{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZYCJ6YKCSPVOSH3P27OBMC6HTR","short_pith_number":"pith:ZYCJ6YKC","canonical_record":{"source":{"id":"1002.1803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-09T09:15:23Z","cross_cats_sorted":[],"title_canon_sha256":"94970e7034cb0ee780bdd8c0fa85208f853f2de0f63d251edfd215c792e0e61a","abstract_canon_sha256":"b1a6d90713c3243640cf3cb828fc45785ae5bee2c9ef54fa86346611d00add70"},"schema_version":"1.0"},"canonical_sha256":"ce049f614293eae91f6fd7dc160bc79c7b16eb7442f190b580009b50328fd406","source":{"kind":"arxiv","id":"1002.1803","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1803","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1803v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1803","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZYCJ6YKCSPVO","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZYCJ6YKCSPVOSH3P","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZYCJ6YKC","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZYCJ6YKCSPVOSH3P27OBMC6HTR","target":"record","payload":{"canonical_record":{"source":{"id":"1002.1803","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-09T09:15:23Z","cross_cats_sorted":[],"title_canon_sha256":"94970e7034cb0ee780bdd8c0fa85208f853f2de0f63d251edfd215c792e0e61a","abstract_canon_sha256":"b1a6d90713c3243640cf3cb828fc45785ae5bee2c9ef54fa86346611d00add70"},"schema_version":"1.0"},"canonical_sha256":"ce049f614293eae91f6fd7dc160bc79c7b16eb7442f190b580009b50328fd406","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.627001Z","signature_b64":"h40iAgrSFPJzTvkWkUrOyJMBz7kd9Fhxp4kKfmuNPfAttPatBB4y7YmUFV/pky5BzjCQIOP4hi3qC9axXOCwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce049f614293eae91f6fd7dc160bc79c7b16eb7442f190b580009b50328fd406","last_reissued_at":"2026-05-18T02:38:18.626346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.626346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.1803","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/BGi0eSmdnvztXII7yJFuZbNH9rJvt8mwBT/aqwO5R2h+mzjDjXDVCBUgb/eW0C5oFwYmQXjYZOMYRhJ4evAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:49:03.522781Z"},"content_sha256":"611e6c1d30be6e413e9ae10cebf210901d50e1ee8dce4334835968f56f9f0e1c","schema_version":"1.0","event_id":"sha256:611e6c1d30be6e413e9ae10cebf210901d50e1ee8dce4334835968f56f9f0e1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZYCJ6YKCSPVOSH3P27OBMC6HTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Milnor invariants and the HOMFLYPT polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Jean-Baptiste Meilhan","submitted_at":"2010-02-09T09:15:23Z","abstract_excerpt":"We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant \\bar{\\mu}_J(L) vanishes for any sequence J with length at most k, then any Milnor \\bar{\\mu}-invariant \\bar{\\mu}_I(L) with length between 3 and 2k+1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the `first non vanishing' Milnor invariants can be always represented as such a linear combination."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1803","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/57cpgNkex3/H32Bjs4yvASJgmEGg/xPJjOOAbxfYGB2qIvbe2zpN/plOXjYSuZFUYaxtvV/1roRsDvjKsxPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:49:03.523125Z"},"content_sha256":"4acd2192312db281377ed6f98aa268b5ed42e60edcf71f410773bef0bf4ded55","schema_version":"1.0","event_id":"sha256:4acd2192312db281377ed6f98aa268b5ed42e60edcf71f410773bef0bf4ded55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYCJ6YKCSPVOSH3P27OBMC6HTR/bundle.json","state_url":"https://pith.science/pith/ZYCJ6YKCSPVOSH3P27OBMC6HTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYCJ6YKCSPVOSH3P27OBMC6HTR/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":"2026-06-22T13:49:03Z","links":{"resolver":"https://pith.science/pith/ZYCJ6YKCSPVOSH3P27OBMC6HTR","bundle":"https://pith.science/pith/ZYCJ6YKCSPVOSH3P27OBMC6HTR/bundle.json","state":"https://pith.science/pith/ZYCJ6YKCSPVOSH3P27OBMC6HTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYCJ6YKCSPVOSH3P27OBMC6HTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZYCJ6YKCSPVOSH3P27OBMC6HTR","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":"b1a6d90713c3243640cf3cb828fc45785ae5bee2c9ef54fa86346611d00add70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-09T09:15:23Z","title_canon_sha256":"94970e7034cb0ee780bdd8c0fa85208f853f2de0f63d251edfd215c792e0e61a"},"schema_version":"1.0","source":{"id":"1002.1803","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1803","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1803v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1803","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZYCJ6YKCSPVO","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZYCJ6YKCSPVOSH3P","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZYCJ6YKC","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:4acd2192312db281377ed6f98aa268b5ed42e60edcf71f410773bef0bf4ded55","target":"graph","created_at":"2026-05-18T02:38:18Z","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 give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant \\bar{\\mu}_J(L) vanishes for any sequence J with length at most k, then any Milnor \\bar{\\mu}-invariant \\bar{\\mu}_I(L) with length between 3 and 2k+1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the `first non vanishing' Milnor invariants can be always represented as such a linear combination.","authors_text":"Akira Yasuhara, Jean-Baptiste Meilhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-09T09:15:23Z","title":"Milnor invariants and the HOMFLYPT polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1803","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":"sha256:611e6c1d30be6e413e9ae10cebf210901d50e1ee8dce4334835968f56f9f0e1c","target":"record","created_at":"2026-05-18T02:38:18Z","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":"b1a6d90713c3243640cf3cb828fc45785ae5bee2c9ef54fa86346611d00add70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-02-09T09:15:23Z","title_canon_sha256":"94970e7034cb0ee780bdd8c0fa85208f853f2de0f63d251edfd215c792e0e61a"},"schema_version":"1.0","source":{"id":"1002.1803","kind":"arxiv","version":2}},"canonical_sha256":"ce049f614293eae91f6fd7dc160bc79c7b16eb7442f190b580009b50328fd406","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce049f614293eae91f6fd7dc160bc79c7b16eb7442f190b580009b50328fd406","first_computed_at":"2026-05-18T02:38:18.626346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.626346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h40iAgrSFPJzTvkWkUrOyJMBz7kd9Fhxp4kKfmuNPfAttPatBB4y7YmUFV/pky5BzjCQIOP4hi3qC9axXOCwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.627001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1803","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:611e6c1d30be6e413e9ae10cebf210901d50e1ee8dce4334835968f56f9f0e1c","sha256:4acd2192312db281377ed6f98aa268b5ed42e60edcf71f410773bef0bf4ded55"],"state_sha256":"7a3ae9e47198444ca3a3129839afde6d02600786f6a1de6082493dac04c7d0b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2r4ViYA7PiHKFU4Oh0VHbDWR97zQ78pVtF1B3t7CPCN9YBfzHkVB2piRNRwNIp7F6aAKNPNdLUD0sA70LoRwCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:49:03.525027Z","bundle_sha256":"9fcc68afd8461693b24654fbe30d5e054da636e880438509517b4f02437d3070"}}