{"as_of":"2026-08-09T21:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:eba4bf12833da953987956ade8ba50c843aa16a549c4f11087115c7d9dc3d476","coverage":[{"denominator":18,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":18,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:06:44.942468Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:07:42.812793Z","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":"2026-08-07T04:12:58.026843Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_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},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.00728","snapshot_observed_at":"2026-08-07T12:07:42.812793Z","title":"Geometric duality between constraints and gauge fields: Mirror symmetry and spencer isomorphisms of compatible pairs on principal bundles","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":26,"source":"arxiv_source","source_observed_at":"2026-08-07T12:07:42.812793Z"},"links":{"cited_paper":"/paper/2506.00728","citing_paper":"/paper/2506.00752"},"observation_digest":"sha256:e73c9ffc74dddee5b85471dd37afdac6e176154e824e616ade223971bf2cd1c8","observation_id":"36f05e03-a066-41cc-8acd-2dcf29062a96","resolution":{"observed_at":"2026-08-07T12:07:42.812793Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.00728","snapshot_observed_at":"2026-08-07T10:20:57.028821Z","title":"Geometric duality between constraints and gauge fields: Mirror symmetry and spencer isomorphisms of compatible pairs on principal bundles","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":28,"source":"arxiv_source","source_observed_at":"2026-08-07T10:20:57.028821Z"},"links":{"cited_paper":"/paper/2506.00728","citing_paper":"/paper/2506.05816"},"observation_digest":"sha256:9f113cb5f353985fa5b1801cd8c0399e55b7dd7e00edf7fb20f04e07aec5fb36","observation_id":"1610ce4c-3660-4efe-b0ae-a60ad5585116","resolution":{"observed_at":"2026-08-07T10:20:57.028821Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.00728","snapshot_observed_at":"2026-08-07T10:20:48.552751Z","title":"Geometric duality between constraints and gauge fields: Mirror symmetry and spencer isomorphisms of compatible pairs on principal bundles","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":20,"source":"arxiv_source","source_observed_at":"2026-08-07T10:20:48.552751Z"},"links":{"cited_paper":"/paper/2506.00728","citing_paper":"/paper/2506.05915"},"observation_digest":"sha256:f9ffa03d62b7b8841913f2c8cda2b1d722ffad43effb91c304d79c94ef2413e1","observation_id":"718be92f-e621-4346-ba38-55616272d2c2","resolution":{"observed_at":"2026-08-07T10:20:48.552751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.00728","snapshot_observed_at":"2026-08-07T05:40:43.297838Z","title":"Geometric duality between constraints and gauge fields: Mirror symmetry and spencer isomorphisms of compatible pairs on principal bundles","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":22,"source":"arxiv_source","source_observed_at":"2026-08-07T05:40:43.297838Z"},"links":{"cited_paper":"/paper/2506.00728","citing_paper":"/paper/2506.07410"},"observation_digest":"sha256:a71292682867ad93b6f675de579bcc38f018f4d8f2f8672ec544290ebb193827","observation_id":"3cf9e489-3f1a-4f17-a187-cb0c0aa29387","resolution":{"observed_at":"2026-08-07T05:40:43.297838Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":"2506.00728","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.00728","snapshot_observed_at":"2026-08-07T04:12:58.026843Z","title":"Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles","venue":"math.GM","work_id":"cba1b2e8-67fd-40bd-ac85-8e4cc23e24f5","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":24,"source":"arxiv_source","source_observed_at":"2026-08-07T04:12:57.875221Z"},"links":{"cited_paper":"/paper/2506.00728","citing_paper":"/paper/2506.11593"},"observation_digest":"sha256:5fd45a0b4a3fb35739f1fd897ae82fe31c497f61fd910e63241cd0f8e97f9880","observation_id":"3c00090f-a6c6-4969-b9b4-4b76b0555242","resolution":{"observed_at":"2026-08-07T04:12:58.045090Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.00728/citation-record","integrity":"/paper/2506.00728/integrity","json":"/paper/2506.00728/citation-record.json","paper":"/paper/2506.00728"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T12:06:47.545534Z","title":"Yeshiva University, Belfer Graduate School of Science, New York (1964)","venue":null,"work_id":"5797f637-aa31-4da5-9647-3b0de5208fdc","year":1964},"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":1,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:43.618767Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:60743b6dd7c8e338491d7377d87bbdaddc4bea5ba9f47d64c651a80db01969d2","observation_id":"44e1997e-b31b-4fea-a56a-33c7ce4849a9","resolution":{"observed_at":"2026-08-07T12:06:47.636383Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:47.365128Z","title":null,"venue":null,"work_id":"2e92eb5c-8528-414c-b2c4-8705fab620dd","year":1974},"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":2,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:43.668741Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:0f164bd392106517e7495d046265ad588835a1987d471c450952060ecac55ebf","observation_id":"d37a216d-b18e-450b-8b61-7827e0b1428d","resolution":{"observed_at":"2026-08-07T12:06:47.410746Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:47.214037Z","title":"Benjam- in/Cummings Publishing Company, Reading (1978)","venue":null,"work_id":"b5a352a4-96d1-4f78-8515-7286161fc659","year":1978},"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":3,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:43.730502Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:0abaa376c180726afd4df76c7235f48ddd3258926d0b1ee9ebac795e2410f92d","observation_id":"d278f117-a50e-4ec1-b093-f1ee53b7ab78","resolution":{"observed_at":"2026-08-07T12:06:47.277507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:43.800071Z","title":"Springer, New York (1989)","venue":null,"work_id":null,"year":1989},"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":4,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:43.800071Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:e0ec3821c776b115cdb3c2b6d8f876cf52fda8fed78157635f7530393ec5948e","observation_id":"680ac7e3-89b6-4a16-afce-816269fe6727","resolution":{"observed_at":"2026-08-07T12:06:43.800071Z","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":"2026-08-07T12:06:47.016765Z","title":null,"venue":null,"work_id":"46bac0b4-9220-40c3-ab4f-87a7b3b2e1e8","year":1954},"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":5,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:43.868608Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:e6ba7079a481284bcad83f5f05b8075153352ddc930f8b4655cc7bf33d98bb0e","observation_id":"a0caeea4-de50-4b86-ba58-5930366d6f33","resolution":{"observed_at":"2026-08-07T12:06:47.104466Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:46.828977Z","title":null,"venue":null,"work_id":"395ad3e1-84e5-49f1-a811-ceb6298bcee7","year":1957},"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":6,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:43.958224Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:832d4792fc32b70a6ab29d0efdd9af057532201dffa083dbc61fbd9d33f8c0b2","observation_id":"421be545-d508-4cad-98e7-52ba0beaabac","resolution":{"observed_at":"2026-08-07T12:06:46.911027Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:46.609806Z","title":"Interscience Publishers, New York (1963)","venue":null,"work_id":"b842a325-1bef-4ea1-8db0-a6a5dc098d81","year":1963},"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":7,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.036873Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:a25a09568f64711b37dd02caf5d8555487ffa6f608d7f0a4aa5e16c03a83df12","observation_id":"e3454c55-f16d-4892-a7b5-3186d94a892f","resolution":{"observed_at":"2026-08-07T12:06:46.717728Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:46.477794Z","title":null,"venue":null,"work_id":"e534519a-b314-4a34-abae-d22453403735","year":1988},"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":8,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.169641Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:5768c2c2facd7fb818cf954c15870252fc802e94afa7ee4974ce8fc55f84768d","observation_id":"98d7de38-95a6-43b7-86f7-0fdb4c32e88d","resolution":{"observed_at":"2026-08-07T12:06:46.543490Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:46.339188Z","title":null,"venue":null,"work_id":"5b63fde5-a9e6-47e8-a6ec-acad9cd64051","year":1962},"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":9,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.299664Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:844c0deb3b92248ce9d8d263f61379191642b6157a66de2af680eda3e643f612","observation_id":"180b8dc9-a94d-4b2e-90f4-e936c52b18e9","resolution":{"observed_at":"2026-08-07T12:06:46.391556Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:46.160167Z","title":"American Mathematical Society, Providence (1999)","venue":null,"work_id":"2d1adca4-3e09-4ef3-bd54-461e1fa70df5","year":1999},"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":10,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.373397Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:6c62284bef0339a95547819b0f03fe9c275e0cf806ab9223c8dbb3ac0f4e6167","observation_id":"3a94d0d0-0eb5-4386-9d3a-ca5f8d909dfe","resolution":{"observed_at":"2026-08-07T12:06:46.226078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:45.954198Z","title":"Springer, New York (1991)","venue":null,"work_id":"2ac887bc-e4bc-48cb-8baf-9e6eceed997f","year":1991},"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":11,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.439811Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:3c49666dddb16edf0f8c9db23b5283443c32552162acabaa62fb44a3866e9e50","observation_id":"c79e6118-faaa-4ef6-80df-93763d50bff3","resolution":{"observed_at":"2026-08-07T12:06:46.059528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:45.823066Z","title":"Hermann, Paris (1945)","venue":null,"work_id":"2ab68b85-fa15-4447-8886-f43bde2cb605","year":1945},"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":12,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.529016Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:faf6c5ba362ce635437ea422052b4e982105b63a8198b118e82894d008014be1","observation_id":"d2b424d6-dea8-47fd-a061-ec12683eb31d","resolution":{"observed_at":"2026-08-07T12:06:45.881096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:45.678166Z","title":"Cambridge University Press, Cambridge (1998)","venue":null,"work_id":"70596859-f21c-4271-abd4-b70b0e5a518c","year":1998},"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":13,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.620072Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:57ff1a77757b842ee8f7e42ceee16079f8ac94a7a0e3792fa93c82870bd7a168","observation_id":"eb22f02f-8a10-4ca6-9ed0-ea69b05d733a","resolution":{"observed_at":"2026-08-07T12:06:45.710313Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:45.548721Z","title":null,"venue":null,"work_id":"5fc14011-4dfc-4397-a496-6492ec4ce877","year":1994},"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":14,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.686245Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:b662c0783e8b6bb2f4e4ed95c2b8106d2bad3369eb6d8fa0f63da566f5931a07","observation_id":"2a93ca25-ab4e-4476-8d93-36e643a5aa0c","resolution":{"observed_at":"2026-08-07T12:06:45.598997Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:45.389692Z","title":null,"venue":null,"work_id":"c931e053-aa7b-46e7-a2df-d94a9a5706e0","year":1996},"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":15,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.717544Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:50f26e38129f829fe293a52ea58a86eedefcad114f33bf2284a63362d27a0167","observation_id":"24710e30-1cd6-4741-adef-d9fe09c54501","resolution":{"observed_at":"2026-08-07T12:06:45.454075Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:45.300050Z","title":"Springer, New York (1993)","venue":null,"work_id":"fbfe742d-0184-4f06-a426-ebd465cefe99","year":1993},"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":16,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.773174Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:fe2e5be4798c2499c44e351e458647ed94e3e8d6b42b8b5e12caf7c739ad6137","observation_id":"2eb6a87d-2023-470f-a396-19b8ae1d3c28","resolution":{"observed_at":"2026-08-07T12:06:45.331519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T12:06:45.101981Z","title":"Springer, New York (2010)","venue":null,"work_id":"38775fc9-f7e6-4cd4-8af8-0e59c6194c2c","year":2010},"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":17,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:44.853462Z"},"links":{"citing_paper":"/paper/2506.00728"},"observation_digest":"sha256:05b5c4b85eeedf4cf1f2095faf024b3121ecd4b40d07187d6dae47f2577048a5","observation_id":"7a014bf2-7fc8-4ca0-83ca-41290191c1be","resolution":{"observed_at":"2026-08-07T12:06:45.192665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":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"}}],"paper":{"arxiv_id":"2506.00728","last_updated":"2025-06-11T05:25:22Z","latest_version":2,"primary_category":"math.GM","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"},"reference_resolution":{"displayed":18,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":18},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 5 inbound Pith citation observations for arXiv:2506.00728."}