{"as_of":"2026-08-08T13:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:395561aeda1c3109fd5f675fa0071b6bf4c78dfd38596f6c8918bbef1f43ce01","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:51:34.544181Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"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":[],"links":{"evidence":"/evidence","html":"/paper/2506.12720/citation-record","integrity":"/paper/2506.12720/integrity","json":"/paper/2506.12720/citation-record.json","paper":"/paper/2506.12720"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:51:34.938627Z","title":"The yang-mills equations over riemann surfaces","venue":null,"work_id":"d4a7e710-7d78-4dc5-a237-b8faef2a418f","year":1983},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.450810Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:c0cd9f34cd832407ef3515aaada7840b78eff442cadb6a4c5f3fe027616a5605","observation_id":"c5be5141-e4d7-455d-828b-4297d0857fbc","resolution":{"observed_at":"2026-08-07T00:51:34.941822Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.928765Z","title":"The index of elliptic operators on compact manifolds","venue":null,"work_id":"18099154-1f3c-4c1e-b433-37bb528b545e","year":1963},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.454482Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:efeb813a337b641a8337f7ff02220192c3a6859646559e1c89e38647e3ca79fc","observation_id":"96a9a23a-e1f9-4d70-86c7-aca664127e4c","resolution":{"observed_at":"2026-08-07T00:51:34.932244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.918963Z","title":"Variétés kählériennes dont la première classe de chern est nulle","venue":null,"work_id":"0f51a2fc-9bf4-4eba-a2ed-066527f67680","year":1983},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.457884Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:b97e7e5b9a623cc8e3c6afe76159993707d60d64b49f984dc90b27883a509959","observation_id":"47bade64-2f32-4832-99ef-57cd75cf7e6d","resolution":{"observed_at":"2026-08-07T00:51:34.922368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.908984Z","title":"Extensions of mixed hodge structures","venue":null,"work_id":"956b83a9-94b0-47f6-9e28-0bf54963b6a4","year":1987},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.461097Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:e53107be9551c72c910e4396f5725547e8edf84e494c2fdb26d65f0dcd15f366","observation_id":"e09f69ac-7b94-4022-8bb0-c9af8a1b7481","resolution":{"observed_at":"2026-08-07T00:51:34.912086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.898982Z","title":"Mixed Hodge structures , volume 52 of Ergebnisse der Mathematik und ihrer Grenzgebiete","venue":null,"work_id":"6dd468d2-627d-4b3b-bd50-f77227d18db3","year":1995},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.464772Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:fd348e32e97bac956014e8ffdbc334137bf5e4185a3c5da01264437622f294ea","observation_id":"85ccc01b-81f9-4a5f-a07d-94bb5db5fc76","resolution":{"observed_at":"2026-08-07T00:51:34.902715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.889650Z","title":"Hodge cycles on abelian varieties","venue":null,"work_id":"e245fe98-264b-4b62-8d29-4a481ff04e80","year":1982},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.468171Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:cb5a717202af6fe2a36bf0ac629256b5cba9f2912e1309e143aa719129becbf5","observation_id":"13d5e7fd-3296-4e7e-84e8-a17674c998d8","resolution":{"observed_at":"2026-08-07T00:51:34.892579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.880372Z","title":"An application of gauge theory to four-dimensional topology","venue":null,"work_id":"15a825c8-0209-4189-91c0-33f1b7822ebd","year":1983},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.471826Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:606764636f8c0d5c425acdc6452e3b53b37654779ac41b408847780c4074cdff","observation_id":"621d57d1-e89e-4fa0-b077-8ae9d44157e1","resolution":{"observed_at":"2026-08-07T00:51:34.883793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.870873Z","title":"Towards mirror symmetry for varieties of general type","venue":null,"work_id":"0269c05e-511c-4b75-a40f-8806b94c740c","year":2017},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.474573Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:5afff35cd4426170a31f28612501a6d8a69a5b79873f124f096b9ef831812e65","observation_id":"27bf5c06-bb6f-4e0c-a4c7-f672af8fc8e5","resolution":{"observed_at":"2026-08-07T00:51:34.873749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.861922Z","title":"Periods of integrals on algebraic manifolds","venue":null,"work_id":"5642cff6-9ec4-4110-bd82-4e9e1248a073","year":1968},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.477317Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:3b4d729db3609d205c765c494c886b07f678d4ae5dd7901d9d3c90be67be581a","observation_id":"92c78cea-47a0-4dc4-9485-0dbba8333b37","resolution":{"observed_at":"2026-08-07T00:51:34.865142Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.852942Z","title":"Standard conjectures on algebraic cycles","venue":null,"work_id":"ebdf379f-4d5e-444e-b71b-05d31e280fa4","year":1968},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.480219Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:615fb902513eb040d062b3f4b98ab96d7fcc9c25d48b21d51d272d82c5719d22","observation_id":"ab3f0ea1-fd56-4a80-9a85-4923ddeb20b5","resolution":{"observed_at":"2026-08-07T00:51:34.856086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.842786Z","title":"Symplectic techniques in physics","venue":null,"work_id":"ddf02dec-dabc-4d15-9f64-9a29ef17b54a","year":1984},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.482916Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:9baaf0db13b7a052b464814d09013049a28eb3766c9a4aeb862809d4133ebb88","observation_id":"b7e2b551-1969-4c5d-bca9-8acb8844b8cf","resolution":{"observed_at":"2026-08-07T00:51:34.846269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.833585Z","title":"The topological invariants of algebraic varieties","venue":null,"work_id":"2fe1fdf8-bd10-42d4-b6de-69d66c5f517d","year":1950},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.485968Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:ab0bf6603d8fff65d974680403f1d0bf6e13cc7c9129964fae270218c54cc42d","observation_id":"6bb38dff-46aa-439d-bd5b-1082590a1018","resolution":{"observed_at":"2026-08-07T00:51:34.836649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.823844Z","title":"The theory and applications of harmonic integrals","venue":null,"work_id":"26262815-08d2-4bb3-a6c2-4ce7bd094bb9","year":1952},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.489323Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:2cbf8a4f215f9283e6f17ede44d6c3774cc39440b0a80c152cfda833b06afbbd","observation_id":"6f50bb71-a455-41be-964c-3d31b599d618","resolution":{"observed_at":"2026-08-07T00:51:34.827578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.814380Z","title":"Introduction to Lie algebras and representation theory , volume 9 of Graduate Texts in Mathematics","venue":null,"work_id":"4a26ad6e-8797-400e-a343-1afd20e498a1","year":1972},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.491957Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:12d1ce1d85c999eb4e074c7e4318f1f380eb2851c9be141b186ebddda88bda24","observation_id":"0eae6429-6865-4aab-8843-a38f4c63ef5b","resolution":{"observed_at":"2026-08-07T00:51:34.817793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.805341Z","title":"Lectures on K3 surfaces , volume 158 of Cambridge Studies in Advanced Mathematics","venue":null,"work_id":"e1887964-15ac-4e43-ac27-094838fa0746","year":2016},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.494917Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:5eeccd247bfddd0890162acfbcc13e44630fa56c7b41fa735f5858397611a341","observation_id":"2fa4cb57-4655-4729-82f5-a6aace8b1051","resolution":{"observed_at":"2026-08-07T00:51:34.808482Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.796073Z","title":"L'analysis situs et la géométrie algébrique","venue":null,"work_id":"b02107d7-ab6e-4920-ba82-014c81fe1950","year":1924},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.497479Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:c66b1a4971b76f9703f3876abc895d149c6ff78f08e4ab5ac522f3dfdf5ebf14","observation_id":"f152e08c-0008-445c-a70e-2080904bf157","resolution":{"observed_at":"2026-08-07T00:51:34.799008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.786443Z","title":"A survey of the Hodge conjecture , volume 10 of CRM Monograph Series","venue":null,"work_id":"9140048f-d192-419f-9eec-d852b951840b","year":1999},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.500097Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:841f56b13e0633574e0df17bd164b21c5c6e4cabb1e95a0015df40756c7e60bc","observation_id":"edad67e8-998f-4716-9a6a-974876eec4f0","resolution":{"observed_at":"2026-08-07T00:51:34.789847Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.776688Z","title":"Geometric invariant theory , volume 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete","venue":null,"work_id":"96485a6c-27f2-497a-8471-6afb83cadde1","year":1994},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.503128Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:b93dc776d37757ffb5fc52cce532f44af598fd48ed4c18188720f07d030bff4e","observation_id":"3e6be488-e6db-49b5-88ca-fc209503f111","resolution":{"observed_at":"2026-08-07T00:51:34.780252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.767751Z","title":"Reduction of symplectic manifolds with symmetry","venue":null,"work_id":"ea3c8811-07bf-4262-a802-63068acfa4d3","year":1974},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.506087Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:c203ade08a6ba2094e6f6619198d2c429fe4c051a6bae14b11be90b5a037ec6f","observation_id":"5e5c97cd-e73e-45de-b166-275c23657d40","resolution":{"observed_at":"2026-08-07T00:51:34.770733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.758246Z","title":"Variation of hodge structure: the singularities of the period mapping","venue":null,"work_id":"30b53432-7217-41d3-acb5-591ef7cde3ba","year":1973},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.508899Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:49dd0ad5a0fa64c087d03acd4f76fc20a9bbdb32884a95d6ab6e92e8c6fd541c","observation_id":"574b28ba-4a8a-44f7-a103-d3b204472fd7","resolution":{"observed_at":"2026-08-07T00:51:34.761690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.748928Z","title":"Deformation of structures on manifolds defined by transitive, continuous pseudogroups","venue":null,"work_id":"c0898358-4b5f-4731-9c20-a41fed6287a7","year":1962},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.512015Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:c1c6a91263df767ac2db4ba00819a6441e16922de19eace2deee5ec075d1d294","observation_id":"ff5637c9-6671-408f-972a-e67ce02236c2","resolution":{"observed_at":"2026-08-07T00:51:34.752133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.739974Z","title":"Hodge theory and complex algebraic geometry I , volume 76 of Cambridge Studies in Advanced Mathematics","venue":null,"work_id":"da31fea9-e50f-4f46-ab32-af1179923533","year":2002},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.514653Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:42e531eea0db7d202d7ac8174b4c4180678b8d4b625070d062ccc570aef02ab6","observation_id":"1b3b6286-2e1c-4bb7-9a36-26ff7341d1d2","resolution":{"observed_at":"2026-08-07T00:51:34.743032Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.730975Z","title":"Hodge theory and complex algebraic geometry II , volume 77 of Cambridge Studies in Advanced Mathematics","venue":null,"work_id":"f1d66378-c9aa-48c7-8d91-42c6ff35c5ac","year":2007},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.517756Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:96a762b22b221cfb59d1250e2e4daa9a5ea2b9a04bef6321b13e9703bd5a6966","observation_id":"51f2aa22-3da8-4ce1-8077-4ad17d3404d5","resolution":{"observed_at":"2026-08-07T00:51:34.734371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.720149Z","title":"Topological quantum field theory","venue":null,"work_id":"142fea7d-4d47-4c99-8e32-b41cb49a551e","year":1988},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.521593Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:d6a594df3a5bc6531dd877f53054adba37bbf35a5d852db8f7666f77530f37e1","observation_id":"a5f30d08-d1fc-42ea-bd7e-3490a28692dc","resolution":{"observed_at":"2026-08-07T00:51:34.724446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.00752","last_updated":"2025-06-11T05:41:47Z","snapshot_observed_at":"2026-08-08T07:35:47.595260Z","submitted_at":"2025-05-31T23:39:45Z","title":"Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles","version":2},"cited_work":{"arxiv_id":"2506.00752","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.00752","snapshot_observed_at":"2026-08-07T00:51:34.701220Z","title":"Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles","venue":"math.GM","work_id":"74795c8e-0892-49a8-9f28-08d43c86eb4a","year":2025},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.524471Z"},"links":{"cited_paper":"/paper/2506.00752","citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:873e61acc87d33d2692d0913d8064620c88158825d1efb75fb4edd0c5dd5b770","observation_id":"2895dd81-10e6-414d-bd8b-302a5a99087d","resolution":{"observed_at":"2026-08-07T00:51:34.705270Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16766","last_updated":"2025-05-25T01:46:02Z","snapshot_observed_at":"2026-08-07T14:53:24.559980Z","submitted_at":"2025-05-22T15:07:59Z","title":"Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling","version":2},"cited_work":{"arxiv_id":"2505.16766","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.16766","snapshot_observed_at":"2026-08-07T00:51:34.688213Z","title":"Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling","venue":"math.GM","work_id":"512742e0-0646-4849-8835-0400317222c9","year":2025},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.527885Z"},"links":{"cited_paper":"/paper/2505.16766","citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:1b0055d496b9b39484ad58e3e004ada7b07aa00a2ea91267f46ca5c3aaf9f677","observation_id":"a51a1de4-97b1-4528-a683-f338f1568367","resolution":{"observed_at":"2026-08-07T00:51:34.691854Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T00:51:34.711330Z","title":"Extension research of principal bundle constraint system theory on ricci-flat k\\\"ahler manifolds","venue":null,"work_id":"f4cae768-cfc0-499f-8532-f5d8a0790f5b","year":2025},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.530812Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:ce570391cb14dbe572dd585ce78b66866e5e968c7687d7ccb82d200f70c24c7b","observation_id":"eb4a89bd-e92f-4572-9d95-8096e37ee0de","resolution":{"observed_at":"2026-08-07T00:51:34.714477Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2506.06610","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:51:34.673371Z","title":"Mirror symmetry in geometric constraints: Analytic and riemann-roch perspectives","venue":null,"work_id":"95b14182-c6b1-4b06-80f5-c2d89a494139","year":2025},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.533526Z"},"links":{"citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:123464e10d434320ae086f537c51dde04d14ab1a8fbe1f74c1e5cacb53ce0ff9","observation_id":"cecc24f5-c109-473d-9ce2-01ed8d14e478","resolution":{"observed_at":"2026-08-07T00:51:34.678979Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.05816","last_updated":"2025-06-11T05:57:48Z","snapshot_observed_at":"2026-08-07T10:11:02.906263Z","submitted_at":"2025-06-06T07:28:03Z","title":"Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems","version":2},"cited_work":{"arxiv_id":"2506.05816","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.05816","snapshot_observed_at":"2026-08-07T00:51:34.601485Z","title":"Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems","venue":"math.GM","work_id":"45a421b4-5be9-4db7-b0d8-ed033674d498","year":2025},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.537790Z"},"links":{"cited_paper":"/paper/2506.05816","citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:fa5c9fa3500f1ff876af2a33279c9060bc259cee5931a1573a7c649e72b74c11","observation_id":"d42d3437-47a4-4260-a904-54ddb55b66b6","resolution":{"observed_at":"2026-08-07T00:51:34.605284Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.07410","last_updated":"2025-06-11T06:43:26Z","snapshot_observed_at":"2026-08-07T05:32:20.686709Z","submitted_at":"2025-06-09T04:13:57Z","title":"Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry","version":2},"cited_work":{"arxiv_id":"2506.07410","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.07410","snapshot_observed_at":"2026-08-07T00:51:34.587882Z","title":"Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry","venue":"math.GM","work_id":"e602d4b4-ec91-4860-819c-1e0331540d13","year":2025},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.541132Z"},"links":{"cited_paper":"/paper/2506.07410","citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:5050518b991043447fc455acfb799f100551aeed75ba84a6a6de9d8ad69e7a19","observation_id":"eaef98b3-5299-4f59-868b-1821681fa827","resolution":{"observed_at":"2026-08-07T00:51:34.591495Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.05915","last_updated":"2025-06-11T06:16:15Z","snapshot_observed_at":"2026-08-07T10:10:52.626576Z","submitted_at":"2025-06-06T09:36:54Z","title":"Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry","version":2},"cited_work":{"arxiv_id":"2506.05915","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.05915","snapshot_observed_at":"2026-08-07T00:51:34.572507Z","title":"Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry","venue":"math.GM","work_id":"6d8a6cd7-95a0-40dc-a1d1-3c86c10af080","year":2025},"citing_paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T00:51:34.544181Z"},"links":{"cited_paper":"/paper/2506.05915","citing_paper":"/paper/2506.12720"},"observation_digest":"sha256:9d464e75462ca0bf1e628d9da374cd4b33cad29f40b97ee1d5887eca8700a45b","observation_id":"cfa724c0-3fc1-4dfa-878f-6a43292b2bf8","resolution":{"observed_at":"2026-08-07T00:51:34.577948Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.12720","last_updated":"2025-06-15T04:55:03Z","latest_version":1,"primary_category":"math.GM","snapshot_observed_at":"2026-08-07T00:41:23.733435Z","submitted_at":"2025-06-15T04:55:03Z","title":"The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":6,"verified_fuzzy":25},"total_outbound_references":31},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2506.12720."}