{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V5IVL7TMNKUPT6AXSLHOL6SRIW","short_pith_number":"pith:V5IVL7TM","canonical_record":{"source":{"id":"1304.0970","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-03T15:01:42Z","cross_cats_sorted":[],"title_canon_sha256":"d9fbb9e2e69275f49671b5db5be7850a801457c4e632abeeedeb63dbefeb76ac","abstract_canon_sha256":"6227769ab410028168c79a52a5ae72a1f0f03bdfc32f26f6f1c4ead0ffff889c"},"schema_version":"1.0"},"canonical_sha256":"af5155fe6c6aa8f9f81792cee5fa51459ec5417c3267f07ed70a90f3223e10ac","source":{"kind":"arxiv","id":"1304.0970","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0970","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0970v2","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0970","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"V5IVL7TMNKUP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V5IVL7TMNKUPT6AX","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V5IVL7TM","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V5IVL7TMNKUPT6AXSLHOL6SRIW","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0970","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-03T15:01:42Z","cross_cats_sorted":[],"title_canon_sha256":"d9fbb9e2e69275f49671b5db5be7850a801457c4e632abeeedeb63dbefeb76ac","abstract_canon_sha256":"6227769ab410028168c79a52a5ae72a1f0f03bdfc32f26f6f1c4ead0ffff889c"},"schema_version":"1.0"},"canonical_sha256":"af5155fe6c6aa8f9f81792cee5fa51459ec5417c3267f07ed70a90f3223e10ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:42.404691Z","signature_b64":"oyUgwkiBdNDxQz6gE0eWnoz4PdlnSguTffk/Vur249xJatlRshNKIwdGAU2WNk2HPQ4GrYT4gAvkq5Sl6YC/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af5155fe6c6aa8f9f81792cee5fa51459ec5417c3267f07ed70a90f3223e10ac","last_reissued_at":"2026-05-18T03:27:42.404223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:42.404223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0970","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":"2026-05-18T03:27:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYNfS8jrBxoql4jo5wRxwSx4Aos0tpqZOgyMM+D/jeJ4cACN0qHrAuW5C8akNF88uQJ9gJm5V18pHMLy3BlgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:19:15.995632Z"},"content_sha256":"499b802d82c62042cc5d64547d2a340ab7f94af79a571990488af195e9a5ef85","schema_version":"1.0","event_id":"sha256:499b802d82c62042cc5d64547d2a340ab7f94af79a571990488af195e9a5ef85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V5IVL7TMNKUPT6AXSLHOL6SRIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum one-cocycles for knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Thomas Fiedler","submitted_at":"2013-04-03T15:01:42Z","abstract_excerpt":"We give a method to construct non symmetric solutions of a global tetrahedron equation from solutions of the Yang-Baxter equation. The solution in the HOMFLYPT case gives rise to the first combinatorial quantum 1-cocycle which represents a non trivial cohomology class in the topological moduli space of long knots. We conjecture that the quotient of its values on Hatchers loop and on the rotation around the long axis is related to the simplicial volume of the knot complement in the 3-sphere and we prove this for the figure eight knot.\n  Surprisingly, the formula for the solution in the HOMFLYPT"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0970","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":"2026-05-18T03:27:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OK8bo0tjKN/w3r99yGAHGJ59G92eSuLZjavpq2N0Dk1Kj0hQMK3FnScGbrpPZ0PG16FRtiX9cf0qe51DqjMzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:19:15.995985Z"},"content_sha256":"cb0a5e8afad4bdf35f0df258eb75d60c93003e0c2e9d95b2f43501c01a1379f5","schema_version":"1.0","event_id":"sha256:cb0a5e8afad4bdf35f0df258eb75d60c93003e0c2e9d95b2f43501c01a1379f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5IVL7TMNKUPT6AXSLHOL6SRIW/bundle.json","state_url":"https://pith.science/pith/V5IVL7TMNKUPT6AXSLHOL6SRIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5IVL7TMNKUPT6AXSLHOL6SRIW/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":"2026-06-27T01:19:15Z","links":{"resolver":"https://pith.science/pith/V5IVL7TMNKUPT6AXSLHOL6SRIW","bundle":"https://pith.science/pith/V5IVL7TMNKUPT6AXSLHOL6SRIW/bundle.json","state":"https://pith.science/pith/V5IVL7TMNKUPT6AXSLHOL6SRIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5IVL7TMNKUPT6AXSLHOL6SRIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V5IVL7TMNKUPT6AXSLHOL6SRIW","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":"6227769ab410028168c79a52a5ae72a1f0f03bdfc32f26f6f1c4ead0ffff889c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-03T15:01:42Z","title_canon_sha256":"d9fbb9e2e69275f49671b5db5be7850a801457c4e632abeeedeb63dbefeb76ac"},"schema_version":"1.0","source":{"id":"1304.0970","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0970","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0970v2","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0970","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"V5IVL7TMNKUP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V5IVL7TMNKUPT6AX","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V5IVL7TM","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:cb0a5e8afad4bdf35f0df258eb75d60c93003e0c2e9d95b2f43501c01a1379f5","target":"graph","created_at":"2026-05-18T03:27:42Z","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 a method to construct non symmetric solutions of a global tetrahedron equation from solutions of the Yang-Baxter equation. The solution in the HOMFLYPT case gives rise to the first combinatorial quantum 1-cocycle which represents a non trivial cohomology class in the topological moduli space of long knots. We conjecture that the quotient of its values on Hatchers loop and on the rotation around the long axis is related to the simplicial volume of the knot complement in the 3-sphere and we prove this for the figure eight knot.\n  Surprisingly, the formula for the solution in the HOMFLYPT","authors_text":"Thomas Fiedler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-03T15:01:42Z","title":"Quantum one-cocycles for knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0970","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":"sha256:499b802d82c62042cc5d64547d2a340ab7f94af79a571990488af195e9a5ef85","target":"record","created_at":"2026-05-18T03:27:42Z","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":"6227769ab410028168c79a52a5ae72a1f0f03bdfc32f26f6f1c4ead0ffff889c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-03T15:01:42Z","title_canon_sha256":"d9fbb9e2e69275f49671b5db5be7850a801457c4e632abeeedeb63dbefeb76ac"},"schema_version":"1.0","source":{"id":"1304.0970","kind":"arxiv","version":2}},"canonical_sha256":"af5155fe6c6aa8f9f81792cee5fa51459ec5417c3267f07ed70a90f3223e10ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af5155fe6c6aa8f9f81792cee5fa51459ec5417c3267f07ed70a90f3223e10ac","first_computed_at":"2026-05-18T03:27:42.404223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:42.404223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oyUgwkiBdNDxQz6gE0eWnoz4PdlnSguTffk/Vur249xJatlRshNKIwdGAU2WNk2HPQ4GrYT4gAvkq5Sl6YC/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:42.404691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0970","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:499b802d82c62042cc5d64547d2a340ab7f94af79a571990488af195e9a5ef85","sha256:cb0a5e8afad4bdf35f0df258eb75d60c93003e0c2e9d95b2f43501c01a1379f5"],"state_sha256":"2e2e839a8caf753de892c952d05561f4bb64c9b841431e0611722e54d5980099"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zHTvaRQ1d8GLMtnsnoQBRQ88WlbsbfulIKA6o8QmrO4qEZFX6XHqoDRLaDf+c2SpT7Fb65zpUlRW5e3H5R+PDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:19:15.997834Z","bundle_sha256":"6aa202faed0a03c9d9d1ea67c5c1bec7eb2d6bc4e41e673b22a8abc72ba70f35"}}