{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JBMBSBGA6OCM5AGYSEEZ3JWXSO","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":"f1d0e809838ff802b8f0deb9699d35cfa98d3526ea95f5c7564a1024bcd4fe1f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-25T08:16:55Z","title_canon_sha256":"30f6e12e6d7a10b6e45bec02f00d95a751dce0cc33aa253fcd74fd0251c4ce52"},"schema_version":"1.0","source":{"id":"2508.17776","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17776","created_at":"2026-07-05T11:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17776v1","created_at":"2026-07-05T11:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17776","created_at":"2026-07-05T11:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"JBMBSBGA6OCM","created_at":"2026-07-05T11:58:47Z"},{"alias_kind":"pith_short_16","alias_value":"JBMBSBGA6OCM5AGY","created_at":"2026-07-05T11:58:47Z"},{"alias_kind":"pith_short_8","alias_value":"JBMBSBGA","created_at":"2026-07-05T11:58:47Z"}],"graph_snapshots":[{"event_id":"sha256:11707b43a8f63a6d1fb9f13f3c9b155e017b388c4a06c5ff6b0730a14bfb1d61","target":"graph","created_at":"2026-07-05T11:58:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.17776/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$-adic representations of $G_{\\mathbb{Q}_p}$ of rank two (a local sign decomposition): a functorial decomposition into free rank one Lagrangian submodules which encodes the $p$-adic variation of Bloch--Kato subgroups via completed epsilon constants, mirroring a symplectic structure.\n  The local sign decomposition has diverse local as well as global arithmetic consequences. This includes compatibility of the Mazur--Rubin arithmetic local constant and completed epsilon constants","authors_text":"Ashay Burungale, Kazuto Ota, Kentaro Nakamura, Shinichi Kobayashi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-25T08:16:55Z","title":"A local sign decomposition for symplectic self-dual Galois representations of rank two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17776","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":"sha256:057c2d6669886aab179258354cb661f57b44b773669400a54fd34d2220df0d2d","target":"record","created_at":"2026-07-05T11:58:47Z","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":"f1d0e809838ff802b8f0deb9699d35cfa98d3526ea95f5c7564a1024bcd4fe1f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-25T08:16:55Z","title_canon_sha256":"30f6e12e6d7a10b6e45bec02f00d95a751dce0cc33aa253fcd74fd0251c4ce52"},"schema_version":"1.0","source":{"id":"2508.17776","kind":"arxiv","version":1}},"canonical_sha256":"48581904c0f384ce80d891099da6d7939f42e9610e36befb05d0f5edd3a1da63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48581904c0f384ce80d891099da6d7939f42e9610e36befb05d0f5edd3a1da63","first_computed_at":"2026-07-05T11:58:47.572511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:58:47.572511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDo0HWbLf7FSlUgluJyIbDzWXDXIW2g1QZUJ3/h1Hpj2VtsBuh+O0gHreaXS5NiR9fXrDHXSU4K8ZPncEhq7Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T11:58:47.572947Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.17776","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:057c2d6669886aab179258354cb661f57b44b773669400a54fd34d2220df0d2d","sha256:11707b43a8f63a6d1fb9f13f3c9b155e017b388c4a06c5ff6b0730a14bfb1d61"],"state_sha256":"a0b71e198067feb578c5f884fadaae602c22ba5005534d2a1ab2dfa9fc60afff"}