{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3ZNRSRZ6JLHV5YB47IIKTX35TV","short_pith_number":"pith:3ZNRSRZ6","canonical_record":{"source":{"id":"1403.0446","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-03T14:41:40Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c420c14dd9af26e8a9d8c9cd766b7464d3b9efb5aae92aae82e6bc8f0eeef30f","abstract_canon_sha256":"3b2ba77e71365ca8635c75ffe1f6f2d77edc709915bb11886fb7fa96ff1ddf19"},"schema_version":"1.0"},"canonical_sha256":"de5b19473e4acf5ee03cfa10a9df7d9d48f2a30f36050d4b53df47af3754b9fd","source":{"kind":"arxiv","id":"1403.0446","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0446","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0446v2","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0446","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"3ZNRSRZ6JLHV","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3ZNRSRZ6JLHV5YB4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3ZNRSRZ6","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3ZNRSRZ6JLHV5YB47IIKTX35TV","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0446","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-03T14:41:40Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c420c14dd9af26e8a9d8c9cd766b7464d3b9efb5aae92aae82e6bc8f0eeef30f","abstract_canon_sha256":"3b2ba77e71365ca8635c75ffe1f6f2d77edc709915bb11886fb7fa96ff1ddf19"},"schema_version":"1.0"},"canonical_sha256":"de5b19473e4acf5ee03cfa10a9df7d9d48f2a30f36050d4b53df47af3754b9fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:15.970465Z","signature_b64":"iCdDHsuDTt0Pb4HKP3T3nlbLXfvdJ2/017SGxTD4MsOP7Et2W3e5uDfL/nm4PiWvQt2F5336pBZPHyo1nBz5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de5b19473e4acf5ee03cfa10a9df7d9d48f2a30f36050d4b53df47af3754b9fd","last_reissued_at":"2026-05-18T00:29:15.969807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:15.969807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0446","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":"2026-05-18T00:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JDvAeycfHybnhM1Uz64uwNAmsq1I1FuSg9EWUQD7HeVvZiB5ZRZ400khp/yFKrZRGtbnsvsc6LxV3DBmiZqKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:00:55.382680Z"},"content_sha256":"aab0fee273b4a36c22255bf19328f34a9c1828fb26d5b0083f49e0b5e799fa6a","schema_version":"1.0","event_id":"sha256:aab0fee273b4a36c22255bf19328f34a9c1828fb26d5b0083f49e0b5e799fa6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3ZNRSRZ6JLHV5YB47IIKTX35TV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant triple intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Delphine Moussard","submitted_at":"2014-03-03T14:41:40Z","abstract_excerpt":"Given a null-homologous knot $K$ in a rational homology 3-sphere $M$, and the standard infinite cyclic covering $\\tilde{X}$ of $(M,K)$, we define an invariant of triples of curves in $\\tilde{X}$, by means of equivariant triple intersections of surfaces. We prove that this invariant provides a map $\\phi$ on $\\Al^{\\otimes 3}$, where $\\Al$ is the Alexander module of $(M,K)$, and that the isomorphism class of $\\phi$ is an invariant of the pair $(M,K)$. For a fixed Blanchfield module $(\\Al,\\bl)$, we consider pairs $(M,K)$ whose Blanchfield modules are isomorphic to $(\\Al,\\bl)$, equipped with a mark"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0446","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":"2026-05-18T00:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIPn5ho6eDXl/GGYFiYgI2hhpEIEfmz4HlXcowbirJLWyHvcYekrjHmk5eIB/OHrOnIrHqTEM60EN6KqY3BLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:00:55.383019Z"},"content_sha256":"d8e4e89ea2232efaa39f94885c2eb830db9956681ec9d28800a655cf92f45c12","schema_version":"1.0","event_id":"sha256:d8e4e89ea2232efaa39f94885c2eb830db9956681ec9d28800a655cf92f45c12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ZNRSRZ6JLHV5YB47IIKTX35TV/bundle.json","state_url":"https://pith.science/pith/3ZNRSRZ6JLHV5YB47IIKTX35TV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ZNRSRZ6JLHV5YB47IIKTX35TV/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":"2026-06-27T03:00:55Z","links":{"resolver":"https://pith.science/pith/3ZNRSRZ6JLHV5YB47IIKTX35TV","bundle":"https://pith.science/pith/3ZNRSRZ6JLHV5YB47IIKTX35TV/bundle.json","state":"https://pith.science/pith/3ZNRSRZ6JLHV5YB47IIKTX35TV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ZNRSRZ6JLHV5YB47IIKTX35TV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3ZNRSRZ6JLHV5YB47IIKTX35TV","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":"3b2ba77e71365ca8635c75ffe1f6f2d77edc709915bb11886fb7fa96ff1ddf19","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-03T14:41:40Z","title_canon_sha256":"c420c14dd9af26e8a9d8c9cd766b7464d3b9efb5aae92aae82e6bc8f0eeef30f"},"schema_version":"1.0","source":{"id":"1403.0446","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0446","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0446v2","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0446","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"3ZNRSRZ6JLHV","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3ZNRSRZ6JLHV5YB4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3ZNRSRZ6","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:d8e4e89ea2232efaa39f94885c2eb830db9956681ec9d28800a655cf92f45c12","target":"graph","created_at":"2026-05-18T00:29:15Z","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":"Given a null-homologous knot $K$ in a rational homology 3-sphere $M$, and the standard infinite cyclic covering $\\tilde{X}$ of $(M,K)$, we define an invariant of triples of curves in $\\tilde{X}$, by means of equivariant triple intersections of surfaces. We prove that this invariant provides a map $\\phi$ on $\\Al^{\\otimes 3}$, where $\\Al$ is the Alexander module of $(M,K)$, and that the isomorphism class of $\\phi$ is an invariant of the pair $(M,K)$. For a fixed Blanchfield module $(\\Al,\\bl)$, we consider pairs $(M,K)$ whose Blanchfield modules are isomorphic to $(\\Al,\\bl)$, equipped with a mark","authors_text":"Delphine Moussard","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-03T14:41:40Z","title":"Equivariant triple intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0446","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:aab0fee273b4a36c22255bf19328f34a9c1828fb26d5b0083f49e0b5e799fa6a","target":"record","created_at":"2026-05-18T00:29:15Z","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":"3b2ba77e71365ca8635c75ffe1f6f2d77edc709915bb11886fb7fa96ff1ddf19","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-03T14:41:40Z","title_canon_sha256":"c420c14dd9af26e8a9d8c9cd766b7464d3b9efb5aae92aae82e6bc8f0eeef30f"},"schema_version":"1.0","source":{"id":"1403.0446","kind":"arxiv","version":2}},"canonical_sha256":"de5b19473e4acf5ee03cfa10a9df7d9d48f2a30f36050d4b53df47af3754b9fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de5b19473e4acf5ee03cfa10a9df7d9d48f2a30f36050d4b53df47af3754b9fd","first_computed_at":"2026-05-18T00:29:15.969807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:15.969807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iCdDHsuDTt0Pb4HKP3T3nlbLXfvdJ2/017SGxTD4MsOP7Et2W3e5uDfL/nm4PiWvQt2F5336pBZPHyo1nBz5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:15.970465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0446","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aab0fee273b4a36c22255bf19328f34a9c1828fb26d5b0083f49e0b5e799fa6a","sha256:d8e4e89ea2232efaa39f94885c2eb830db9956681ec9d28800a655cf92f45c12"],"state_sha256":"d93ca8f837e01410bc2c904e8729edeb42edb478a1c7d38b58355b9d37fcd2dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHKwB8MgwZHvJMgfgNF1Dnh7oFjoN0v5Bk5x9nTCyIZpZuIoO8HzM3eutLhEblIqJCVBsdAWdKsttE7NTOFLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:00:55.384924Z","bundle_sha256":"3d81e9c692b7d7a5a95bdef8b4cba2cf4fce39af880e32d0bcad237ee0c98819"}}