{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:PI7REREK4NOBTG22SAVPGAULRN","short_pith_number":"pith:PI7REREK","schema_version":"1.0","canonical_sha256":"7a3f12448ae35c199b5a902af3028b8b6c5d6d4e5bae8e6c647ee141ba1443f7","source":{"kind":"arxiv","id":"math/0504305","version":2},"attestation_state":"computed","paper":{"title":"The C-polynomial of a knot","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Stavros Garoufalidis, Xinyu Sun","submitted_at":"2005-04-14T19:19:03Z","abstract_excerpt":"In an earlier paper the first author defined a non-commutative A-polynomial for knots in 3-space, using the colored Jones function. The idea is that the colored Jones function of a knot satisfies a non-trivial linear q-difference equation. Said differently, the colored Jones function of a knot is annihilated by a non-zero ideal of the Weyl algebra which is generalted (after localization) by the non-commutative A-polynomial of a knot.\n  In that paper, it was conjectured that this polynomial (which has to do with representations of the quantum group U_q(SL_2)) specializes at q=1 to the better kn"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0504305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-04-14T19:19:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"50df967cc7ac2fd4429a8a7fb0e92baf16e7a50c7248c10f0e4e5e4c60c0bb2b","abstract_canon_sha256":"8c2b06245004e01756539440770bebb533788258aacae10bcfc6387ca4877cee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:41:56.893806Z","signature_b64":"iDrhSeCXd5xoXzbAaF3RmtYvyoe2yqrgFAbaPXvvKw+GUCJ3yqiQ3mFhjEmcAxWbloFAjEqZfKUB1WqewgkyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a3f12448ae35c199b5a902af3028b8b6c5d6d4e5bae8e6c647ee141ba1443f7","last_reissued_at":"2026-07-04T15:41:56.893431Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:41:56.893431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The C-polynomial of a knot","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Stavros Garoufalidis, Xinyu Sun","submitted_at":"2005-04-14T19:19:03Z","abstract_excerpt":"In an earlier paper the first author defined a non-commutative A-polynomial for knots in 3-space, using the colored Jones function. The idea is that the colored Jones function of a knot satisfies a non-trivial linear q-difference equation. Said differently, the colored Jones function of a knot is annihilated by a non-zero ideal of the Weyl algebra which is generalted (after localization) by the non-commutative A-polynomial of a knot.\n  In that paper, it was conjectured that this polynomial (which has to do with representations of the quantum group U_q(SL_2)) specializes at q=1 to the better kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504305","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0504305/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0504305","created_at":"2026-07-04T15:41:56.893495+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0504305v2","created_at":"2026-07-04T15:41:56.893495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504305","created_at":"2026-07-04T15:41:56.893495+00:00"},{"alias_kind":"pith_short_12","alias_value":"PI7REREK4NOB","created_at":"2026-07-04T15:41:56.893495+00:00"},{"alias_kind":"pith_short_16","alias_value":"PI7REREK4NOBTG22","created_at":"2026-07-04T15:41:56.893495+00:00"},{"alias_kind":"pith_short_8","alias_value":"PI7REREK","created_at":"2026-07-04T15:41:56.893495+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2606.24497","citing_title":"More on Kashaev limits of the quantum $A$-polynomials","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2605.31588","citing_title":"Two roles of Alexander in two Kashaev phases","ref_index":78,"is_internal_anchor":true},{"citing_arxiv_id":"2605.22560","citing_title":"Shading A-polynomials via huge representations of $U_q(\\mathfrak{su}_N)$","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN","json":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN.json","graph_json":"https://pith.science/api/pith-number/PI7REREK4NOBTG22SAVPGAULRN/graph.json","events_json":"https://pith.science/api/pith-number/PI7REREK4NOBTG22SAVPGAULRN/events.json","paper":"https://pith.science/paper/PI7REREK"},"agent_actions":{"view_html":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN","download_json":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN.json","view_paper":"https://pith.science/paper/PI7REREK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0504305&json=true","fetch_graph":"https://pith.science/api/pith-number/PI7REREK4NOBTG22SAVPGAULRN/graph.json","fetch_events":"https://pith.science/api/pith-number/PI7REREK4NOBTG22SAVPGAULRN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN/action/storage_attestation","attest_author":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN/action/author_attestation","sign_citation":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN/action/citation_signature","submit_replication":"https://pith.science/pith/PI7REREK4NOBTG22SAVPGAULRN/action/replication_record"}},"created_at":"2026-07-04T15:41:56.893495+00:00","updated_at":"2026-07-04T15:41:56.893495+00:00"}