{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6R5CNG3O4ZAFFIFROOZII5LAUE","short_pith_number":"pith:6R5CNG3O","canonical_record":{"source":{"id":"1410.1347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-06T12:32:10Z","cross_cats_sorted":[],"title_canon_sha256":"a45f08f5f41a57a2d13bdc66ce465781ab9c1b9ac65fddfe95e2a99240c52315","abstract_canon_sha256":"53bf1e292377c20c879392aa154a906b321881ca7a7af4f4d4cefed3b4e94b39"},"schema_version":"1.0"},"canonical_sha256":"f47a269b6ee64052a0b173b2847560a11f2bccd66ae3ad1234ae94767ad01ae1","source":{"kind":"arxiv","id":"1410.1347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1347","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1347v1","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1347","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"6R5CNG3O4ZAF","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6R5CNG3O4ZAFFIFR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6R5CNG3O","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6R5CNG3O4ZAFFIFROOZII5LAUE","target":"record","payload":{"canonical_record":{"source":{"id":"1410.1347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-06T12:32:10Z","cross_cats_sorted":[],"title_canon_sha256":"a45f08f5f41a57a2d13bdc66ce465781ab9c1b9ac65fddfe95e2a99240c52315","abstract_canon_sha256":"53bf1e292377c20c879392aa154a906b321881ca7a7af4f4d4cefed3b4e94b39"},"schema_version":"1.0"},"canonical_sha256":"f47a269b6ee64052a0b173b2847560a11f2bccd66ae3ad1234ae94767ad01ae1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:02.260477Z","signature_b64":"G05n7AuwqW4TO+37zDHiHtrUgg2xbydFB6UfL2ZkegUSc8cdF54C1HgstPwMQ6LI0WnTGt8eDG92N12zTzqHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f47a269b6ee64052a0b173b2847560a11f2bccd66ae3ad1234ae94767ad01ae1","last_reissued_at":"2026-05-18T02:41:02.259768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:02.259768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.1347","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":"2026-05-18T02:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yVEAlgIHzgvFdW7jieLE3BWCIbIQbf8QgkA+PXEKgNwC5bQzjweGU1bruAvEA9xb+eGC1CH/YATaEYnv7Kh4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:54:00.729218Z"},"content_sha256":"afb44b0e057507e9e209c82459e5cd5fd7f01ba50435a9484ff42b15979c4175","schema_version":"1.0","event_id":"sha256:afb44b0e057507e9e209c82459e5cd5fd7f01ba50435a9484ff42b15979c4175"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6R5CNG3O4ZAFFIFROOZII5LAUE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Congruences of algebraic $L$-functions of motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jyoti Prakash Saha, Olivier Fouquet","submitted_at":"2014-10-06T12:32:10Z","abstract_excerpt":"We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$-functions of congruent motives. We show that algebraic local Euler factors satisfy precise interpolation properties in $p$-adic families of motives and that algebraic $p$-adic $L$-functions exist in quite large generality for $p$-adic families of automorphic motives. We formulate two conjectures refining (and correcting) the currently existing formulation of the Equivariant Tamagawa Number Conjecture with coefficients in Hecke algebras and pointing out the links between conjectu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1347","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":"2026-05-18T02:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lN++s7tswZ49iqchcOo7QxzPVB478ivsGFYFki7QfQxWi88jBN25ghU/rdFxULzOEfqSLo8VpT0peHAvDp2FBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:54:00.730029Z"},"content_sha256":"a610f7b3dc930d2478c910be72cca73286e8a5731f7d3e4eb946529d2e4ee042","schema_version":"1.0","event_id":"sha256:a610f7b3dc930d2478c910be72cca73286e8a5731f7d3e4eb946529d2e4ee042"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6R5CNG3O4ZAFFIFROOZII5LAUE/bundle.json","state_url":"https://pith.science/pith/6R5CNG3O4ZAFFIFROOZII5LAUE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6R5CNG3O4ZAFFIFROOZII5LAUE/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":"2026-05-26T21:54:00Z","links":{"resolver":"https://pith.science/pith/6R5CNG3O4ZAFFIFROOZII5LAUE","bundle":"https://pith.science/pith/6R5CNG3O4ZAFFIFROOZII5LAUE/bundle.json","state":"https://pith.science/pith/6R5CNG3O4ZAFFIFROOZII5LAUE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6R5CNG3O4ZAFFIFROOZII5LAUE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6R5CNG3O4ZAFFIFROOZII5LAUE","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":"53bf1e292377c20c879392aa154a906b321881ca7a7af4f4d4cefed3b4e94b39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-06T12:32:10Z","title_canon_sha256":"a45f08f5f41a57a2d13bdc66ce465781ab9c1b9ac65fddfe95e2a99240c52315"},"schema_version":"1.0","source":{"id":"1410.1347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1347","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1347v1","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1347","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"6R5CNG3O4ZAF","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6R5CNG3O4ZAFFIFR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6R5CNG3O","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:a610f7b3dc930d2478c910be72cca73286e8a5731f7d3e4eb946529d2e4ee042","target":"graph","created_at":"2026-05-18T02:41:02Z","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":"We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$-functions of congruent motives. We show that algebraic local Euler factors satisfy precise interpolation properties in $p$-adic families of motives and that algebraic $p$-adic $L$-functions exist in quite large generality for $p$-adic families of automorphic motives. We formulate two conjectures refining (and correcting) the currently existing formulation of the Equivariant Tamagawa Number Conjecture with coefficients in Hecke algebras and pointing out the links between conjectu","authors_text":"Jyoti Prakash Saha, Olivier Fouquet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-06T12:32:10Z","title":"Congruences of algebraic $L$-functions of motives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1347","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:afb44b0e057507e9e209c82459e5cd5fd7f01ba50435a9484ff42b15979c4175","target":"record","created_at":"2026-05-18T02:41:02Z","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":"53bf1e292377c20c879392aa154a906b321881ca7a7af4f4d4cefed3b4e94b39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-06T12:32:10Z","title_canon_sha256":"a45f08f5f41a57a2d13bdc66ce465781ab9c1b9ac65fddfe95e2a99240c52315"},"schema_version":"1.0","source":{"id":"1410.1347","kind":"arxiv","version":1}},"canonical_sha256":"f47a269b6ee64052a0b173b2847560a11f2bccd66ae3ad1234ae94767ad01ae1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f47a269b6ee64052a0b173b2847560a11f2bccd66ae3ad1234ae94767ad01ae1","first_computed_at":"2026-05-18T02:41:02.259768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:02.259768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G05n7AuwqW4TO+37zDHiHtrUgg2xbydFB6UfL2ZkegUSc8cdF54C1HgstPwMQ6LI0WnTGt8eDG92N12zTzqHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:02.260477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afb44b0e057507e9e209c82459e5cd5fd7f01ba50435a9484ff42b15979c4175","sha256:a610f7b3dc930d2478c910be72cca73286e8a5731f7d3e4eb946529d2e4ee042"],"state_sha256":"245ad455a54db4b2e1d9530d65aab441cc0543183705d33db8f9d1eca537b353"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WCuikwX5mi2g5v/RWVqQ0l0MdcYzYKesIwxdt0kasYMAJeWlNqiLc9SGzT+E11Db4MEiAp/0wkQUpaTUdc/RAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:54:00.734005Z","bundle_sha256":"e8e514598f8b7293e3f250c5d12895489eaac298402acf031f408ed75157f226"}}