{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:FRT6WIREMBUHBFWW77WFTMMYKC","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":"e8dda0f9e86a92bea386273856c7b6e74045ec2f36b901e3a6e3e2520509bde9","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-05-21T04:14:52Z","title_canon_sha256":"b049ef2e4c12a5ed4ce27cf3322db4d020f38364b92c1250a7aff76fb2f152d1"},"schema_version":"1.0","source":{"id":"math/0405403","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0405403","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0405403v6","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0405403","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"FRT6WIREMBUH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"FRT6WIREMBUHBFWW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"FRT6WIRE","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:adc75a6dd65994f87c1ee672525331a3f879214f43fe983a231d8d35ed9ad380","target":"graph","created_at":"2026-05-18T02:41:32Z","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 show that the Alexander-Conway polynomial Delta is obtainable via a particular one-variable reduction of each two-variable Links-Gould invariant LG^{m,1}, where m is a positive integer. Thus there exist infinitely many two-variable generalisations of Delta. This result is not obvious since in the reduction, the representation of the braid group generator used to define LG^{m,1} does not satisfy a second-order characteristic identity unless m=1. To demonstrate that the one-variable reduction of LG^{m,1} satisfies the defining skein relation of Delta, we evaluate the kernel of a quantum trace","authors_text":"Atsushi Ishii, David De Wit, Jon Links","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-05-21T04:14:52Z","title":"Infinitely many two-variable generalisations of the Alexander-Conway polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405403","kind":"arxiv","version":6},"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":"sha256:264eda108ea79a9c7965f0b8f53c4121fc560cb7b0c01a40c09fc2d9e613a7d8","target":"record","created_at":"2026-05-18T02:41:32Z","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":"e8dda0f9e86a92bea386273856c7b6e74045ec2f36b901e3a6e3e2520509bde9","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-05-21T04:14:52Z","title_canon_sha256":"b049ef2e4c12a5ed4ce27cf3322db4d020f38364b92c1250a7aff76fb2f152d1"},"schema_version":"1.0","source":{"id":"math/0405403","kind":"arxiv","version":6}},"canonical_sha256":"2c67eb222460687096d6ffec59b19850834d997b89df48021df2ca586b1c9050","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c67eb222460687096d6ffec59b19850834d997b89df48021df2ca586b1c9050","first_computed_at":"2026-05-18T02:41:32.425717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:32.425717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Pb7UQzE386Ml66QQKNzOcJM+BKj5m94bAOOdZccx+N7m67FPP/34EBoMPEXYCxvU8k9PnTUhzC6wwohTFaMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:32.426100Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0405403","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:264eda108ea79a9c7965f0b8f53c4121fc560cb7b0c01a40c09fc2d9e613a7d8","sha256:adc75a6dd65994f87c1ee672525331a3f879214f43fe983a231d8d35ed9ad380"],"state_sha256":"c0bf987ec839b5e9cdffad24a6478c5c1dacb2fa7c3a89a71180b84b8e3b10ea"}