{"as_of":"2026-08-08T11:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e2a6c841004fb6f1231da19c7ed3d0a84f4b8240e17722bd23cc2a933d1ee2f6","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:04:48.200565Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:07:42.706925Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-07T00:51:34.688213Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16766","snapshot_observed_at":"2026-08-07T12:06:44.942468Z","title":"arXiv preprint arXiv:2505.16766 (2025) 19","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.00728","last_updated":"2025-06-11T05:25:22Z","snapshot_observed_at":"2026-08-07T11:57:05.982296Z","submitted_at":"2025-05-31T22:04:53Z","title":"Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.942468Z"},"links":{"cited_paper":"/paper/2505.16766","citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:1114cecb955de9a894016f7b3710ebb7cb15b60208aceec6cbe6896afd85c511","observation_id":"41e2b58f-1574-4491-bdb8-5a9a7a309e5a","resolution":{"observed_at":"2026-08-07T12:06:44.942468Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16766","snapshot_observed_at":"2026-08-07T12:07:42.706925Z","title":"Dynamical geometric theory of principal bundle constrained systems: Strong transversality conditions and variational framework for gauge field coupling","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T12:07:42.706925Z"},"links":{"cited_paper":"/paper/2505.16766","citing_paper":"/paper/2506.00752"},"observation_digest":"sha256:6efc5bd26ad6b7177c67e4d869022f5151a9b17ad441aebfba7bd4f885bc6f7a","observation_id":"c230c275-36fc-47e6-8f09-8e127943b69f","resolution":{"observed_at":"2026-08-07T12:07:42.706925Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16766","snapshot_observed_at":"2026-08-07T10:20:56.937734Z","title":"Dynamical geometric theory of principal bundle constrained systems: Strong transversality conditions and variational framework for gauge field coupling","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T10:20:56.937734Z"},"links":{"cited_paper":"/paper/2505.16766","citing_paper":"/paper/2506.05816"},"observation_digest":"sha256:8c7b7bf99269381a5970b8f662dff4c7beb28e11b9777b1d87d52296e4f3ba86","observation_id":"abffbb8e-73d5-4f77-973f-7e29de23109a","resolution":{"observed_at":"2026-08-07T10:20:56.937734Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16766","snapshot_observed_at":"2026-08-07T10:20:48.546906Z","title":"Dynamical geometric theory of principal bundle constrained systems: Strong transversality conditions and variational framework for gauge field coupling","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T10:20:48.546906Z"},"links":{"cited_paper":"/paper/2505.16766","citing_paper":"/paper/2506.05915"},"observation_digest":"sha256:d638793559b2a61f989fe584bfff5b313896abd79a693bc3e707f6a272e218aa","observation_id":"e18042d6-670f-4127-826d-95c5434d1eeb","resolution":{"observed_at":"2026-08-07T10:20:48.546906Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16766","snapshot_observed_at":"2026-08-07T05:40:43.294098Z","title":"Dynamical geometric theory of principal bundle constrained systems: Strong transversality conditions and variational framework for gauge field coupling","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T05:40:43.294098Z"},"links":{"cited_paper":"/paper/2505.16766","citing_paper":"/paper/2506.07410"},"observation_digest":"sha256:88b29bf8a1f9af135d9932a7d05898ab46fa90db770ed67ce575c9eb11dcac02","observation_id":"7a536ba5-d95e-421a-acb1-edede85ee38c","resolution":{"observed_at":"2026-08-07T05:40:43.294098Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16766","snapshot_observed_at":"2026-08-07T04:12:57.872230Z","title":"Dynamical geometric theory of principal bundle constrained systems: Strong transversality conditions and variational framework for gauge field coupling","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.11593","last_updated":"2025-06-13T09:01:35Z","snapshot_observed_at":"2026-08-07T05:52:23.620173Z","submitted_at":"2025-06-13T09:01:35Z","title":"Extension Research of Principal Bundle Constraint System Theory on Ricci-flat K\\\"ahler Manifolds","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T04:12:57.872230Z"},"links":{"cited_paper":"/paper/2505.16766","citing_paper":"/paper/2506.11593"},"observation_digest":"sha256:af8904c6ee7c6a21f2b2f8ab1d6ea8906c93c2883e1198e792f5879bed3e6ada","observation_id":"afd65e9a-153d-41d1-8849-1d6b69f1bae9","resolution":{"observed_at":"2026-08-07T04:12:57.872230Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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"}}],"links":{"evidence":"/evidence","html":"/paper/2505.16766/citation-record","integrity":"/paper/2505.16766/integrity","json":"/paper/2505.16766/citation-record.json","paper":"/paper/2505.16766"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:04:48.383741Z","title":"Desaint, Paris (1788)","venue":null,"work_id":"3118bc56-c162-4860-9be0-41a6fb521b50","year":null},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.139431Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:4a3ba423d55761e370e7d8751d5430e46efaf640d559adbc4bd1f595f3cce511","observation_id":"9233f2dd-6b0a-443f-8a7d-960017e7f4b1","resolution":{"observed_at":"2026-08-07T15:04:48.388169Z","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":"2026-08-07T15:04:48.373600Z","title":"Canadian Journal of Mathematics2, 129–148 (1950)","venue":null,"work_id":"019f74f4-7de9-46d0-9fa3-ff652bb113ff","year":1950},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.144093Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:de72654bdf28a87e1c9f486abfbd9743bd6918f5fc0b28c24731583bb727cb0d","observation_id":"d25d0799-641b-4a34-b6eb-ccb2c99c9444","resolution":{"observed_at":"2026-08-07T15:04:48.377198Z","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":"2026-08-07T15:04:48.363251Z","title":"Graduate Texts in Mathematics, vol","venue":null,"work_id":"fd5addc3-3c8e-462c-b4d2-2f74e5df8257","year":1989},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.148241Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:a42b1ea1b04153960095712e6aeea4bb4642ab51ce393a8ef5d85c0aff1d399b","observation_id":"9439de06-d48f-427d-869f-a810a19f352a","resolution":{"observed_at":"2026-08-07T15:04:48.367203Z","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":"2026-08-07T15:04:48.353674Z","title":"Inventiones Mathematicae10(4), 305–331 (1970)","venue":null,"work_id":"cff82686-f36b-4d17-94d2-27670ffa33ab","year":1970},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.152992Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:7003c8bd1c6287a71dc25d3f5d6f90be61ea1e9872de31beabcd4ece86ecc03c","observation_id":"ac24cbf8-92e7-4eae-be42-98468396bd8f","resolution":{"observed_at":"2026-08-07T15:04:48.357065Z","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":"2026-08-07T15:04:48.342041Z","title":"Benjamin/Cummings Publishing Company, Reading, Massachusetts (1978)","venue":null,"work_id":"d4ad6990-2b5e-413f-b982-1a150826a31e","year":1978},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.157834Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:0c8f75b62ec183ddf3fd28dbc309959c9f27f7f4f6155977bb0e62f12b7d007b","observation_id":"780b5b9c-0b0e-479e-a8be-8448c8cb8d99","resolution":{"observed_at":"2026-08-07T15:04:48.346037Z","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":"2026-08-07T15:04:48.330822Z","title":"Reports on Mathematical Physics5(1), 121–130 (1974)","venue":null,"work_id":"22d5f031-9c9b-4e8f-87ff-4e94c2772224","year":1974},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.161699Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:629e3511ae2792b2bc5a7df52fa5e142409c0adccda274370a4a5168d9f52b87","observation_id":"36c7e4ce-9287-40ad-97d7-99813d5ca3bc","resolution":{"observed_at":"2026-08-07T15:04:48.335107Z","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":"2026-08-07T15:04:48.320073Z","title":"Texts in Applied Mathematics, vol","venue":null,"work_id":"c3e4c911-c11b-4109-8d7e-b321713b6a66","year":1999},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.165744Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:0471c487dbb84529395c86cdd6ab12fb2e0a22c6be5b2f75986a06f212b37d46","observation_id":"a5996fcf-e84e-40db-9774-f4f9b273fa6e","resolution":{"observed_at":"2026-08-07T15:04:48.323938Z","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":"2026-08-07T15:04:48.310390Z","title":null,"venue":null,"work_id":"53250145-7cdf-4cb0-92ec-19bf89b9f7d7","year":1963},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.169990Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:89afbf5bfdf2f1da6a1c84f83f4f6c70c273eaa696d2c2e442d65145a7bcdbef","observation_id":"6b26e501-11b3-48a3-9a5d-6cb6b9b52de1","resolution":{"observed_at":"2026-08-07T15:04:48.313623Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"2026-08-07T15:04:48.299225Z","title":"Transactions of the American Mathematical Society85(1), 181–207 (1957)","venue":null,"work_id":"95b36084-e3a5-460f-bcdb-3c62d9f2d5a5","year":1957},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.173808Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:866d559dcca982ad281f32f28d1824351f29e9837cd384621cf58c3b70d0afd9","observation_id":"cc32a7bc-014b-4e94-bf23-224beb5eef67","resolution":{"observed_at":"2026-08-07T15:04:48.303088Z","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":"2026-08-07T15:04:48.287263Z","title":"Springer, Berlin (1993)","venue":null,"work_id":"06da53b7-9318-4c23-9fa8-f9c6982b4a8f","year":1993},"citing_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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.177754Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:e855026e720c8787d7d3f5613f7766592191c93739428a2b95a6cbec6c86d346","observation_id":"36c1d532-87e3-490d-bd46-2e823d350c15","resolution":{"observed_at":"2026-08-07T15:04:48.291285Z","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":"2026-08-07T15:04:48.275246Z","title":"Mathematical Surveys and Monographs, vol","venue":null,"work_id":"c76c54a1-1604-4bc7-a478-a1c568d95962","year":2002},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.182647Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:b880101d7b5e6250a5b2cda009cafaef4fac55a96f90309bea53707ab43ebed8","observation_id":"f286ecb4-0b52-41c4-b15b-069383a37315","resolution":{"observed_at":"2026-08-07T15:04:48.279688Z","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":"2026-08-07T15:04:48.263242Z","title":"International Journal of Geometric Methods in Modern Physics5(07), 1163–1188 (2008)","venue":null,"work_id":"2c1fbf9b-8cbe-4892-b289-45cacd4d69d5","year":2008},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.187162Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:14741791283efc329949336e337f85da8cf1bc6bfaaf4fdcb1a8cfd08d9d9d43","observation_id":"e47c9529-aa9c-4d99-8945-84198f5fc7f9","resolution":{"observed_at":"2026-08-07T15:04:48.268017Z","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":"2026-08-07T15:04:48.252028Z","title":"Annals of Mathematics157(2), 575–620 (2006)","venue":null,"work_id":"6b5c8739-c969-448c-b702-1b4323f57d54","year":2006},"citing_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},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.192278Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:f2f4ead5713cd6dcacbf8465be68366f8ad65a9fe5ded47f94d1fc4fd5c83b38","observation_id":"6510b28c-9963-4f6a-860b-831a5bfb0df5","resolution":{"observed_at":"2026-08-07T15:04:48.256009Z","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":"2026-08-07T15:04:48.240903Z","title":"International Journal of Geometric Methods in Modern Physics6(2), 213–250 (2009)","venue":null,"work_id":"bfed2366-22f5-47f0-9964-a946a8249d6d","year":2009},"citing_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},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.196356Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:87d8334a2b5f3a027b3081de69f7e769396c8bfb94780451105aca4d86dcd50b","observation_id":"058546ce-862a-4c8f-b5af-f17643505be6","resolution":{"observed_at":"2026-08-07T15:04:48.245151Z","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":"2026-08-07T15:04:48.226564Z","title":"Proceedings of the National Academy of Sciences53(5), 1047–1052 (1965) 99","venue":null,"work_id":"4bdaff33-b186-48ba-a6db-010505018ca8","year":1965},"citing_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},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T15:04:48.200565Z"},"links":{"citing_paper":"/paper/2505.16766"},"observation_digest":"sha256:944c51306d1b9ef849150fcad2e32b94ce8c6ee5a9c7820f95422d3f574430ea","observation_id":"2cf0346d-19aa-4ce2-a1d0-5373ba3adce6","resolution":{"observed_at":"2026-08-07T15:04:48.231716Z","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"}}],"paper":{"arxiv_id":"2505.16766","last_updated":"2025-05-25T01:46:02Z","latest_version":2,"primary_category":"math.GM","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"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":14},"total_outbound_references":15},"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 15 of 15 outbound references and 7 inbound Pith citation observations for arXiv:2505.16766."}