{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:C4B7QMOO25QHQUG77ACHP36JHZ","short_pith_number":"pith:C4B7QMOO","canonical_record":{"source":{"id":"1210.7574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-29T06:25:17Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"552068fabcb771d1442ba8264ec276d116513413090bdb0dca796b562437f065","abstract_canon_sha256":"62d15ec047944420f609a48fae3ac60fe799f31801751985245d80883d74c5e6"},"schema_version":"1.0"},"canonical_sha256":"1703f831ced7607850dff80477efc93e4dc61c3d45a00040abb3beea72892e72","source":{"kind":"arxiv","id":"1210.7574","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7574","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7574v2","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7574","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"C4B7QMOO25QH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C4B7QMOO25QHQUG7","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C4B7QMOO","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:C4B7QMOO25QHQUG77ACHP36JHZ","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-29T06:25:17Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"552068fabcb771d1442ba8264ec276d116513413090bdb0dca796b562437f065","abstract_canon_sha256":"62d15ec047944420f609a48fae3ac60fe799f31801751985245d80883d74c5e6"},"schema_version":"1.0"},"canonical_sha256":"1703f831ced7607850dff80477efc93e4dc61c3d45a00040abb3beea72892e72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:38.237024Z","signature_b64":"YrzEM4leQIFKssS2DVSiZcHg5PQNvB/hKDUZQe1NUP+0omEYtzY/ZAgASlwoLN5nwIUsyYE5Nhh4P2ib9t1MBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1703f831ced7607850dff80477efc93e4dc61c3d45a00040abb3beea72892e72","last_reissued_at":"2026-05-18T03:40:38.236387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:38.236387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7574","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":"2026-05-18T03:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/KzHT/BPJrVT/Oic6MLBwlPA0tJcITIh2NY8FRzDk7bTVa+eT+U0H/YJJt8LUX1+IKPfpp5Oiv+kniVVh00BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:18:21.149945Z"},"content_sha256":"9e4e7066e643020d2514cfc60debac4c960943c6e43d2ea9cd36e1a9c0d1f9a6","schema_version":"1.0","event_id":"sha256:9e4e7066e643020d2514cfc60debac4c960943c6e43d2ea9cd36e1a9c0d1f9a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:C4B7QMOO25QHQUG77ACHP36JHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the formulae for the colored HOMFLY polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.GT","authors_text":"Kenichi Kawagoe","submitted_at":"2012-10-29T06:25:17Z","abstract_excerpt":"We provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are obtained. As an application, we calculate some examples for hyperbolic knots and links, and we study a generalization of the volume conjecture by means of numerical calculations. In these examples, we observe that asymptotic behaviors of invariants seem to have relations to the volume conjecure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7574","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":"2026-05-18T03:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8dXHAPicdGsHGw9eb7kv5BXyMTB+65Arak5hnQsJYopBBfFqPDxlExeXfDzfO20D9ZOfUwgKAdIhwsYWZgMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:18:21.150299Z"},"content_sha256":"9fbbea993fcf8b7b7af9e80275d92341bd62865343c6129137491541e3241121","schema_version":"1.0","event_id":"sha256:9fbbea993fcf8b7b7af9e80275d92341bd62865343c6129137491541e3241121"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4B7QMOO25QHQUG77ACHP36JHZ/bundle.json","state_url":"https://pith.science/pith/C4B7QMOO25QHQUG77ACHP36JHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4B7QMOO25QHQUG77ACHP36JHZ/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":"2026-06-24T07:18:21Z","links":{"resolver":"https://pith.science/pith/C4B7QMOO25QHQUG77ACHP36JHZ","bundle":"https://pith.science/pith/C4B7QMOO25QHQUG77ACHP36JHZ/bundle.json","state":"https://pith.science/pith/C4B7QMOO25QHQUG77ACHP36JHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4B7QMOO25QHQUG77ACHP36JHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C4B7QMOO25QHQUG77ACHP36JHZ","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":"62d15ec047944420f609a48fae3ac60fe799f31801751985245d80883d74c5e6","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-29T06:25:17Z","title_canon_sha256":"552068fabcb771d1442ba8264ec276d116513413090bdb0dca796b562437f065"},"schema_version":"1.0","source":{"id":"1210.7574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7574","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7574v2","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7574","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"C4B7QMOO25QH","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C4B7QMOO25QHQUG7","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C4B7QMOO","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:9fbbea993fcf8b7b7af9e80275d92341bd62865343c6129137491541e3241121","target":"graph","created_at":"2026-05-18T03:40:38Z","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 provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are obtained. As an application, we calculate some examples for hyperbolic knots and links, and we study a generalization of the volume conjecture by means of numerical calculations. In these examples, we observe that asymptotic behaviors of invariants seem to have relations to the volume conjecure.","authors_text":"Kenichi Kawagoe","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-29T06:25:17Z","title":"On the formulae for the colored HOMFLY polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7574","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":"sha256:9e4e7066e643020d2514cfc60debac4c960943c6e43d2ea9cd36e1a9c0d1f9a6","target":"record","created_at":"2026-05-18T03:40:38Z","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":"62d15ec047944420f609a48fae3ac60fe799f31801751985245d80883d74c5e6","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-29T06:25:17Z","title_canon_sha256":"552068fabcb771d1442ba8264ec276d116513413090bdb0dca796b562437f065"},"schema_version":"1.0","source":{"id":"1210.7574","kind":"arxiv","version":2}},"canonical_sha256":"1703f831ced7607850dff80477efc93e4dc61c3d45a00040abb3beea72892e72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1703f831ced7607850dff80477efc93e4dc61c3d45a00040abb3beea72892e72","first_computed_at":"2026-05-18T03:40:38.236387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:38.236387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YrzEM4leQIFKssS2DVSiZcHg5PQNvB/hKDUZQe1NUP+0omEYtzY/ZAgASlwoLN5nwIUsyYE5Nhh4P2ib9t1MBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:38.237024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e4e7066e643020d2514cfc60debac4c960943c6e43d2ea9cd36e1a9c0d1f9a6","sha256:9fbbea993fcf8b7b7af9e80275d92341bd62865343c6129137491541e3241121"],"state_sha256":"bdc1b5e944c51910cde71cf69b185d44de24c6559f9880b534c5b68d6ccd71de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqZg4KKfp9pUuiY7dXqwQwtdrMlWPmhgLlvtc/BaYS+yGNtjEnNIR4srXHJZCRF1Uej3zgGUjOrVjFGLoiV7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:18:21.152334Z","bundle_sha256":"cbd783861a016cecc316700a086e68a07841819c331fec99c362f3b69f1d812c"}}