{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:QNWQBDEUK66XT4RXW3EEGWBAUR","short_pith_number":"pith:QNWQBDEU","canonical_record":{"source":{"id":"math/0508182","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-08-10T13:43:56Z","cross_cats_sorted":[],"title_canon_sha256":"cf5596843e9f0371d51cb5969093a99dcdcfbcccddb57c6bb69299baa93fac8f","abstract_canon_sha256":"2c8bde76af9c4216cdae5c5372e4e8c50e207cb404d62f3c96b01b12b1ee7a2b"},"schema_version":"1.0"},"canonical_sha256":"836d008c9457bd79f237b6c8435820a4792b0d11adb7b8c4a4a9c60ee1e5d12b","source":{"kind":"arxiv","id":"math/0508182","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508182","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508182v2","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508182","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"QNWQBDEUK66X","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"QNWQBDEUK66XT4RX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"QNWQBDEU","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:QNWQBDEUK66XT4RXW3EEGWBAUR","target":"record","payload":{"canonical_record":{"source":{"id":"math/0508182","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-08-10T13:43:56Z","cross_cats_sorted":[],"title_canon_sha256":"cf5596843e9f0371d51cb5969093a99dcdcfbcccddb57c6bb69299baa93fac8f","abstract_canon_sha256":"2c8bde76af9c4216cdae5c5372e4e8c50e207cb404d62f3c96b01b12b1ee7a2b"},"schema_version":"1.0"},"canonical_sha256":"836d008c9457bd79f237b6c8435820a4792b0d11adb7b8c4a4a9c60ee1e5d12b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:01.903948Z","signature_b64":"yh1Isr6B3gKNgCn+45FofqdhlFWnCbyce5CTGH05NjnH3LFXnvxNr+WC/ZOYXIlOJHb6Q68Fx2EPUtnOd7iHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"836d008c9457bd79f237b6c8435820a4792b0d11adb7b8c4a4a9c60ee1e5d12b","last_reissued_at":"2026-05-18T03:55:01.903453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:01.903453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0508182","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"znNalvJotPna23BQVSTZr3dB1EpmI452PtraoCk5GmmAICd9P4YRkP+G+TCvmEJtx6mReoZQfyUOiD4sSdtlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:28:51.851650Z"},"content_sha256":"03c52cf012208a5294c91c099289bd52b8a41ab0604d7227eaab7e9e2a41d21f","schema_version":"1.0","event_id":"sha256:03c52cf012208a5294c91c099289bd52b8a41ab0604d7227eaab7e9e2a41d21f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:QNWQBDEUK66XT4RXW3EEGWBAUR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the equivariant main conjecture of Iwasawa theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Malte Witte","submitted_at":"2005-08-10T13:43:56Z","abstract_excerpt":"Recently, D. Burns and C. Greither (Invent. Math., 2003) deduced an equivariant version of the main conjecture for abelian number fields. This was the key to their proof of the equivariant Tamagawa number conjecture. A. Huber and G. Kings (Duke Math. J., 2003) also use a variant of the Iwasawa main conjecture to prove the Tamagawa number conjecture for Dirichlet motives. We use the result of the second pair of authors and the Theorem of Ferrero-Washington to reprove the equivariant main conjecture in a slightly more general form. The main idea of the proof is essentially the same as in the pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508182","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hz5dQDNifZXB6gMcWZGtk+4x5b60Q510o2/+MudsfVeI1o0iYrKB2GeabMrRPWUuKzMCCf+GOLTfWtIcTBtkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:28:51.852350Z"},"content_sha256":"f2d3a11dfd458300a14881f09f188bcb2609116083076d0941726633e4e1fd08","schema_version":"1.0","event_id":"sha256:f2d3a11dfd458300a14881f09f188bcb2609116083076d0941726633e4e1fd08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNWQBDEUK66XT4RXW3EEGWBAUR/bundle.json","state_url":"https://pith.science/pith/QNWQBDEUK66XT4RXW3EEGWBAUR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNWQBDEUK66XT4RXW3EEGWBAUR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T22:28:51Z","links":{"resolver":"https://pith.science/pith/QNWQBDEUK66XT4RXW3EEGWBAUR","bundle":"https://pith.science/pith/QNWQBDEUK66XT4RXW3EEGWBAUR/bundle.json","state":"https://pith.science/pith/QNWQBDEUK66XT4RXW3EEGWBAUR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNWQBDEUK66XT4RXW3EEGWBAUR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:QNWQBDEUK66XT4RXW3EEGWBAUR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2c8bde76af9c4216cdae5c5372e4e8c50e207cb404d62f3c96b01b12b1ee7a2b","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-08-10T13:43:56Z","title_canon_sha256":"cf5596843e9f0371d51cb5969093a99dcdcfbcccddb57c6bb69299baa93fac8f"},"schema_version":"1.0","source":{"id":"math/0508182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508182","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508182v2","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508182","created_at":"2026-05-18T03:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"QNWQBDEUK66X","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"QNWQBDEUK66XT4RX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"QNWQBDEU","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f2d3a11dfd458300a14881f09f188bcb2609116083076d0941726633e4e1fd08","target":"graph","created_at":"2026-05-18T03:55:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Recently, D. Burns and C. Greither (Invent. Math., 2003) deduced an equivariant version of the main conjecture for abelian number fields. This was the key to their proof of the equivariant Tamagawa number conjecture. A. Huber and G. Kings (Duke Math. J., 2003) also use a variant of the Iwasawa main conjecture to prove the Tamagawa number conjecture for Dirichlet motives. We use the result of the second pair of authors and the Theorem of Ferrero-Washington to reprove the equivariant main conjecture in a slightly more general form. The main idea of the proof is essentially the same as in the pap","authors_text":"Malte Witte","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-08-10T13:43:56Z","title":"On the equivariant main conjecture of Iwasawa theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508182","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:03c52cf012208a5294c91c099289bd52b8a41ab0604d7227eaab7e9e2a41d21f","target":"record","created_at":"2026-05-18T03:55:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2c8bde76af9c4216cdae5c5372e4e8c50e207cb404d62f3c96b01b12b1ee7a2b","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-08-10T13:43:56Z","title_canon_sha256":"cf5596843e9f0371d51cb5969093a99dcdcfbcccddb57c6bb69299baa93fac8f"},"schema_version":"1.0","source":{"id":"math/0508182","kind":"arxiv","version":2}},"canonical_sha256":"836d008c9457bd79f237b6c8435820a4792b0d11adb7b8c4a4a9c60ee1e5d12b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"836d008c9457bd79f237b6c8435820a4792b0d11adb7b8c4a4a9c60ee1e5d12b","first_computed_at":"2026-05-18T03:55:01.903453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:01.903453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yh1Isr6B3gKNgCn+45FofqdhlFWnCbyce5CTGH05NjnH3LFXnvxNr+WC/ZOYXIlOJHb6Q68Fx2EPUtnOd7iHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:01.903948Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03c52cf012208a5294c91c099289bd52b8a41ab0604d7227eaab7e9e2a41d21f","sha256:f2d3a11dfd458300a14881f09f188bcb2609116083076d0941726633e4e1fd08"],"state_sha256":"e1ed43ead135065c8ccd8bb1c883c57b986fdb90ac29a32a2463e208bbade388"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E20sF4ebr4YYd3p93G9+AT99zXTdGGvAoUm41d87C9mY8O+HZpwTiTWWG/B3dXaKP7BT2k5vrF38lnD3zhOSBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:28:51.857011Z","bundle_sha256":"55bf0c3e2a247cff3d6a137085814527c28f29852e3bc4ca3e9cab43840c9df9"}}