{"as_of":"2026-08-10T06:58:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a0e8dc72037e40cf7b64e290bac34ef89680fa142032538ee459a1b0780933aa","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T11:55:39.667740Z","state":"measured"},{"denominator":58,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":58,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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":"2026-07-15T11:45:20.771019Z","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":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.02239","snapshot_observed_at":"2026-07-15T11:45:20.771019Z","title":"Canonical Forms as Dual Volumes,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.28453","last_updated":"2026-07-14T09:39:43Z","snapshot_observed_at":"2026-08-08T00:31:56.878386Z","submitted_at":"2026-03-30T13:56:24Z","title":"Global Convergence of the Return Dynamics in the Class $\\mathcal{O}_C$","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-15T11:45:20.771019Z"},"links":{"cited_paper":"/paper/2509.02239","citing_paper":"/paper/2603.28453"},"observation_digest":"sha256:0cc81c1a6c7b8243a5610773ececfa08c1448c8e6f812c12c4e867a73d7c378a","observation_id":"f980cdb2-b7fa-4bcf-8aab-6f7983ee4ca0","resolution":{"observed_at":"2026-07-15T11:45:20.771019Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2509.02239/citation-record","integrity":"/paper/2509.02239/integrity","json":"/paper/2509.02239/citation-record.json","paper":"/paper/2509.02239"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1312.2007","last_updated":"2013-12-06T21:00:01Z","snapshot_observed_at":"2026-07-06T03:30:14.117217Z","submitted_at":"2013-12-06T21:00:01Z","title":"The Amplituhedron","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1312.2007","snapshot_observed_at":"2026-08-05T11:55:37.048036Z","title":"The Amplituhedron","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.048036Z"},"links":{"cited_paper":"/paper/1312.2007","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:f8e58d5d4db2662e1308124c404f793dd468d8f5973cbf16a83ecd11d5a8672d","observation_id":"acbebccc-7e8c-462f-97a6-e33d22567d11","resolution":{"observed_at":"2026-08-05T11:55:37.048036Z","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":"2026-08-05T11:55:37.056166Z","title":"Grassmannian Geometry of Scattering Amplitudes","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.056166Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:ff281a1a3dc3fa18e0f35d813cf47f38abbd05d4424415ff349c6d07f215dc40","observation_id":"97e33197-9429-4883-b190-f3fb101decd7","resolution":{"observed_at":"2026-08-05T11:55:37.056166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.475821Z","title":"Positive geometries and canonical forms","venue":null,"work_id":"0da27f53-9736-48d8-be75-0ef982315e75","year":2017},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.064140Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:2863401a687d759a0319a3713fb3cfd1a98e9d87612311257412d2525fc3f0e5","observation_id":"f3cdce7a-d6b5-4c2f-86a9-5afb053b5f1e","resolution":{"observed_at":"2026-08-05T11:55:40.479756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.06527","last_updated":"2024-02-09T16:38:25Z","snapshot_observed_at":"2026-07-06T17:28:02.037844Z","submitted_at":"2024-02-09T16:38:25Z","title":"Adjoints and Canonical Forms of Tree Amplituhedra","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.06527","snapshot_observed_at":"2026-08-05T11:55:37.072371Z","title":"Adjoints and Canonical Forms of Tree Amplituhedra","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.072371Z"},"links":{"cited_paper":"/paper/2402.06527","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:b6021298e6870f61fb256ef5c78fb1d694de03237eb6d7c77fcb29f132c6da32","observation_id":"93f3e1ff-fdd8-4019-a7c1-8662855e119b","resolution":{"observed_at":"2026-08-05T11:55:37.072371Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.462634Z","title":"Scattering Forms and the Positive Geometry of Kine- matics, Color and the Worldsheet","venue":null,"work_id":"fc207b09-0b45-49b9-b5aa-4d944efdfc5a","year":2018},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.080353Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:c0427ee128a832ed1f961b95f865bd73f3ca8c0295064a79abcce7384daec2a5","observation_id":"801587a1-9d5d-4ead-a93c-9268144ad8ee","resolution":{"observed_at":"2026-08-05T11:55:40.466891Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:37.087669Z","title":"The ABJM Amplituhedron","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.087669Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:ea8b5dd0f9b4c86cc680c860ad13669cc72d51f3f8aeea49c3774180d383718a","observation_id":"cd29aea0-c51e-47e1-9631-5d6478e44e8e","resolution":{"observed_at":"2026-08-05T11:55:37.087669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1701.00453","last_updated":"2017-09-07T11:42:55Z","snapshot_observed_at":"2026-08-08T20:12:28.250582Z","submitted_at":"2017-01-02T17:10:58Z","title":"The Correlahedron","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1701.00453","snapshot_observed_at":"2026-08-05T11:55:37.108807Z","title":"The Correlahedron","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.108807Z"},"links":{"cited_paper":"/paper/1701.00453","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:3b756bd8843399e2b11c69513ad45d78b925ec096f683562febf04cad43d21fa","observation_id":"24c843d6-b4dc-4a7a-90c4-9e6284e9f79b","resolution":{"observed_at":"2026-08-05T11:55:37.108807Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.434691Z","title":"Cosmological Polytopes and the Wavefunction of the Universe","venue":null,"work_id":"1299e204-4d4c-4b01-ae96-4192b9726d44","year":2017},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.162613Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:3b16c13aefa3beeeaada7fa771f99b321bcfb635909796bd92539625a4cb4ef7","observation_id":"ced9fc76-4c7d-496b-8208-3d845b135652","resolution":{"observed_at":"2026-08-05T11:55:40.438975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.420420Z","title":"Stokes polytopes: the pos- itive geometry for ϕ4 interactions","venue":null,"work_id":"7f92f59c-1058-465d-952d-b3e76409932a","year":2019},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.216290Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:222db1f17569e6afe9c662045c08b96947be5d4ee87b93d713cfb22bbb21346d","observation_id":"e47a7955-4f91-44ad-8f4c-2ae484e7ff54","resolution":{"observed_at":"2026-08-05T11:55:40.424915Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1906.02985","last_updated":"2019-06-07T09:42:27Z","snapshot_observed_at":"2026-08-05T19:28:40.334486Z","submitted_at":"2019-06-07T09:42:27Z","title":"The positive geometry for $\\phi^{p}$ interactions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.02985","snapshot_observed_at":"2026-08-05T11:55:37.274334Z","title":"The positive geometry for ϕp interactions","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.274334Z"},"links":{"cited_paper":"/paper/1906.02985","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:efdd0bfd2084dd6a72299ec8fab88db74f7220348e24017def6fce10e5ba2d1f","observation_id":"778fcc8a-acb2-43eb-8424-112cccde5e33","resolution":{"observed_at":"2026-08-05T11:55:37.274334Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1911.06008","last_updated":"2020-01-12T11:40:57Z","snapshot_observed_at":"2026-08-08T23:45:34.663195Z","submitted_at":"2019-11-14T09:46:45Z","title":"On Positive Geometries of Quartic Interactions II : Stokes polytopes, Lower Forms on Associahedra and Worldsheet Forms","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1911.06008","snapshot_observed_at":"2026-08-05T11:55:37.318519Z","title":"On positive geometries of quartic interactions: Stokes poly- topes, lower forms on associahedra and world-sheet forms","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.318519Z"},"links":{"cited_paper":"/paper/1911.06008","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:9ecf1a7e57c8824911515fa410587145df9eb955dd817a4b6f9af97b6554dbf7","observation_id":"fb3edd03-f299-4cb0-8297-59a8ab87e9f4","resolution":{"observed_at":"2026-08-05T11:55:37.318519Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.12145","last_updated":"2020-07-23T17:20:15Z","snapshot_observed_at":"2026-08-05T08:07:25.654024Z","submitted_at":"2020-07-23T17:20:15Z","title":"On the Positive Geometry of Quartic Interactions III : One Loop Integrands from Polytopes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.12145","snapshot_observed_at":"2026-08-05T11:55:37.367146Z","title":"On positive geometries of quartic inter- actions: one loop integrands from polytopes","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.367146Z"},"links":{"cited_paper":"/paper/2007.12145","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:ec7e37a28ae67dafb6d86fdc3ad32e676e57c83cc961e5401decb7f41fc79b66","observation_id":"b112d50c-4787-42be-965b-a2c0b6447691","resolution":{"observed_at":"2026-08-05T11:55:37.367146Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.07979","last_updated":"2022-06-16T07:42:25Z","snapshot_observed_at":"2026-08-09T12:13:46.455941Z","submitted_at":"2022-06-16T07:42:25Z","title":"Towards Positive Geometries of Massive Scalar field theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.07979","snapshot_observed_at":"2026-08-05T11:55:37.451112Z","title":"Towards Positive Geometries of Massive Scalar field theories","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.451112Z"},"links":{"cited_paper":"/paper/2206.07979","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:1380ec749425e6a7409d9f16a993b1b095f5f32661f289990e93772382c4d5c4","observation_id":"e018fb12-1da6-438c-9dfc-6d0ec6080c37","resolution":{"observed_at":"2026-08-05T11:55:37.451112Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.406694Z","title":"Positive Geometries of S-matrix without Color","venue":null,"work_id":"f43f023a-4a69-4421-89e8-9814fb56e4d1","year":2023},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.485602Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:c421170f76b9cea6c89ef4c315106fef28a5cc7bede61bbf18936c7546c9aa6b","observation_id":"836c39b1-6256-49ff-9bf4-3e1c27d3be1b","resolution":{"observed_at":"2026-08-05T11:55:40.411148Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.391965Z","title":"Cosmohedra","venue":null,"work_id":"2b0af04b-7b5a-4936-8a2e-011958c3855d","year":2024},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.546398Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:616f6117b56eb6cb72958a2b5f6cc597a7383c1fad5a9e67772de3209567149d","observation_id":"b046c2e9-9a30-495d-85d3-377ece8cee48","resolution":{"observed_at":"2026-08-05T11:55:40.396863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.378278Z","title":"An invitation to positive geometries","venue":null,"work_id":"c7b08da1-d7e5-4f60-98d4-66cf0968b17d","year":2022},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.610149Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:d23336dc876e96f752664c42f91196878753bcc3da3014ecee1cc37ebc190ec0","observation_id":"06c9035a-7ada-4cbd-844f-26a76475d02d","resolution":{"observed_at":"2026-08-05T11:55:40.382342Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.364680Z","title":"What is Positive Geom- etry?","venue":null,"work_id":"e236fbd6-c500-41b2-ab91-615118f6a414","year":2025},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.688505Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:db0efc8eea240443d7af067882763aa7837be175ea31cceb35a94c26e3379260","observation_id":"4930f6b3-bc9b-4340-bf22-0b5c8d3d93ed","resolution":{"observed_at":"2026-08-05T11:55:40.368728Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.351441Z","title":"Algebraic and Positive Geometry of the Universe: from Particles to Galaxies","venue":null,"work_id":"3fd7fccd-4eb8-46e6-a5af-f84f275caf64","year":2025},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.744331Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:12a457764fd9839044ab1e551a122cbf49e80ad5f82090d3aedb83ab230f518d","observation_id":"a8213cbc-7e77-488b-8a76-5d80b4275bbc","resolution":{"observed_at":"2026-08-05T11:55:40.355621Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.337944Z","title":"Eliminating spurious poles from gauge-theoretic amplitudes","venue":null,"work_id":"f3cbb208-a932-49ed-8a2b-8ef68732c3d2","year":2013},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.801710Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:d9371232e88c136854db27483471b622157700b70a296638ce2830e28018b880","observation_id":"ed08edde-5999-4911-92d6-2ab82cf5c33d","resolution":{"observed_at":"2026-08-05T11:55:40.342431Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.324516Z","title":"Canonical forms of polytopes from adjoints","venue":null,"work_id":"45983a00-1cc6-4259-92ce-e0c37bd86686","year":2025},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.862434Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:2fb58d2cd197dd21e87ec479f3dda942e60c48d559d8ef46ec0bb749f2b78ffa","observation_id":"ee4eb79e-b9f0-41b1-a1cb-1a9a195e2439","resolution":{"observed_at":"2026-08-05T11:55:40.328932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.311048Z","title":"Positivity properties of scattering ampli- tudes","venue":null,"work_id":"f56e7706-126c-4244-8484-38c108510e55","year":2025},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.948284Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:75fb4e523709ca94814c0872ff408711084f5d8b03c93b05e7412b4ebc64e45d","observation_id":"c97ae7e6-be26-4274-8d1a-72f730050db4","resolution":{"observed_at":"2026-08-05T11:55:40.315238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.297831Z","title":"Laplace transform (PMS-6)","venue":null,"work_id":"ac996a9b-d660-4b91-9a8c-344fb0a65878","year":2015},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.017784Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:8da38eb5649f2c62eb44e7327a07c25fcdd6d9258a503271c2c0737e844d49f6","observation_id":"bdab2150-bef4-40cf-bb45-ff2a2d3345dc","resolution":{"observed_at":"2026-08-05T11:55:40.301692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/jhep01(2021)035","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Positive geometry, local triangulations, and the dual of the Amplituhedron","venue":"Journal of High Energy Physics","work_id":"46fb39d5-8eeb-4da7-afaa-3b2737aba542","year":2021},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.089743Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:c8878d83b78dbb6b748d141be8a957bfb207610ab09f8e18aaacea092ba17746","observation_id":"7b2069c1-4762-4640-9382-ae507811f16f","resolution":{"observed_at":"2026-08-05T11:55:39.771100Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1512.04954","last_updated":"2016-03-02T16:54:59Z","snapshot_observed_at":"2026-08-09T03:30:53.481520Z","submitted_at":"2015-12-15T21:00:14Z","title":"Towards the Amplituhedron Volume","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1512.04954","snapshot_observed_at":"2026-08-05T11:55:38.149451Z","title":"Towards the Amplituhedron Volume","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.149451Z"},"links":{"cited_paper":"/paper/1512.04954","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:91804ba61d135b0634409b319d90d0e2997f6db89d3d2ee259e85b1ba1d69060","observation_id":"6d20a8f8-6e2d-4db6-9f22-52d8c5f6df07","resolution":{"observed_at":"2026-08-05T11:55:38.149451Z","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":"10.1007/jhep08(2015","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.752147Z","title":"Positive Amplitudes In The Amplituhedron","venue":null,"work_id":"c76b1a9e-1e68-49b7-a943-d976a208a08a","year":2015},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.219849Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:8d721f011911ac73355d660bc7ea97e10d0a23cfe22127044c6557069cc7bac9","observation_id":"ac1bbf83-b514-49f2-968f-758581e9bd10","resolution":{"observed_at":"2026-08-05T11:55:39.756541Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/jhep02(2017)112","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Multi-loop positivity of the planar N = 4 SYM six-point amplitude","venue":"Journal of High Energy Physics","work_id":"71c27ccb-8cf1-43f5-ae5d-25baafd33f45","year":2017},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.351555Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:0959f2c3335bf9abaf99996b15341b6d9fdecc3a5958b8826c672e01eee8baea","observation_id":"39f6b0ad-f28c-4914-bb8f-2e7996bca68e","resolution":{"observed_at":"2026-08-05T11:55:39.742120Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/jhep04(2025","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.720067Z","title":"Positivity properties of five-point two-loop Wilson loops with Lagrangian insertion","venue":null,"work_id":"1c7cac7f-f72e-4a89-a368-b74851a0a836","year":2025},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.411283Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:72b080a899976cc4c5375ea9e59ee568c08070c6912619f76909fa8611998d25","observation_id":"a829f4ae-839f-48e3-a6a8-6a551d6f9366","resolution":{"observed_at":"2026-08-05T11:55:39.726861Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.17620","last_updated":"2025-07-23T15:52:37Z","snapshot_observed_at":"2026-08-06T14:42:32.272264Z","submitted_at":"2025-07-23T15:52:37Z","title":"Exterior Cyclic Polytopes and Convexity of Amplituhedra","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.17620","snapshot_observed_at":"2026-08-05T11:55:38.508952Z","title":"Exterior Cyclic Polytopes and Convexity of Amplituhedra","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.508952Z"},"links":{"cited_paper":"/paper/2507.17620","citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:5eef5f7cd416c7f2c8e1626b8b673da336e9d76249329e9e5ffb2f4a56bc6c70","observation_id":"297f401e-f280-478b-ba4f-9c84e0d00d6c","resolution":{"observed_at":"2026-08-05T11:55:38.508952Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.257339Z","title":"Barrier functions in interior point methods","venue":null,"work_id":"5e423596-525d-4b8b-a7a8-864d623486f3","year":1996},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.570536Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:35a64e3a9cb8bc31259df9aea318fd71dc6580fc94ee304966c318d26d4dc066","observation_id":"2dc4812a-f383-430d-92b7-e238836b91a9","resolution":{"observed_at":"2026-08-05T11:55:40.261385Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.284417Z","title":"8478 [hep-th]","venue":null,"work_id":"506adf59-e585-4f18-8db5-0cd53e3c2abb","year":null},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.307227Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:2cc4c1da300c96c6df099f0d71b10c2e4691c899a58a0eb295be77490e70478e","observation_id":"49594834-939b-46cd-bbdc-407fe8bf03e7","resolution":{"observed_at":"2026-08-05T11:55:40.288905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.270675Z","title":"11456 [hep-th]","venue":null,"work_id":"1c16cd40-82e0-451d-bfcf-703176cf58f8","year":null},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.446417Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:9e04c22594c186fc9cee9ed8294eb859ea5e212d8f2f8eb88ccfffd0afef80ac","observation_id":"3074cdb5-fa55-4edc-a1eb-5a48f2abc307","resolution":{"observed_at":"2026-08-05T11:55:40.275078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.217198Z","title":"Positivity certifi- cates via integral representations","venue":null,"work_id":"ae8973fd-c958-4189-951e-a73b2a669679","year":2019},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.772735Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:c5211117d4f3143762e3390bc7c3b103a0c03250840d1b42cacb9d3fd2e3efc7","observation_id":"dd2275d9-82da-4779-8614-13262b4af1dc","resolution":{"observed_at":"2026-08-05T11:55:40.221553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.244361Z","title":"Exponential varieties","venue":null,"work_id":"b5b8431f-8cc1-4c40-92f2-5c5b48dafad0","year":2016},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.629770Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:ccebdea836de215b5525f6b1c9c1028b1d5dbadb2a9178ab34969c33b8ab9d68","observation_id":"76ea7f61-469d-445a-9ebe-e8859f6675f4","resolution":{"observed_at":"2026-08-05T11:55:40.248295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.230484Z","title":"Complete monotonicity for inverse powers of some combinatorially defined polynomials","venue":null,"work_id":"deaee021-b7db-44bd-b2bc-5f48ac7c292b","year":2014},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.697481Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:7dfcbbba960a3cf04e10438252b48ac424f399d3bf9b494045fb827103998f3e","observation_id":"1ca63627-3064-4d2b-9864-65aba3af9d1e","resolution":{"observed_at":"2026-08-05T11:55:40.235155Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.178165Z","title":"The analysis of linear partial differential operators","venue":null,"work_id":"7b18ed56-941d-408d-b88a-c7c953a0287c","year":1983},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.963919Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:d9ab2f953abf6001b696fe0a487d2463ce0f1138895713fe393ac909dcd342fc","observation_id":"1d5161e8-4bff-465c-b628-669cb9a74949","resolution":{"observed_at":"2026-08-05T11:55:40.182287Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.204471Z","title":"An Inequality for Hyperbolic Polynomials","venue":null,"work_id":"19c5acc7-1009-457b-bd91-d44d4c4b5440","year":1959},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.844256Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:35bb357199671eb3399287f97111433a31564fa5a7f725d2ac433f1c85bcdba3","observation_id":"f3305440-57cd-45b5-8ff0-8cb3016da608","resolution":{"observed_at":"2026-08-05T11:55:40.208372Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.190979Z","title":"Lacunas for hyperbolic differential oper- ators with constant coefficients I","venue":null,"work_id":"250f4e9b-516c-497c-a612-7ab06a1476b8","year":1970},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:38.902198Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:37a5b2ab6904f4a67b838a498b603da492e7005b49cefed283bd8aa159ad4138","observation_id":"1c4bbc83-c732-4593-bccf-927ef2d0678e","resolution":{"observed_at":"2026-08-05T11:55:40.195220Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.163644Z","title":"On the fundamental solutions of a class of elliptic quartic operators in dimension 3","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.163644Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:8b7ab91dc57bb43114a359b19444035d72c183e94c14a89fd553122a7a8616e9","observation_id":"ee822d1e-de60-47ca-b40b-af026427d68f","resolution":{"observed_at":"2026-08-05T11:55:39.163644Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.164940Z","title":"A fundamental solution of N. Zeilon’s operator","venue":null,"work_id":"af63ed01-2586-43bd-a320-d153d71d403f","year":2000},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.021742Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:d470c82cb04ae571f6006b94ceb66aeb4f366264577d175ee91b4a6f3ed1a68f","observation_id":"96da9957-5e5c-416c-974f-7a831807d10f","resolution":{"observed_at":"2026-08-05T11:55:40.168985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.151507Z","title":"Fundamental solutions of real homogeneous cubic operators of principal type in three dimensions","venue":null,"work_id":"228adb24-eba5-4d4f-858c-b574e17048e4","year":1999},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.092819Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:68ac2bedb676eb79229ba8a419719ad53f9dee1ab71966d83da65f29a2aacde7","observation_id":"4dfdaf90-5a84-441c-a0eb-b790cd58940e","resolution":{"observed_at":"2026-08-05T11:55:40.155790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.111068Z","title":"Deux exemples classiques de repr´ esentation int´ egrale","venue":null,"work_id":"33ea6f75-9e07-469f-a4c7-bf470714b457","year":1969},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.404764Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:7f4da29c4ca78c6e72dd155ae9a94cb140fc3f74cc3dd096b624fcb9ce0b6146","observation_id":"d5ff7873-64eb-4536-b843-47e4ff2cdb59","resolution":{"observed_at":"2026-08-05T11:55:40.115275Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.138532Z","title":"On the fundamental solutions of a class of hyperbolic quartic op- erators in dimension 3","venue":null,"work_id":"6a52832f-f121-4533-801a-08b539cc62c4","year":2005},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.247921Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:9f714e0584720843bf8bea53d91730d1ee0f307e8f935de91adb355db6fb5e22","observation_id":"ea6ebe20-d8b6-4a15-9092-6a6903657475","resolution":{"observed_at":"2026-08-05T11:55:40.142533Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.124789Z","title":"Positive geometries and canonical forms via mixed Hodge theory","venue":null,"work_id":"321751d0-6b6b-4b36-9130-673c57294834","year":2025},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.358523Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:0c5abee2dbafae50afe83942719292cffa7edbd12e5abc5b6fcd4ec31209df46","observation_id":"d1db0bcd-dc84-4a3a-a159-0af31aee2aec","resolution":{"observed_at":"2026-08-05T11:55:40.129517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.070358Z","title":"Linear hyperbolic partial differential equations with constant co- efficients","venue":null,"work_id":"d5f5157f-8602-4594-b640-ee4550d4be57","year":1951},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.619045Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:c63bfe52a66f50beeb5af3eee786feab1200b0cdee111b268cc0836abe9b5254","observation_id":"6edb0237-5046-4b6d-922a-fa6b204b5f50","resolution":{"observed_at":"2026-08-05T11:55:40.074485Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.097453Z","title":"Hyperbolic Polynomials and Interior Point Methods for Convex Programming","venue":null,"work_id":"00727315-0c74-4064-9ab7-d447e97d105e","year":1997},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.501443Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:62959ce8ccb3b0fd81546baecfb70baf11f585240966580b38b2fafafce35c47","observation_id":"a70de7a2-719b-4c86-8237-b6f3e2410831","resolution":{"observed_at":"2026-08-05T11:55:40.101754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.083437Z","title":"Generalized functions","venue":null,"work_id":"39c1a7cc-0d09-4fbd-8a0a-c6b04d80391e","year":1968},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.546925Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:c07b13fe7823c9a4716d34d5fb8798c5c5315a26027a8fa0e21419acf3d2bf0e","observation_id":"9cc8637b-72fa-49bd-9374-e2e8fccfd49d","resolution":{"observed_at":"2026-08-05T11:55:40.087508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.028660Z","title":"Adjoints and Canonical Forms of Polypols","venue":null,"work_id":"05d585b3-8c78-43cd-ba7b-bc15eb2df30c","year":2024},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.640474Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:dc806087d62209b6b476934647b9424573b716a912653994f3ec54866ba878d9","observation_id":"2a82c50b-b434-4ba2-bccc-5fdcf1d58ce4","resolution":{"observed_at":"2026-08-05T11:55:40.033164Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.057242Z","title":"The analysis of linear partial differential operators","venue":null,"work_id":"29996989-a086-4d4c-8f72-75cc6ed1f195","year":1983},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.632223Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:ccc16dd03059a4125018a04c7e33af4de82d0ab47ef4a2cbad5f78d89cbe989e","observation_id":"fdf7dcbd-b84e-4b41-8cf8-caeddf278626","resolution":{"observed_at":"2026-08-05T11:55:40.061442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.042783Z","title":"Algebraic boundaries of convex semi-algebraic sets","venue":null,"work_id":"ef55a4cf-79dc-4519-9e59-0c4db5b3608c","year":2015},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.636573Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:16029eb818541e40a0a3c80a4e8e5e2aa0c4d3641068be688b55923630787196","observation_id":"89cd8038-a5fc-4395-8a1d-cd38bc3a09a9","resolution":{"observed_at":"2026-08-05T11:55:40.047147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.981721Z","title":"Linear matrix inequality representation of sets","venue":null,"work_id":"03619047-8cec-4aa0-a912-955f573587e4","year":2007},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.652410Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:84d2d177e8021289bece678e265154c6f42e9c63354551954297f0336d48bad3","observation_id":"44462c8f-b11f-4123-b20c-a12ee0298501","resolution":{"observed_at":"2026-08-05T11:55:39.986019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.011609Z","title":"The Analysis of Linear Partial Differential Operators: Distribu- tion theory and Fourier analysis","venue":null,"work_id":"5157908c-e5a1-415b-9550-7a78c8194925","year":1983},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.644442Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:647ddd99bbdae904c3454d36c4b19ca737cbaa9728d601dba8a886ac91a57473","observation_id":"0adab6f6-b918-4535-ac34-f7bb4c9d3454","resolution":{"observed_at":"2026-08-05T11:55:40.017813Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.995584Z","title":"A Note on the Hyperbolicity Cone of the Specialized V´ amos Polynomial","venue":null,"work_id":"f94b3514-d67d-46eb-8825-9df4420277c6","year":2015},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.648694Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:9d714f2bbc55d07906c4654c5b26d0b8953e5516ce6b78116005a46c1ac545c7","observation_id":"66bbdc1b-770b-4447-8a37-4a44432c69a3","resolution":{"observed_at":"2026-08-05T11:55:40.000417Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.952396Z","title":"From polygons and sym- bols to polylogarithmic functions","venue":null,"work_id":"8f24c4ac-98d3-4f4a-a7ae-369119428732","year":2012},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.663984Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:e23e6afc724856b0265f981dea9755df08ddafff4026a080030b11a69a4f2319","observation_id":"7e5c4284-b21f-406c-95dd-03166a71b2a4","resolution":{"observed_at":"2026-08-05T11:55:39.957056Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.967036Z","title":"Hyperbolicity cones of elementary symmetric polynomials are spectrahedral","venue":null,"work_id":"782de341-1ac9-4414-8b8a-d5056a34fbe4","year":2014},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.656289Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:664e0d584770253a237bae4b91dff7d7e5adb8a2f15150f54d439ba1320adeab","observation_id":"52ef7ed4-9833-4867-913b-4cb9af1429e8","resolution":{"observed_at":"2026-08-05T11:55:39.971890Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.660137Z","title":"Classical Polylogarithms for Amplitudes and Wil- son Loops","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.660137Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:0feda8abd2759b2adf53b1283581d17dbf52a89e616158c94d4232ac3c554167","observation_id":"31734c65-4a31-40c8-a00a-d2b8be22ff23","resolution":{"observed_at":"2026-08-05T11:55:39.660137Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:39.937366Z","title":"Byrd and Morris D","venue":null,"work_id":"2056ec75-14c9-4f1d-8946-5f5ed0d1c2a7","year":2013},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:39.667740Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:8b513b8e2852ec0f05f360c50f6ea90689f67d5605e457319efea89d0d9452f1","observation_id":"f377f3fa-5284-4fc7-a33b-03ef6a066173","resolution":{"observed_at":"2026-08-05T11:55:39.941887Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:55:40.448360Z","title":"00951 [hep-th]","venue":null,"work_id":"ca692594-c34d-4681-96b0-ebff6696189d","year":null},"citing_paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes","version":1},"reference_index":165,"source":"pdf_text","source_observed_at":"2026-08-05T11:55:37.101362Z"},"links":{"citing_paper":"/paper/2509.02239"},"observation_digest":"sha256:876579c0c742312992761ac9006efd89a51f883049ec9fa0e7497719488b2794","observation_id":"2f19a5fb-a8dc-4aee-9e07-93ece49bc2a8","resolution":{"observed_at":"2026-08-05T11:55:40.453070Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.02239","last_updated":"2025-09-02T12:07:36Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-06T05:25:43.517086Z","submitted_at":"2025-09-02T12:07:36Z","title":"Canonical Forms as Dual Volumes"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":6,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":4,"verified_fuzzy":37},"total_outbound_references":57},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 1 inbound Pith citation observation for arXiv:2509.02239."}