{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:R6ZF42CKDRKSNH6RRRF45TPU2D","short_pith_number":"pith:R6ZF42CK","schema_version":"1.0","canonical_sha256":"8fb25e684a1c55269fd18c4bcecdf4d0e14e0693069c252a95f811e1db2495c3","source":{"kind":"arxiv","id":"1902.07002","version":1},"attestation_state":"computed","paper":{"title":"On the theory of higher rank Euler, Kolyvagin and Stark systems, III: applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Burns, Ryotaro Sakamoto, Takamichi Sano","submitted_at":"2019-02-19T11:32:50Z","abstract_excerpt":"In an earlier article we proved the existence of a canonical Kolyvagin derivative homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) that are associated to $p$-adic representations over number fields. We now explain how the existence of such a homomorphism leads to new results on the structure of the Selmer modules of Galois representations over Gorenstein orders and to a strategy for verifying (refinements of) the Tamagawa number conjecture of Bloch and Kato. We describe concrete applications relating to the multiplicative group over arbitrary number fields an"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.07002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-19T11:32:50Z","cross_cats_sorted":[],"title_canon_sha256":"534c77be2ae6089ee0b037384c26da46d96dd37381427e066521cd949226e380","abstract_canon_sha256":"2d7b59c9f5d85f70913e971cba12987d7a6a4b17b6267ee288dc3b341c3efd91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:40.195249Z","signature_b64":"lreclvqDsRVFZ9V/JW2aeE5EBgHhWaJDgloNOr+mSCPx2mfSMnEOTAI2F5PzKjGsR7NjhDdM4lCUHaX81w6gAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fb25e684a1c55269fd18c4bcecdf4d0e14e0693069c252a95f811e1db2495c3","last_reissued_at":"2026-05-17T23:53:40.194627Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:40.194627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the theory of higher rank Euler, Kolyvagin and Stark systems, III: applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Burns, Ryotaro Sakamoto, Takamichi Sano","submitted_at":"2019-02-19T11:32:50Z","abstract_excerpt":"In an earlier article we proved the existence of a canonical Kolyvagin derivative homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) that are associated to $p$-adic representations over number fields. We now explain how the existence of such a homomorphism leads to new results on the structure of the Selmer modules of Galois representations over Gorenstein orders and to a strategy for verifying (refinements of) the Tamagawa number conjecture of Bloch and Kato. We describe concrete applications relating to the multiplicative group over arbitrary number fields an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07002","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.07002","created_at":"2026-05-17T23:53:40.194713+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.07002v1","created_at":"2026-05-17T23:53:40.194713+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07002","created_at":"2026-05-17T23:53:40.194713+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6ZF42CKDRKS","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6ZF42CKDRKSNH6R","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6ZF42CK","created_at":"2026-05-18T12:33:27.125529+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D","json":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D.json","graph_json":"https://pith.science/api/pith-number/R6ZF42CKDRKSNH6RRRF45TPU2D/graph.json","events_json":"https://pith.science/api/pith-number/R6ZF42CKDRKSNH6RRRF45TPU2D/events.json","paper":"https://pith.science/paper/R6ZF42CK"},"agent_actions":{"view_html":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D","download_json":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D.json","view_paper":"https://pith.science/paper/R6ZF42CK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.07002&json=true","fetch_graph":"https://pith.science/api/pith-number/R6ZF42CKDRKSNH6RRRF45TPU2D/graph.json","fetch_events":"https://pith.science/api/pith-number/R6ZF42CKDRKSNH6RRRF45TPU2D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D/action/storage_attestation","attest_author":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D/action/author_attestation","sign_citation":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D/action/citation_signature","submit_replication":"https://pith.science/pith/R6ZF42CKDRKSNH6RRRF45TPU2D/action/replication_record"}},"created_at":"2026-05-17T23:53:40.194713+00:00","updated_at":"2026-05-17T23:53:40.194713+00:00"}