{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ATO4AN4PRU5AQAGEIDUGVGCOYY","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":"fb4b0c138ba883ea2ac7de3b66f150b1529c32424aa72f227f9f8ac605e8a432","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-26T07:12:22Z","title_canon_sha256":"ad6b99529657ca13c789e62d85224ec945db35ce14d61a95857137b0064ce197"},"schema_version":"1.0","source":{"id":"1008.4443","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4443","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4443v3","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4443","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"ATO4AN4PRU5A","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ATO4AN4PRU5AQAGE","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ATO4AN4P","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:c4568d0df99d1fcc63615f49f441feb549262fc5a7b15386fb2b2b925d5b1d01","target":"graph","created_at":"2026-05-18T00:44:46Z","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 introduce three spectral sequences which give some expressions of colored Jones polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of them are derived from a bicomplex of the colored Jones polynomial. The other is the spectral sequence that deduces a colored Rasmussen invariant of links. We also introduce three functors between categories of nanophrases, generalizations of links, and obtain their applications using colored Jones polynomials and their categorifications.","authors_text":"Noboru Ito","cross_cats":["math.CO","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-26T07:12:22Z","title":"Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4443","kind":"arxiv","version":3},"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":"sha256:079bdc1231f338f2f01d792a808d395f4f51df7404e910c643313b5a410b4862","target":"record","created_at":"2026-05-18T00:44:46Z","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":"fb4b0c138ba883ea2ac7de3b66f150b1529c32424aa72f227f9f8ac605e8a432","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-26T07:12:22Z","title_canon_sha256":"ad6b99529657ca13c789e62d85224ec945db35ce14d61a95857137b0064ce197"},"schema_version":"1.0","source":{"id":"1008.4443","kind":"arxiv","version":3}},"canonical_sha256":"04ddc0378f8d3a0800c440e86a984ec63bd8c33741388a4f0f0fac2561965165","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04ddc0378f8d3a0800c440e86a984ec63bd8c33741388a4f0f0fac2561965165","first_computed_at":"2026-05-18T00:44:46.464340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:46.464340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pj2lhOjzPxJ/OS1dnoL2mBFgwvygkxMWk9q4dpolcRKIusPJhRtWjr6IoTzJPJLmH2DjT5SI7lDtTUOH9grjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:46.464807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4443","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:079bdc1231f338f2f01d792a808d395f4f51df7404e910c643313b5a410b4862","sha256:c4568d0df99d1fcc63615f49f441feb549262fc5a7b15386fb2b2b925d5b1d01"],"state_sha256":"97c79603eb99a4d81807fce12fd9d519b5b0ad13c0ed92f6048f8291609111d4"}