{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NLB2XOQIMJU2CJ7H2ASZU4U5DQ","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":"2c4ac5ddceac2bd8c90da836eb057b03fafdb5174058ec324cdfe181f3a805f9","cross_cats_sorted":["math.GT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-09T13:45:34Z","title_canon_sha256":"eeef0b5e3c7e5ff42835d393d83677b1a651829cd61d13563c08506b6e2694d4"},"schema_version":"1.0","source":{"id":"1901.02743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02743","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02743v1","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02743","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"NLB2XOQIMJU2","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NLB2XOQIMJU2CJ7H","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NLB2XOQI","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:8600df96749d84db51b17cdd25d9ca6435e6c774bffcfb491ac81d07e40826f1","target":"graph","created_at":"2026-05-17T23:39:47Z","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 study a topological aspect of rank-1 double affine Hecke algebra (DAHA). Clarified is a relationship between the DAHA of A1-type (resp. CC1-type) and the skein algebra on a once-punctured torus (resp. a 4-punctured sphere), and the SL(2;Z) actions of DAHAs are identified with the Dehn twists on the surfaces. Combining these two types of DAHA, we construct the DAHA representation for the skein algebra on a genus-two surface, and we propose a DAHA polynomial for a double-torus knot, which is a simple closed curve on a genus two Heegaard surface in S3. Discussed is a relationship between the D","authors_text":"Kazuhiro Hikami","cross_cats":["math.GT","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-09T13:45:34Z","title":"DAHA and skein algebra on surface: double-torus knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02743","kind":"arxiv","version":1},"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":"sha256:89375b5321168eeabb937f558a8f816224d0e3d05c05ac7e0fad4a5644c88aaf","target":"record","created_at":"2026-05-17T23:39:47Z","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":"2c4ac5ddceac2bd8c90da836eb057b03fafdb5174058ec324cdfe181f3a805f9","cross_cats_sorted":["math.GT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-09T13:45:34Z","title_canon_sha256":"eeef0b5e3c7e5ff42835d393d83677b1a651829cd61d13563c08506b6e2694d4"},"schema_version":"1.0","source":{"id":"1901.02743","kind":"arxiv","version":1}},"canonical_sha256":"6ac3abba086269a127e7d0259a729d1c31bf6feaa0dfd41dcc93428fbb6ed66b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ac3abba086269a127e7d0259a729d1c31bf6feaa0dfd41dcc93428fbb6ed66b","first_computed_at":"2026-05-17T23:39:47.429223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:47.429223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sn/usK/1pdek6h9Nbys6glJSzA2YrHcUwc90DjvYfcYDRyVz8TySqXTA8XR0gciLnbxkxGdRdaQHg5HZf7pGCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:47.429818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89375b5321168eeabb937f558a8f816224d0e3d05c05ac7e0fad4a5644c88aaf","sha256:8600df96749d84db51b17cdd25d9ca6435e6c774bffcfb491ac81d07e40826f1"],"state_sha256":"01179500599c78ba326dda9697c030bb0762ad97325750a2a1463e92e3927c98"}