{"as_of":"2026-08-12T15:08:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:811e218dee25ccc0a340efa4d343e689b199e09534b3adbc2a0e757041f6fadb","coverage":[{"denominator":56,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":56,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:57:10.465070Z","state":"measured"},{"denominator":56,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":56,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2501.07105/citation-record","integrity":"/paper/2501.07105/integrity","json":"/paper/2501.07105/citation-record.json","paper":"/paper/2501.07105"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:57:11.422511Z","title":"Critical p-adic L-functions","venue":null,"work_id":"3502aefa-be2c-4c3f-b42e-597de173740a","year":2012},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.186948Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:2704e2eb6f669d6e61440a162f6fc9e45edbcdf518a5b3d8384bc1b354d6bafd","observation_id":"f6af94d5-b84f-4358-b4fc-f7b4f5bc0a0d","resolution":{"observed_at":"2026-08-10T20:57:11.427623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.405268Z","title":"Ranks of Selmer groups in an analytic fam ily","venue":null,"work_id":"8573fba5-0591-47bf-8d1a-c6fd1b0cc22c","year":2012},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.192643Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:5bce401f0340914f8b384ded1768f2882c19f074751397ba64257e1f42c27282","observation_id":"976f5ce0-e2cf-4208-b42c-13f1ef99dc0d","resolution":{"observed_at":"2026-08-10T20:57:11.410743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.386301Z","title":"Families of Galois representations and Selmer groups","venue":null,"work_id":"97824e01-9fc0-470b-add1-dd37830d4388","year":2009},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.197585Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:b7373458125bdf4e109a788b402aca6fd0014b3aa462f16fc4d5d3a827bf8a7e","observation_id":"ae302276-1206-42c4-b838-bae89f46055a","resolution":{"observed_at":"2026-08-10T20:57:11.393329Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.369801Z","title":"L-functions and Tamagawa numbers of mo- tives","venue":null,"work_id":"ee02364f-f7eb-417f-bbd8-1bc7114c522a","year":1990},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.202655Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:e4ea9af0175b8b2dbba4b062f945e69a2ddd3e9dc4d62c5b1f641f4830a094fc","observation_id":"78b31ef8-46af-4ee5-9110-10817a428fcd","resolution":{"observed_at":"2026-08-10T20:57:11.374838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.353486Z","title":"Demuškin groups with group actions and a pplications to de- formations of Galois representations","venue":null,"work_id":"05a1dc46-fa8c-496b-a222-d9b1f3bbd83e","year":2000},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.207899Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:d61d0764961ddc0f3d9682a5c6538a2a917524a788ce849265253e77cdde69e9","observation_id":"11d00e28-1f7e-462e-966b-1c32af5ae914","resolution":{"observed_at":"2026-08-10T20:57:11.358683Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.335327Z","title":"Motivic L-functions and Galois module struc- tures","venue":null,"work_id":"1d6e2726-24f8-444d-b3a0-5897bd943b15","year":1996},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.212980Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:fa533885233a3dada7d5b3a39b9f1a6da835b20ca28eb30e250fcc1889ad9c1e","observation_id":"63b9e797-7092-4f40-9d3e-f83839cc91c2","resolution":{"observed_at":"2026-08-10T20:57:11.340989Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.317895Z","title":"La conjecture de Birch et Swinnerton-Dye rp-adique","venue":null,"work_id":"ba2627c0-0423-48dc-b784-65aff4f9d0a8","year":2004},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.219011Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:5069f119870138ea411d952caf1eb6e9273e2533a9c223d405052d1e068fe725","observation_id":"0b070766-e0a4-4f52-84cd-08f6b3fc9d0d","resolution":{"observed_at":"2026-08-10T20:57:11.323517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.302238Z","title":"Représentations de GL2(Qp) et (φ, Γ) -modules","venue":null,"work_id":"d9ecf8c9-4ba0-407e-abbb-0d411b7ab266","year":2010},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.223816Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:0ba74b439498512ead3ad0c7307ffb8857ab483018c3a535e4de2b9f31076b3f","observation_id":"25b8ad89-5189-4d7e-9540-a97995895209","resolution":{"observed_at":"2026-08-10T20:57:11.307087Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.286458Z","title":"Valeurs de fonctions L et périodes d’intégrales","venue":null,"work_id":"960e5ef9-6eaf-4a3c-96d9-0f21a5b8ab9e","year":1977},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.228741Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:cc532e9ceccfdd179097180a174835d753f4cc5db7bf484ca819fd24822cfea8","observation_id":"60c7ac69-744f-4afc-a506-59ba6d58f275","resolution":{"observed_at":"2026-08-10T20:57:11.291481Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.270361Z","title":"The Tamagawa n umber conjecture of adjoint motives of modular forms","venue":null,"work_id":"ce8e746d-fc17-4885-b630-7cf9e7304732","year":2004},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.234045Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:453367d635a53ad25c72710f66262fcebcf3d79d18940b1c80e926df5d7c7317","observation_id":"54e7d4a3-57cc-4619-837b-255fa83bfbcc","resolution":{"observed_at":"2026-08-10T20:57:11.275517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.255137Z","title":"Varia tion of Iwasawa invariants in Hida families","venue":null,"work_id":"d657ff9a-421b-4060-a841-2fe36548c292","year":2006},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.239536Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:b8d0023227efe61512fbeb7b81f043d22bdbecacb85b8713890d0a104f1fdafc","observation_id":"9f8a095a-1cfa-4680-822b-2db8b31611b8","resolution":{"observed_at":"2026-08-10T20:57:11.260017Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.239027Z","title":"Valeurs spéciales des fonctions L des motifs","venue":null,"work_id":"820ed90b-216c-417b-b927-6d368fc232ae","year":1992},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.244317Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:edda92fb3fdb02e63a764e5748c712bb49fb588a85a0e87e4b0833fa66ad4812","observation_id":"711b9f17-e637-4b80-92fe-6242c910eb42","resolution":{"observed_at":"2026-08-10T20:57:11.244218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.222261Z","title":"p-adic properties of motivic fundamental lines","venue":null,"work_id":"1b5c3983-c0d3-46f8-a953-868956cc83ae","year":2017},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.249137Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:defa0fc4a58dd533473e9a42983e6f099fca99b6d37a5227c635b77d9e4e60dc","observation_id":"90530b4c-56c2-447c-9c9e-05dd200844a3","resolution":{"observed_at":"2026-08-10T20:57:11.227269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.204858Z","title":"Congruences and the Iwasawa Main Conj ecture for modular forms","venue":null,"work_id":"387e5ec0-0f12-4cf8-9f78-d36ae58d9d43","year":2024},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.253898Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:6a77b07d3db3de525518251c3627dee6cd762c47896a9f01abe01f61d00c320c","observation_id":"ecf101a5-65f3-4262-a4d4-7e9f3efc98dc","resolution":{"observed_at":"2026-08-10T20:57:11.210418Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.187663Z","title":"Control theorems f or Selmer groups of nearly ordinary deformations","venue":null,"work_id":"0ae4ca58-7c85-4477-85e4-c2a00c543d90","year":2012},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.258358Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:4aded5a6550a03a7b81837a58c8c2af9da90930b3590eba11fb9bf2003ed2cc4","observation_id":"87a39336-7f97-495e-b204-f0ab2ab34314","resolution":{"observed_at":"2026-08-10T20:57:11.193532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2107.13726","last_updated":"2022-04-08T23:31:01Z","snapshot_observed_at":"2026-07-06T11:33:33.002637Z","submitted_at":"2021-07-29T03:27:41Z","title":"The Iwasawa Main Conjecture for universal families of modular motives","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.13726","snapshot_observed_at":"2026-08-10T20:57:10.263035Z","title":"The Iwasawa Main Conjectur e for modular motives","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.263035Z"},"links":{"cited_paper":"/paper/2107.13726","citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:94ed3ee1e447c1e0de1fb1a9671f9df20c07a5b0032fb5a161fc1025eade9480","observation_id":"037cddaa-075b-4923-b1b5-fe116c7ad413","resolution":{"observed_at":"2026-08-10T20:57:10.263035Z","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":"2026-08-10T20:57:11.172295Z","title":"Deformation rings and Hecke algebr as in the totally real case, 1999","venue":null,"work_id":"277670c8-593d-4878-ba69-164b782fb667","year":1999},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.269106Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:94d666e221c1bccd87d0921b83c8d4c7f1d90f7a608acef4fe001dedefe50e25","observation_id":"e05d4ff9-0121-4137-8868-478a1cdc37ce","resolution":{"observed_at":"2026-08-10T20:57:11.177147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.156425Z","title":"A formulation of conject ures on p-adic zeta functions in noncommutative Iwasawa theory","venue":null,"work_id":"b6d5d04a-bdad-4fd0-9119-9c2aab2cf2ef","year":2006},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.273687Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:e22e2d91fdf14e40bc9626f3842d4fd32a18b856767809d20bec6757271d5173","observation_id":"aed4adf7-cc12-4d56-b8f7-04b4af9fd310","resolution":{"observed_at":"2026-08-10T20:57:11.162030Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.139362Z","title":"Gouvêa and Barry Mazur","venue":null,"work_id":"a3628db2-954e-4ff4-99f4-77b98cdb2fa5","year":1998},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.278753Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:62d20aeb5703e1c0ee824f7b8e0c4011a08519f3017dfa085a30983ad37d8b7c","observation_id":"49e8ceae-44a4-4356-b55c-ea6657729d20","resolution":{"observed_at":"2026-08-10T20:57:11.144736Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.121868Z","title":"Galois theory for the Selmer group of a n abelian variety","venue":null,"work_id":"e0194fdf-e78b-4b9f-a587-8e3df38a677a","year":2003},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.283528Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:7c06dcb252de1756c2eb3cc844073361dcd5a1ff148e339279e2408c639608af","observation_id":"61cac8e4-fa19-4d14-90fd-4f3a27676666","resolution":{"observed_at":"2026-08-10T20:57:11.127057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.103643Z","title":"Gross and Don B","venue":null,"work_id":"6b6f3018-cece-42d4-bec8-8e53166e75a8","year":1986},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.288470Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:4f6c596d54c2de3ac6a7c9acc6f2861a072868f3d04ca3cf782ba10b6cdbfaa6","observation_id":"cbd9e8fd-899e-4053-8ba8-520497025751","resolution":{"observed_at":"2026-08-10T20:57:11.109099Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.086665Z","title":"Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms","venue":null,"work_id":"70b8635c-0a3b-4e2f-bb6b-f3ef8305c000","year":1986},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.293510Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:892ef94b8475ad4a57127358ca02aa5c2fd125d6c01ae134b01f4fca36eade20","observation_id":"a0e980e4-e8a4-4c7b-af41-b587fb8ab211","resolution":{"observed_at":"2026-08-10T20:57:11.092385Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.070153Z","title":"On nearly ordinary Hecke algebras for GL(2) over totally real ﬁelds","venue":null,"work_id":"cd2674fa-128c-48ef-96d3-b8e25dbd0567","year":1989},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.298558Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:416db280da2293651a373568b395aa764c00639f63810e8484ea5154768b0582","observation_id":"509612a4-380f-4cc7-a060-082a1ebffc23","resolution":{"observed_at":"2026-08-10T20:57:11.075439Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.053016Z","title":"Analogies between number ﬁelds and f unction ﬁelds","venue":null,"work_id":"d24447fa-d699-4759-9a24-8da5bb47dd89","year":1965},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.303543Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:aabe5176f493279953da234d4def2fd107d99e9d2f0a217e7750bf2a955c5050","observation_id":"934a07d8-424f-41a2-9949-288a6f07c5d8","resolution":{"observed_at":"2026-08-10T20:57:11.058448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.035945Z","title":"The Birch and Swinnerton-Dyer formula for elliptic curves of analytic ra nk one","venue":null,"work_id":"295bfee1-e84f-44c9-83d6-4d33e0736365","year":2017},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.308903Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:bfa508dce7b948dbdf19b16898634bda9992ae9560a811610f7676054ad016b6","observation_id":"321b95b5-dc58-4155-b42a-7afddd9dbc69","resolution":{"observed_at":"2026-08-10T20:57:11.041508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.019044Z","title":"Iwasawa theory and p-adic Hodge theory","venue":null,"work_id":"a022d7c2-08ef-49bc-bebc-d9333c3af666","year":1993},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.313773Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:53c654b45107f6b9d6cd97481cdd03da639e1fe296d5924f49dad88752da25e7","observation_id":"5caf6530-4c08-46ab-a285-bd5daec5fcc2","resolution":{"observed_at":"2026-08-10T20:57:11.024379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:11.001214Z","title":"Lectures on the approach to Iwasawa theory for Hasse-Weil L- functions via BdR","venue":null,"work_id":"6a0a6cf4-c468-40ab-a7b3-24b727b7826a","year":1991},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.319393Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:9708a25d9f6388cb1086003b1033bcf3ec342ff5820b6d7734637bbbddf79c34","observation_id":"d655b0c4-cf73-4749-b752-8566441401d1","resolution":{"observed_at":"2026-08-10T20:57:11.006780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.983339Z","title":"Euler systems, Iwasawa theory, and Selmer groups","venue":null,"work_id":"e34fcfbc-8b3c-416f-a2da-4b820156a553","year":1999},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.324360Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:219293ac470ae0f6bb0b8e4d52db50bb3be4cc4c9f3fa2e15b65e6bea38938f9","observation_id":"256b8849-a69c-4821-949f-af50746bef43","resolution":{"observed_at":"2026-08-10T20:57:10.989468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.967533Z","title":"p-adic Hodge theory and values of zeta functions of modular forms","venue":null,"work_id":"781df099-68eb-4bb4-9e1c-6ec33a8c96fa","year":2004},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.329246Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:b589dfe5c85148b2583c072c6d3e060b9cb77268d79344e029ac050caef70759","observation_id":"a05afed1-d7e3-4bb2-a6d9-f044d06d396f","resolution":{"observed_at":"2026-08-10T20:57:10.972594Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.951606Z","title":"Iwasawa theory and generalizations","venue":null,"work_id":"1a9ee011-cdb0-40c9-9d20-6df538a9eef5","year":2007},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.334483Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:a6812292e4dd77ca14d8851f6bc8d3b1d91b7fd8e4acdd02bacd86eb092bf964","observation_id":"36353f03-ae59-478e-bf68-1b29a3f606a1","resolution":{"observed_at":"2026-08-10T20:57:10.956368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.934877Z","title":"Moduli of ﬁnite ﬂat group schemes, and modul arity","venue":null,"work_id":"168b08dc-c16c-4a1d-a6e9-b97c443807d7","year":2009},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.339505Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:8bd0065e40a6c6dcd85509e1001133db25327017e8e64dc122c7b353d0d3c78d","observation_id":"ab783bec-4abb-4f48-a3f9-17cadeb47ff2","resolution":{"observed_at":"2026-08-10T20:57:10.940285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.918098Z","title":"Iwasawa theory for elliptic curv es at supersingular primes","venue":null,"work_id":"81fe6262-4ff3-4a34-ab61-f9aa66bf9b39","year":2003},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.344370Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:c7d1919d9b135c09bbee18d42339f83fadce9ea74e76114a11c024398b6373a1","observation_id":"634e0882-b0f2-4b21-9e69-9142ed66b691","resolution":{"observed_at":"2026-08-10T20:57:10.923655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.900852Z","title":"Euler systems","venue":null,"work_id":"3422d1db-f8bc-4ec7-8b8e-e03b6b38f62d","year":1990},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.348943Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:98a682eb59b7c5281dbe63c86b790e40ee4225067f92f73c03cbb27a27a277f1","observation_id":"a55e2aa5-ce78-4a80-bba8-f849704b5873","resolution":{"observed_at":"2026-08-10T20:57:10.906866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.882343Z","title":"Eine p-adische Theorie der Zetawerte","venue":null,"work_id":"1984ab9d-5c28-407c-846c-1f3a58a2044c","year":1964},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.353630Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:13b66d863ed368535a37a7de857ecae66784d9b5484cc837a449525db0aecd1d","observation_id":"67dcd980-3355-4aa9-b050-77677771e906","resolution":{"observed_at":"2026-08-10T20:57:10.887623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.865386Z","title":null,"venue":null,"work_id":"36fc6361-9501-4937-8686-026953af08a4","year":1976},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.358267Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:0455a1aab2294ed00299c29e92dcefbcd84c36b4294ce87485894e1144590ffb","observation_id":"16a04ded-2e35-452b-8acf-f37aecf42c2b","resolution":{"observed_at":"2026-08-10T20:57:10.870562Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.847641Z","title":"On the arithmetic of special values of L functions","venue":null,"work_id":"2509948d-c527-4f9c-b63d-3900d6cfb747","year":1979},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.363464Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:005c2ba4b2337d02ea53aaab0352675f8709dbb86e3afb0b3648a41759c5a5a6","observation_id":"ab4a7da0-b648-4a56-a393-2ba54a0ab192","resolution":{"observed_at":"2026-08-10T20:57:10.852772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.830845Z","title":"Arithmetic of W eil curves","venue":null,"work_id":"ada91675-857b-4803-96d9-415d48b2cc7b","year":1974},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.368115Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:91972d3c8bb1d3201dce3d8a6da5541d31b7f06b507eaebd37b58c06f1f3d9a1","observation_id":"537c6a73-3e98-4a25-b06b-db22b705aa98","resolution":{"observed_at":"2026-08-10T20:57:10.836110Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.813223Z","title":"Tate, and J","venue":null,"work_id":"0cb13cad-5d35-46a4-9f34-75590d21f4ff","year":1986},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.373253Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:3595f19133e517cf605c6ea45065c4e712f2cb703d3b2aab5058840b756d0f1b","observation_id":"7d1fb50d-c3ae-471d-868e-ad442e4ea61b","resolution":{"observed_at":"2026-08-10T20:57:10.818104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.797621Z","title":"Class ﬁelds of abelian ext ensions of Q","venue":null,"work_id":"1a645424-7fdb-4a30-be42-b3b809e1e9b8","year":1984},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.377873Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:5faca2c9312f80cfff60ed32f8ffc5285b12702759c92168f2fa2200f2bf7f35","observation_id":"0e6ff23b-4b87-47df-aa08-b7d218632026","resolution":{"observed_at":"2026-08-10T20:57:10.802523Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.781494Z","title":"Zeta morphisms for rank two universa l deformations","venue":null,"work_id":"b1ff96ed-1c2d-4347-b59d-ac6d28f86dbd","year":2023},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.382520Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:6bdb982ec0d756afd7ef18a8d03a06af0c3adec26aca298b8d7e7d6d76e5314b","observation_id":"932aae9e-01e7-4694-b173-b5cfdb60633c","resolution":{"observed_at":"2026-08-10T20:57:10.786944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.765265Z","title":"Selmer complexes","venue":null,"work_id":"fb100f39-3cdd-450d-b05a-a46aed66429f","year":2006},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.387380Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:bda8b090d01148eff3399968f0b0f4e95807630d64f44878ac236bda0d8d71b0","observation_id":"e7e8c7fb-dec9-4c60-b22c-98d52eaf3a61","resolution":{"observed_at":"2026-08-10T20:57:10.770335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.749879Z","title":"On the two-variable Iwasawa main conje cture","venue":null,"work_id":"0e380b53-ffa1-4090-86fe-88b30db92ffd","year":2006},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.392101Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:477bfc3284a690e095673a71d3f971e4ebf6cb64e7e1feec23ffd466862d4c64","observation_id":"da259832-6b09-43a9-80b5-8d54f1e5acdc","resolution":{"observed_at":"2026-08-10T20:57:10.754928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.732959Z","title":"The image of Colmez’s Montreal functor","venue":null,"work_id":"049751d3-a40d-4fbb-8da4-55b2d02d2c30","year":2013},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.397055Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:0d5a18d8249a04ea5a5718ca4b1c8f0c418c65cc98e088428684a040f7b4c313","observation_id":"096288d2-3954-4393-8a93-760c2ec277aa","resolution":{"observed_at":"2026-08-10T20:57:10.738799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.716014Z","title":"Fonctions L p-adiques des représentations p-adiques","venue":null,"work_id":"8b42b870-26d3-436c-9b74-dbcc409faec0","year":1995},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.402992Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:5fa873352377f20535b0825ee897d45d309bf5fbb0c0c40d77dca401ed344917","observation_id":"98a73b99-2075-4412-9d06-44db0b278db5","resolution":{"observed_at":"2026-08-10T20:57:10.721163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.700828Z","title":"On the p-adicL-function of a modular form at a supersingular prime","venue":null,"work_id":"51ec5e73-f9d0-4ac7-a80a-56d493044fe2","year":2003},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.408910Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:51dbbd0e703105406b4429bd02ec1021023ade7f4bc2b71486a6f74488830bfc","observation_id":"80ed9096-0154-4240-872f-0596036bbfe3","resolution":{"observed_at":"2026-08-10T20:57:10.705676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.685022Z","title":"On a variation of Mazur’s deformatio n functor","venue":null,"work_id":"57255f30-6ee9-4cc0-a948-1dacec9357d6","year":1993},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.413821Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:86cd79b8f496115d79ec156062f88b17abb2496c5e688868f79e06fb61bba0c1","observation_id":"31458dcd-9f16-4dd0-ba46-d1e51e2969f2","resolution":{"observed_at":"2026-08-10T20:57:10.690059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.669337Z","title":"Rohrlich","venue":null,"work_id":"c1e55761-4271-4f7a-a14a-234e8b6a51e0","year":1989},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.420077Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:b79b8e887449c68fd80667755b5a663b10136f0428495ffbbc97943b5b142013","observation_id":"8530f1af-43b1-453e-b1c8-c50e2cea69e1","resolution":{"observed_at":"2026-08-10T20:57:10.673966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.653598Z","title":null,"venue":null,"work_id":"5d3905f1-8a0d-4cb2-85b2-ce91c7b3ee49","year":1990},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.424760Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:4d596d1c10285560dcd2695a1d21ae022f1bcb616617f2efe9f8ea9aede63a2a","observation_id":"a95c7942-4669-4400-9e49-e4413e2fe7e6","resolution":{"observed_at":"2026-08-10T20:57:10.658729Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.636783Z","title":"Local deformation rings for GL2 and a Breuil-Mézard conjecture when ℓ ⁄=p","venue":null,"work_id":"1bcfc4a4-ec61-42c1-b9af-76bb70bd2fbe","year":2016},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.430002Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:f82e70fca1a04414bf0b92249bd4674baf267fd16bb5a9ef92d0c7d39195d8ee","observation_id":"45099bfe-0183-4a01-a29e-46e1bc733afa","resolution":{"observed_at":"2026-08-10T20:57:10.642256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.620745Z","title":null,"venue":null,"work_id":"72dbaaae-4856-4933-89d5-704b9fde89a4","year":2000},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.435097Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:d8f79bb230fd64786f7803b8c53fc5bed14b501914ece257b27b84858a238a4e","observation_id":"a84af29c-79cf-44b9-9fcf-b50f0e192800","resolution":{"observed_at":"2026-08-10T20:57:10.625823Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.603265Z","title":"The Iwasawa main co njectures for GL2","venue":null,"work_id":"937d6979-08e9-4f37-bb3a-726023acf36f","year":2014},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.439790Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:ac356562a4441bd5b59aca5d8993d3f29031e67f8db84de3134d104212c71376","observation_id":"928421ef-6f2f-4a04-a063-da2db74a4220","resolution":{"observed_at":"2026-08-10T20:57:10.608824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.586163Z","title":"Iwasawa theory for elliptic curves at s upersingular primes: a pair of main conjectures","venue":null,"work_id":"d415fe29-bbd7-4823-bfd5-a4666d5fe9f9","year":2012},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.444804Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:574cd5820fd88e63dea247b82c595c8b2b6b97ea6686dad11841c797ff74491d","observation_id":"4a0d9b4a-4ae3-4294-85d2-bae0bcc8119e","resolution":{"observed_at":"2026-08-10T20:57:10.591206Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.568983Z","title":"Ring-theoretic prope rties of certain Hecke algebras","venue":null,"work_id":"739a8569-b2a5-4467-abb7-23dfd9f7612a","year":1995},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.450373Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:d438b9ee7bffc7e30baf36c55198b032b9e8c4a4c3c8524d6dd8d4ad88a126e9","observation_id":"80e72eef-c352-49a6-abac-4ee4ccc7bf38","resolution":{"observed_at":"2026-08-10T20:57:10.574723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.551320Z","title":"Bordeaux","venue":null,"work_id":"40044fb1-055f-43e4-8a72-c0b37fb49353","year":2024},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.454872Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:e5ea51f3e177ec3d68fdb3666d82572b2ca9fc5795197e1910bd32702edc0098","observation_id":"5f3aeb26-04d3-4d06-a2bb-64150cb3581a","resolution":{"observed_at":"2026-08-10T20:57:10.556377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.533585Z","title":"From the Birch and Swinnerton-Dyer Con jecture to non- commutative Iwasa theory via the Equivariant Tamagawa Number Conjecture-a survey","venue":null,"work_id":"74f037f1-fc2e-4a4d-a75f-6d467ec862aa","year":2004},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.460035Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:c24f735f1b889aeb2bf184350e3512ad1c755f67ad61ad8d2f0236470baf594e","observation_id":"e92ac8df-e1ee-41a5-9f41-2b76fb1369f4","resolution":{"observed_at":"2026-08-10T20:57:10.539877Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:57:10.515877Z","title":null,"venue":null,"work_id":"bc2c0143-f750-4da2-8a3c-0e33e57cfc0b","year":1976},"citing_paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-10T20:57:10.465070Z"},"links":{"citing_paper":"/paper/2501.07105"},"observation_digest":"sha256:dba2517ce8164bd12187199405ca8f9f7de9712836747c2a7169f5ab029def67","observation_id":"f52a3690-60d0-4415-a206-5b944f4e8376","resolution":{"observed_at":"2026-08-10T20:57:10.521854Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.07105","last_updated":"2025-01-13T07:38:03Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-11T05:08:25.318923Z","submitted_at":"2025-01-13T07:38:03Z","title":"The Equivariant Tamagawa Number Conjectures for modular motives with coefficients in Hecke algebra"},"reference_resolution":{"displayed":56,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":51},"total_outbound_references":56},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 0 inbound Pith citation observations for arXiv:2501.07105."}