{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YWQ5AHPI7W55WMELDQ5QEDEBBV","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":"05cc95c1db9642aafd4223e7a4e5ed1286abba41b63ab97be282067abde7497f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-19T21:52:48Z","title_canon_sha256":"16e222039517fa852fda166bc9cee0bef68c9b7296314bebbf7fa81f0a7202d2"},"schema_version":"1.0","source":{"id":"1906.08377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08377","created_at":"2026-05-17T23:42:32Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08377v2","created_at":"2026-05-17T23:42:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08377","created_at":"2026-05-17T23:42:32Z"},{"alias_kind":"pith_short_12","alias_value":"YWQ5AHPI7W55","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YWQ5AHPI7W55WMEL","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YWQ5AHPI","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:bb39e283b08b3b644ef7495e486db8e4471731b5d7f556a8632837548a04785e","target":"graph","created_at":"2026-05-17T23:42:32Z","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":"We prove consequences of functional equations of p-adic L-functions for elliptic curves at supersingular primes p. The results include a relationship between the leading and sub-leading terms (for which we use ideas of Wuthrich and Bianchi), a parity result of orders of vanishing, and invariance of Iwasaswa invariants under conjugate twists of the p-adic L-functions.","authors_text":"C\\'edric Dion, Florian Ito Sprung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-19T21:52:48Z","title":"Consequences of functional equations for pairs of p-adic L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08377","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:cf35a1748597e0b3a81476cde36a8a9d255f7007b1e523c3163ab80c21cfa92b","target":"record","created_at":"2026-05-17T23:42:32Z","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":"05cc95c1db9642aafd4223e7a4e5ed1286abba41b63ab97be282067abde7497f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-19T21:52:48Z","title_canon_sha256":"16e222039517fa852fda166bc9cee0bef68c9b7296314bebbf7fa81f0a7202d2"},"schema_version":"1.0","source":{"id":"1906.08377","kind":"arxiv","version":2}},"canonical_sha256":"c5a1d01de8fdbbdb308b1c3b020c810d496333ebacda84a2be32ff16c8656b75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5a1d01de8fdbbdb308b1c3b020c810d496333ebacda84a2be32ff16c8656b75","first_computed_at":"2026-05-17T23:42:32.206019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:32.206019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R1+bZUp9bZnTIHh+UerTnmUn+WR9aWPUgKM/QQD4WacwJEHmEI5afR04H0LX8BNQyDI6gq85vSgGxQKC1ph+AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:32.206650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf35a1748597e0b3a81476cde36a8a9d255f7007b1e523c3163ab80c21cfa92b","sha256:bb39e283b08b3b644ef7495e486db8e4471731b5d7f556a8632837548a04785e"],"state_sha256":"b80783e0d7299ffcf274ea652aca195c8891883fedbee4ac2ef43734ee68bfd3"}