fedbc8fb0d","observation_id":"b263c4b3-4334-45ab-9fd9-e17d69ab1ff7","resolution":{"observed_at":"2026-08-03T18:06:22.897659Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:22.995965Z","title":"Heinen, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:22.995965Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:0795a92a6b4b2132bdcf93929d269edd7131c736c2f4da617f9386ce43d69338","observation_id":"178b0c09-7fd7-4ab6-9ad0-26d4245d2fb7","resolution":{"observed_at":"2026-08-03T18:06:22.995965Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.058216Z","title":"Helgaker, P","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.058216Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:c8311b89289de86ec088b5589b9b270f072184009e302c4a776e05116cc5b73e","observation_id":"e8d47b29-eb07-414b-9111-1cd79ee570e0","resolution":{"observed_at":"2026-08-03T18:06:23.058216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.101246Z","title":"Holtz, T","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.101246Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:1c8c1795aa8d1bd2509ea5884b9215c7748ad99d0c936434b8184b697c1ea748","observation_id":"20933785-9e02-48db-91b3-8be1a9ef1765","resolution":{"observed_at":"2026-08-03T18:06:23.101246Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.184003Z","title":"Holtz, T","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.184003Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:3e3cbf40b7da7ad30c3f0fb25657610164a60321cd4b7695d0627104dfbf735f","observation_id":"1630e71b-7ee5-43f4-805d-20d86fe94b1e","resolution":{"observed_at":"2026-08-03T18:06:23.184003Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.247669Z","title":"Huh and B","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.247669Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:c962883820cf548f89161fe9d3575983284a31a9936d5f0bcc161693447e6181","observation_id":"9429c10f-42e7-47c0-8593-e5bf08bc5831","resolution":{"observed_at":"2026-08-03T18:06:23.247669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.281437Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.281437Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:e0670c3830ed826981482a1c3e21353f47c5d0082a7fb03d86f8b3727b64a091","observation_id":"dc5d0828-9d6e-4933-8d29-636416b363bf","resolution":{"observed_at":"2026-08-03T18:06:23.281437Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.345066Z","title":"Kahle, H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.345066Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:3963d5dd7427792cfccfdad30c03fc5bef3b9a24adf195a7fb7ef92c5a90e0e8","observation_id":"b8fcef2e-10f8-4a80-b095-0af0f2c760ca","resolution":{"observed_at":"2026-08-03T18:06:23.345066Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.404730Z","title":"Kayser, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.404730Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:28577c226bf52c2f6f094ba1108f0e5ab0ed731e7f2c17668684e974cc83571a","observation_id":"ed669eed-5a78-40da-b70b-5f689e47dc29","resolution":{"observed_at":"2026-08-03T18:06:23.404730Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.449910Z","title":"Krumnow, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.449910Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:9258d4a076a043c20ae423afdbb1c03312cf75909e3a320b61f898138673df54","observation_id":"1e65991b-e9d1-4287-88d8-749f0462818a","resolution":{"observed_at":"2026-08-03T18:06:23.449910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.490190Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.490190Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:17ddc83bb38b89b88c707f8a1ff0b5e79cc88ba2f85ced9a29bb914e10dcaae9","observation_id":"abf61bf0-a8c2-4529-9ef7-2dbe6c0cdd4e","resolution":{"observed_at":"2026-08-03T18:06:23.490190Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.557157Z","title":"Legat, Chris Coey, Robin Deits, Joey Huchette, and Amelia Perry","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.557157Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:9e1ebd5e9bd8b00ac0e02ee61c3b576eb267c2cba422080e78044f86d6384439","observation_id":"c3b35305-802c-4363-ac21-b0c5a7eeb210","resolution":{"observed_at":"2026-08-03T18:06:23.557157Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.599551Z","title":"Lin and J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.599551Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:fb7d5ca81ffa579a67415e8a0bbd8e9cbb0b45d99f4f45646f780106f10a42fa","observation_id":"e40846a8-18fe-4a8d-be37-59b62df9e2c8","resolution":{"observed_at":"2026-08-03T18:06:23.599551Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.665632Z","title":"Lubin, O","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.665632Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:fa456a661a1dd6a883af1fba9684fe007b8b027d11f16a4fd3a36d2cb623d3c2","observation_id":"68892525-727c-4c87-8c04-2dc5b5f1e6f4","resolution":{"observed_at":"2026-08-03T18:06:23.665632Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.705317Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.705317Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:e9d285c7f53cffbeba2ece5bc579c297b6830b043aea5100f52e98cc53cab5b6","observation_id":"b884aa4c-9f08-414e-a838-b763a3b02ef8","resolution":{"observed_at":"2026-08-03T18:06:23.705317Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.793803Z","title":"OSCAR - Open Source Computer Algebra Research system, Version 1.5.0, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.793803Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:a04acec9f072eca5d7b50fefe008a64ea6edc57d4047307ae8b15415d320b48a","observation_id":"f624b1e6-6ea0-4415-ba94-71f8549c63df","resolution":{"observed_at":"2026-08-03T18:06:23.793803Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.841216Z","title":"Oseledets","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.841216Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:13e18c11e318f8c83852ff7f8c15919828347805cf07cde880c76c8b713e73e7","observation_id":"b444b65a-d520-480e-8891-7ad11a002871","resolution":{"observed_at":"2026-08-03T18:06:23.841216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.916122Z","title":"Oseledets and E","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.916122Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:04c7fc092de7ca2ff8ef9f219ba4245fe4a1b48c0bc4399bdec78c29dac9f245","observation_id":"d391dca9-b2b4-465c-8922-662fb1c06c01","resolution":{"observed_at":"2026-08-03T18:06:23.916122Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:23.996274Z","title":"Ranestad","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:23.996274Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:e81d9f589d940f66187c2904fbb68c6fe264dffc70712fb69cf2d03fc990ced4","observation_id":"f8a33609-d889-417b-96e2-775b335f8f03","resolution":{"observed_at":"2026-08-03T18:06:23.996274Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.038330Z","title":"Restuccia and G","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.038330Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:1867c589a68c14aae9f5467927e3e16f77265ed6d9b8cde6b8cbbb57db10fd88","observation_id":"f820882d-57c8-4bc6-9dde-c175478bae1e","resolution":{"observed_at":"2026-08-03T18:06:24.038330Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.108093Z","title":"Salizzoni, L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.108093Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:651b9295185b07209fd8f5c058be7215f8a1554edb316a0600055fd8bfdb20e2","observation_id":"b429a6a5-b651-424f-9a6a-47b531c7f3e6","resolution":{"observed_at":"2026-08-03T18:06:24.108093Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.158658Z","title":"Salizzoni, L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.158658Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:03c0f56f73bd488c064e4fd2a5a4b6b375ec6f5a48b3425cb3cee1b2c4124cc3","observation_id":"a45b7a6f-b269-4634-82f4-9ad913db25a0","resolution":{"observed_at":"2026-08-03T18:06:24.158658Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.226297Z","title":"Schollw¨ ock","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.226297Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:efad8d33a0d916a078fe3d2691f29256b95588ac22e9a525df934ef5732c5a7d","observation_id":"49e3799e-6326-4dc0-af38-b60ebfa347a7","resolution":{"observed_at":"2026-08-03T18:06:24.226297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.275912Z","title":null,"venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.275912Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:7490126e4f7603836a4d5fcbbdbe180342b5392b88f4b055ff2fb923c70b8148","observation_id":"c4c0419a-188c-472c-807d-5d6b1fffffd0","resolution":{"observed_at":"2026-08-03T18:06:24.275912Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2509.09463","last_updated":"2025-09-11T13:44:49Z","snapshot_observed_at":"2026-08-20T00:24:05.851234Z","submitted_at":"2025-09-11T13:44:49Z","title":"Minimality of Tree Tensor Network Ranks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.09463","snapshot_observed_at":"2026-08-03T18:06:24.322685Z","title":"Seynnaeve, J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.322685Z"},"links":{"cited_paper":"/paper/2509.09463","citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:2238882f0e1d3cfd3564bafe13cedc6c27fa25013293f173ea9b3c1ba960ca44","observation_id":"828099f5-9896-474d-9139-04d6c0085aee","resolution":{"observed_at":"2026-08-03T18:06:24.322685Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.375533Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.375533Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:36498973119bd52d0dc740f6d426170a73e2174e564bee0f36d87fbe108cb60c","observation_id":"679fde95-163e-4596-8338-4862a9a4a2f5","resolution":{"observed_at":"2026-08-03T18:06:24.375533Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.410450Z","title":"Szalay, Max Pfeffer, Valentin Murg, Gergely Barcza, Frank Verstraete, Reinhold Schneider, and ¨Ors Legeza","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.410450Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:7ccb1e8b0c8d4c6b15bca5171cb06195dc7e3a231475d560911dcbf6172536f1","observation_id":"2728779f-abb7-4f2d-92fb-ceb82cf7efd1","resolution":{"observed_at":"2026-08-03T18:06:24.410450Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.637770Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.637770Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:808098de556ea87dfbde3f345f390fd0f5853f7dcf23788c0415fd4ca2815327","observation_id":"ef346323-f52e-4a9e-aac7-1d4f4634afda","resolution":{"observed_at":"2026-08-03T18:06:24.637770Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.714311Z","title":"Tyrtyshnikov","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.714311Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:007cfbbec2ccc5da4a7920c14739552ec98fbb0febda7b420b8bfcb9bb587959","observation_id":"318ff5d7-0fbd-4dd0-be9e-d8f8e3cc9ed4","resolution":{"observed_at":"2026-08-03T18:06:24.714311Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T18:06:24.802524Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-03T18:06:24.802524Z"},"links":{"citing_paper":"/paper/2512.06939"},"observation_digest":"sha256:fa55bf0d4fb5fd10d8073bb4003067255ac47f906b0a6cab64b7f5653c493f3f","observation_id":"58d06e5f-6887-4dcd-90be-cf6a2ea2b0e7","resolution":{"observed_at":"2026-08-03T18:06:24.802524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.06939","last_updated":"2026-06-18T08:08:35Z","latest_version":2,"primary_category":"math.AG","snapshot_observed_at":"2026-08-20T00:24:20.087764Z","submitted_at":"2025-12-07T17:46:31Z","title":"Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties"},"reference_resolution":{"displayed":46,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":45,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":46},"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 20 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 3 inbound Pith citation observations for arXiv:2512.06939."}