{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PTU24MRYNM4ALBFYP3E24Z2SOU","short_pith_number":"pith:PTU24MRY","canonical_record":{"source":{"id":"1209.0668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-04T15:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"4b55273dd128fc8f03e34ef00990aea176edbada2d59cb5e2b0f9182cc24159b","abstract_canon_sha256":"6300e6228be4f3a72f9fb6bfebe88b3c266bdb4d193e620eb20ce92ad8725ba7"},"schema_version":"1.0"},"canonical_sha256":"7ce9ae32386b380584b87ec9ae6752751cd990584d228c887d72afd4455d7566","source":{"kind":"arxiv","id":"1209.0668","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0668","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0668v2","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0668","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"pith_short_12","alias_value":"PTU24MRYNM4A","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PTU24MRYNM4ALBFY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PTU24MRY","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PTU24MRYNM4ALBFYP3E24Z2SOU","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-04T15:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"4b55273dd128fc8f03e34ef00990aea176edbada2d59cb5e2b0f9182cc24159b","abstract_canon_sha256":"6300e6228be4f3a72f9fb6bfebe88b3c266bdb4d193e620eb20ce92ad8725ba7"},"schema_version":"1.0"},"canonical_sha256":"7ce9ae32386b380584b87ec9ae6752751cd990584d228c887d72afd4455d7566","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:41.792227Z","signature_b64":"7DMPE2k4xH0CfigAi+qpGGnPO7TsTv5h6lhpf77ELjK8QlqYxKf35lH3D762Ta+hD2A563Dj29/5TquQoQiXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ce9ae32386b380584b87ec9ae6752751cd990584d228c887d72afd4455d7566","last_reissued_at":"2026-05-18T03:43:41.791694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:41.791694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0668","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":"2026-05-18T03:43:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0og+D4ckLQsFD6rMrB9/1s1nGc1zcFnkzNKVkYM13FLEMZWWCeMrxiyVwCUgdzAiF13GTBM1zV68MfOY4ZGFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:28:06.898166Z"},"content_sha256":"ea6e7b1d4478469b824335791999f6c8b17e9311cc4491d978204e4e033bd89e","schema_version":"1.0","event_id":"sha256:ea6e7b1d4478469b824335791999f6c8b17e9311cc4491d978204e4e033bd89e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PTU24MRYNM4ALBFYP3E24Z2SOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of a Conjectured Formula for the Alexander Invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Peter Lee","submitted_at":"2012-09-04T15:23:02Z","abstract_excerpt":"In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0668","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":"2026-05-18T03:43:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTAqJWdnnn/6T/c/kAZL/KhIZEKYt9ogVHj4Un3rQ0PEqnEftyAoBie3Z28ZBoMfWOxatG/Q/iSB4Ba19bQ4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:28:06.898569Z"},"content_sha256":"575fe4ee8fe3bbc63076f1c7cd592c3eae1d496871f52db9b2e6a0d1bfcfa2cd","schema_version":"1.0","event_id":"sha256:575fe4ee8fe3bbc63076f1c7cd592c3eae1d496871f52db9b2e6a0d1bfcfa2cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTU24MRYNM4ALBFYP3E24Z2SOU/bundle.json","state_url":"https://pith.science/pith/PTU24MRYNM4ALBFYP3E24Z2SOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTU24MRYNM4ALBFYP3E24Z2SOU/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":"2026-06-11T21:28:06Z","links":{"resolver":"https://pith.science/pith/PTU24MRYNM4ALBFYP3E24Z2SOU","bundle":"https://pith.science/pith/PTU24MRYNM4ALBFYP3E24Z2SOU/bundle.json","state":"https://pith.science/pith/PTU24MRYNM4ALBFYP3E24Z2SOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTU24MRYNM4ALBFYP3E24Z2SOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PTU24MRYNM4ALBFYP3E24Z2SOU","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":"6300e6228be4f3a72f9fb6bfebe88b3c266bdb4d193e620eb20ce92ad8725ba7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-04T15:23:02Z","title_canon_sha256":"4b55273dd128fc8f03e34ef00990aea176edbada2d59cb5e2b0f9182cc24159b"},"schema_version":"1.0","source":{"id":"1209.0668","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0668","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0668v2","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0668","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"pith_short_12","alias_value":"PTU24MRYNM4A","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PTU24MRYNM4ALBFY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PTU24MRY","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:575fe4ee8fe3bbc63076f1c7cd592c3eae1d496871f52db9b2e6a0d1bfcfa2cd","target":"graph","created_at":"2026-05-18T03:43:41Z","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":"In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND].","authors_text":"Peter Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-04T15:23:02Z","title":"Proof of a Conjectured Formula for the Alexander Invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0668","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:ea6e7b1d4478469b824335791999f6c8b17e9311cc4491d978204e4e033bd89e","target":"record","created_at":"2026-05-18T03:43:41Z","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":"6300e6228be4f3a72f9fb6bfebe88b3c266bdb4d193e620eb20ce92ad8725ba7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-04T15:23:02Z","title_canon_sha256":"4b55273dd128fc8f03e34ef00990aea176edbada2d59cb5e2b0f9182cc24159b"},"schema_version":"1.0","source":{"id":"1209.0668","kind":"arxiv","version":2}},"canonical_sha256":"7ce9ae32386b380584b87ec9ae6752751cd990584d228c887d72afd4455d7566","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ce9ae32386b380584b87ec9ae6752751cd990584d228c887d72afd4455d7566","first_computed_at":"2026-05-18T03:43:41.791694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:41.791694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7DMPE2k4xH0CfigAi+qpGGnPO7TsTv5h6lhpf77ELjK8QlqYxKf35lH3D762Ta+hD2A563Dj29/5TquQoQiXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:41.792227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0668","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea6e7b1d4478469b824335791999f6c8b17e9311cc4491d978204e4e033bd89e","sha256:575fe4ee8fe3bbc63076f1c7cd592c3eae1d496871f52db9b2e6a0d1bfcfa2cd"],"state_sha256":"75930b2b8bc782161bf712e9723d2e69f5c6287181389d6198d29c967996991c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBLQardlggVtfKcdHNdW1g1VXiuinxRjsURz8smvxh/SX7Ifh4yOSxVJSQ79NJdoWExLgX1pAxIRlBmpkXNICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:28:06.900928Z","bundle_sha256":"e830750d8eb23d3a876b96ab759ba7665126c5ea9cdded01ab5efb0fb009f5fc"}}