{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JHNHYG7QY6AZDRDEU22YM7T4PB","short_pith_number":"pith:JHNHYG7Q","canonical_record":{"source":{"id":"1405.5001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-20T09:11:22Z","cross_cats_sorted":[],"title_canon_sha256":"3b1f3377dc23fa6e5aae5d479635e5638261eef37fe2d6dc9a8e7ed86ebea11d","abstract_canon_sha256":"8f7672e04c44a077a7a30d89ab5e6ebfa3b690bef460ea58841c0e2ff1c087a9"},"schema_version":"1.0"},"canonical_sha256":"49da7c1bf0c78191c464a6b5867e7c784bb4737d02f8c3a703aa9cc0afe36b15","source":{"kind":"arxiv","id":"1405.5001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5001","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5001v1","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5001","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"pith_short_12","alias_value":"JHNHYG7QY6AZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JHNHYG7QY6AZDRDE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JHNHYG7Q","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JHNHYG7QY6AZDRDEU22YM7T4PB","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-20T09:11:22Z","cross_cats_sorted":[],"title_canon_sha256":"3b1f3377dc23fa6e5aae5d479635e5638261eef37fe2d6dc9a8e7ed86ebea11d","abstract_canon_sha256":"8f7672e04c44a077a7a30d89ab5e6ebfa3b690bef460ea58841c0e2ff1c087a9"},"schema_version":"1.0"},"canonical_sha256":"49da7c1bf0c78191c464a6b5867e7c784bb4737d02f8c3a703aa9cc0afe36b15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:32.414026Z","signature_b64":"gaR4cKDxVhBKYj9T6lO7JZEYB431ls62GamyiToWze3Us4iwmp9W0Zd4aXJ8kSvRzZlvBC1hNcG8UTdPatJGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49da7c1bf0c78191c464a6b5867e7c784bb4737d02f8c3a703aa9cc0afe36b15","last_reissued_at":"2026-05-18T02:51:32.413285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:32.413285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5001","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ihlWuuOSYxBWOa9ET1tb8Mx/cixYEl2AaIx1ruVlBH4osU2WyRG4rEbDBDtqYdM3Ks/8j+WNeHXmNvKIiE/7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:15:04.208589Z"},"content_sha256":"928bb8d3287a4e9a2fe4b9855d78a9caf51f36bd974b678ba7a5ce3fa74db106","schema_version":"1.0","event_id":"sha256:928bb8d3287a4e9a2fe4b9855d78a9caf51f36bd974b678ba7a5ce3fa74db106"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JHNHYG7QY6AZDRDEU22YM7T4PB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Macias Castillo, Werner Bley","submitted_at":"2014-05-20T09:11:22Z","abstract_excerpt":"Let A be an abelian variety over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we obtain a reinterpretation of the equivariant Tamagawa number conjecture (eTNC) for A, F/k and p as an explicit family of p-adic congru- ences involving values of derivatives of the Hasse-Weil L-functions of twists of A, normalised by completely explicit twisted regulators. This reinterpretation makes the eTNC amenable to numerical verification and furthermore leads to explicit predictions which refine well-known conjectures of Mazur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5001","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JciU22xlJtIwHnN0oCLnNGgN7y/0U7Q14kbawo4XE0XvSTNLXXsNxVnvmZ4/jPH5ZVU3LWSWG5FDw5oN4EA9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:15:04.208935Z"},"content_sha256":"07f2060b6faeace065a0d50cbc86f603a82e9dd87ccd40e044933527660e9a6e","schema_version":"1.0","event_id":"sha256:07f2060b6faeace065a0d50cbc86f603a82e9dd87ccd40e044933527660e9a6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JHNHYG7QY6AZDRDEU22YM7T4PB/bundle.json","state_url":"https://pith.science/pith/JHNHYG7QY6AZDRDEU22YM7T4PB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JHNHYG7QY6AZDRDEU22YM7T4PB/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":"2026-06-25T11:15:04Z","links":{"resolver":"https://pith.science/pith/JHNHYG7QY6AZDRDEU22YM7T4PB","bundle":"https://pith.science/pith/JHNHYG7QY6AZDRDEU22YM7T4PB/bundle.json","state":"https://pith.science/pith/JHNHYG7QY6AZDRDEU22YM7T4PB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JHNHYG7QY6AZDRDEU22YM7T4PB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JHNHYG7QY6AZDRDEU22YM7T4PB","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":"8f7672e04c44a077a7a30d89ab5e6ebfa3b690bef460ea58841c0e2ff1c087a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-20T09:11:22Z","title_canon_sha256":"3b1f3377dc23fa6e5aae5d479635e5638261eef37fe2d6dc9a8e7ed86ebea11d"},"schema_version":"1.0","source":{"id":"1405.5001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5001","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5001v1","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5001","created_at":"2026-05-18T02:51:32Z"},{"alias_kind":"pith_short_12","alias_value":"JHNHYG7QY6AZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JHNHYG7QY6AZDRDE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JHNHYG7Q","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:07f2060b6faeace065a0d50cbc86f603a82e9dd87ccd40e044933527660e9a6e","target":"graph","created_at":"2026-05-18T02:51:32Z","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":"Let A be an abelian variety over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we obtain a reinterpretation of the equivariant Tamagawa number conjecture (eTNC) for A, F/k and p as an explicit family of p-adic congru- ences involving values of derivatives of the Hasse-Weil L-functions of twists of A, normalised by completely explicit twisted regulators. This reinterpretation makes the eTNC amenable to numerical verification and furthermore leads to explicit predictions which refine well-known conjectures of Mazur","authors_text":"Daniel Macias Castillo, Werner Bley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-20T09:11:22Z","title":"Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5001","kind":"arxiv","version":1},"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":"sha256:928bb8d3287a4e9a2fe4b9855d78a9caf51f36bd974b678ba7a5ce3fa74db106","target":"record","created_at":"2026-05-18T02:51:32Z","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":"8f7672e04c44a077a7a30d89ab5e6ebfa3b690bef460ea58841c0e2ff1c087a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-20T09:11:22Z","title_canon_sha256":"3b1f3377dc23fa6e5aae5d479635e5638261eef37fe2d6dc9a8e7ed86ebea11d"},"schema_version":"1.0","source":{"id":"1405.5001","kind":"arxiv","version":1}},"canonical_sha256":"49da7c1bf0c78191c464a6b5867e7c784bb4737d02f8c3a703aa9cc0afe36b15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49da7c1bf0c78191c464a6b5867e7c784bb4737d02f8c3a703aa9cc0afe36b15","first_computed_at":"2026-05-18T02:51:32.413285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:32.413285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gaR4cKDxVhBKYj9T6lO7JZEYB431ls62GamyiToWze3Us4iwmp9W0Zd4aXJ8kSvRzZlvBC1hNcG8UTdPatJGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:32.414026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:928bb8d3287a4e9a2fe4b9855d78a9caf51f36bd974b678ba7a5ce3fa74db106","sha256:07f2060b6faeace065a0d50cbc86f603a82e9dd87ccd40e044933527660e9a6e"],"state_sha256":"d435f5ddc6c3311e7f63136eb15a4d9b574c4ab7c874b5c43a69268cd16194de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B32uyONwGZO5yi0SjFSbVCblTKsqC4BoogLD3yzLSN5wzXqI/x3x9K5xjRuuiIrr4ZeokR2e+uS07eZA99SJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:15:04.210850Z","bundle_sha256":"ecaa53660f2c48b855014fb82f000be3f9ddeef4e9e6bf1069e00fba283dd751"}}