{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YWQ5AHPI7W55WMELDQ5QEDEBBV","short_pith_number":"pith:YWQ5AHPI","canonical_record":{"source":{"id":"1906.08377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-19T21:52:48Z","cross_cats_sorted":[],"title_canon_sha256":"16e222039517fa852fda166bc9cee0bef68c9b7296314bebbf7fa81f0a7202d2","abstract_canon_sha256":"05cc95c1db9642aafd4223e7a4e5ed1286abba41b63ab97be282067abde7497f"},"schema_version":"1.0"},"canonical_sha256":"c5a1d01de8fdbbdb308b1c3b020c810d496333ebacda84a2be32ff16c8656b75","source":{"kind":"arxiv","id":"1906.08377","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YWQ5AHPI7W55WMELDQ5QEDEBBV","target":"record","payload":{"canonical_record":{"source":{"id":"1906.08377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-19T21:52:48Z","cross_cats_sorted":[],"title_canon_sha256":"16e222039517fa852fda166bc9cee0bef68c9b7296314bebbf7fa81f0a7202d2","abstract_canon_sha256":"05cc95c1db9642aafd4223e7a4e5ed1286abba41b63ab97be282067abde7497f"},"schema_version":"1.0"},"canonical_sha256":"c5a1d01de8fdbbdb308b1c3b020c810d496333ebacda84a2be32ff16c8656b75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:32.206650Z","signature_b64":"R1+bZUp9bZnTIHh+UerTnmUn+WR9aWPUgKM/QQD4WacwJEHmEI5afR04H0LX8BNQyDI6gq85vSgGxQKC1ph+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5a1d01de8fdbbdb308b1c3b020c810d496333ebacda84a2be32ff16c8656b75","last_reissued_at":"2026-05-17T23:42:32.206019Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:32.206019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.08377","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":"2026-05-17T23:42:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8awZvQsPu7wBuScHqwB/3dpKi5ZlM/+VEB/i4O3lbCJes0FBU9ppY6djOElaSylChO4gDmUn5Cy6JiEaf7RmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:23:46.089185Z"},"content_sha256":"cf35a1748597e0b3a81476cde36a8a9d255f7007b1e523c3163ab80c21cfa92b","schema_version":"1.0","event_id":"sha256:cf35a1748597e0b3a81476cde36a8a9d255f7007b1e523c3163ab80c21cfa92b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YWQ5AHPI7W55WMELDQ5QEDEBBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Consequences of functional equations for pairs of p-adic L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C\\'edric Dion, Florian Ito Sprung","submitted_at":"2019-06-19T21:52:48Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08377","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":"2026-05-17T23:42:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/qN2giMoyifFDVtrUqIIxVDjgWLCxDf9Ekybb9D/IF+AU3iAolyB7M+SR1dWWrrBaVyiOJ09To6Wl1KhAs1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:23:46.089915Z"},"content_sha256":"bb39e283b08b3b644ef7495e486db8e4471731b5d7f556a8632837548a04785e","schema_version":"1.0","event_id":"sha256:bb39e283b08b3b644ef7495e486db8e4471731b5d7f556a8632837548a04785e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWQ5AHPI7W55WMELDQ5QEDEBBV/bundle.json","state_url":"https://pith.science/pith/YWQ5AHPI7W55WMELDQ5QEDEBBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWQ5AHPI7W55WMELDQ5QEDEBBV/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":"2026-05-26T07:23:46Z","links":{"resolver":"https://pith.science/pith/YWQ5AHPI7W55WMELDQ5QEDEBBV","bundle":"https://pith.science/pith/YWQ5AHPI7W55WMELDQ5QEDEBBV/bundle.json","state":"https://pith.science/pith/YWQ5AHPI7W55WMELDQ5QEDEBBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWQ5AHPI7W55WMELDQ5QEDEBBV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RV3dgjkIhqkXx4kX585i+LQrZ4l2C9BJiDhe6QXNQQZmmr1pKvjq5SIU9cb+dkZ7sZbonQTOwPL1/qAip81qDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:23:46.093275Z","bundle_sha256":"4b3a441a9f272bc4ef03bbf2a545857790c55ef3c0c7dbb332e814159fe9dc4e"}}