{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LA5BEAAPNJ7XMI62J25XOMVODG","short_pith_number":"pith:LA5BEAAP","schema_version":"1.0","canonical_sha256":"583a12000f6a7f7623da4ebb7732ae1983633e5b6bfc3eedbdcbcecadb7d5b67","source":{"kind":"arxiv","id":"1112.2654","version":2},"attestation_state":"computed","paper":{"title":"Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"A. Mironov, A. Morozov, An. Morozov","submitted_at":"2011-12-12T18:40:39Z","abstract_excerpt":"Character expansion is introduced and explicitly constructed for the (non-colored) HOMFLY polynomials of the simplest knots. Expansion coefficients are not the knot invariants and can depend on the choice of the braid realization. However, the method provides the simplest systematic way to construct HOMFLY polynomials directly in terms of the variable A=q^N: a much better way than the standard approach making use of the skein relations. Moreover, representation theory of the simplest quantum group SU_q(2) is sufficient to get the answers for all braids with m<5 strands. Most important we revea"},"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":"1112.2654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-12-12T18:40:39Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"1512ac27e49c7be7a02acca266ea66455aaa1d0aa0123e2ee5a62f5c9c3934e4","abstract_canon_sha256":"acaaf3b2986db882189c6e6396eb0e52323d879a930d96857ccef4a0a2e9a897"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:11.607889Z","signature_b64":"wu0QxPOBef6PcFAjnFnkSVqNSIyr9VCtK2PAPO1rvN/FswnnZd/Ymxe8JoYI/9rv/iLScmI3mZ7fHj94t2G8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"583a12000f6a7f7623da4ebb7732ae1983633e5b6bfc3eedbdcbcecadb7d5b67","last_reissued_at":"2026-05-18T01:59:11.607081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:11.607081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"A. Mironov, A. Morozov, An. Morozov","submitted_at":"2011-12-12T18:40:39Z","abstract_excerpt":"Character expansion is introduced and explicitly constructed for the (non-colored) HOMFLY polynomials of the simplest knots. Expansion coefficients are not the knot invariants and can depend on the choice of the braid realization. However, the method provides the simplest systematic way to construct HOMFLY polynomials directly in terms of the variable A=q^N: a much better way than the standard approach making use of the skein relations. Moreover, representation theory of the simplest quantum group SU_q(2) is sufficient to get the answers for all braids with m<5 strands. Most important we revea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2654","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.2654","created_at":"2026-05-18T01:59:11.607217+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.2654v2","created_at":"2026-05-18T01:59:11.607217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2654","created_at":"2026-05-18T01:59:11.607217+00:00"},{"alias_kind":"pith_short_12","alias_value":"LA5BEAAPNJ7X","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LA5BEAAPNJ7XMI62","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LA5BEAAP","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":7,"internal_anchor_count":5,"sample":[{"citing_arxiv_id":"2505.10629","citing_title":"The HZ character expansion and a hyperbolic extension of torus knots","ref_index":4,"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":31,"is_internal_anchor":true},{"citing_arxiv_id":"2507.03116","citing_title":"Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2603.03628","citing_title":"A relation between the HOMFLY-PT and Kauffman polynomials via characters","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2603.21688","citing_title":"Racah matrices for the symmetric representation of the SO(5) group","ref_index":5,"is_internal_anchor":true},{"citing_arxiv_id":"2605.04016","citing_title":"Entangling gates for the SU(N) anyons","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01584","citing_title":"Reductions in Khovanov-Rozansky operator formalism","ref_index":29,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG","json":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG.json","graph_json":"https://pith.science/api/pith-number/LA5BEAAPNJ7XMI62J25XOMVODG/graph.json","events_json":"https://pith.science/api/pith-number/LA5BEAAPNJ7XMI62J25XOMVODG/events.json","paper":"https://pith.science/paper/LA5BEAAP"},"agent_actions":{"view_html":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG","download_json":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG.json","view_paper":"https://pith.science/paper/LA5BEAAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.2654&json=true","fetch_graph":"https://pith.science/api/pith-number/LA5BEAAPNJ7XMI62J25XOMVODG/graph.json","fetch_events":"https://pith.science/api/pith-number/LA5BEAAPNJ7XMI62J25XOMVODG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG/action/storage_attestation","attest_author":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG/action/author_attestation","sign_citation":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG/action/citation_signature","submit_replication":"https://pith.science/pith/LA5BEAAPNJ7XMI62J25XOMVODG/action/replication_record"}},"created_at":"2026-05-18T01:59:11.607217+00:00","updated_at":"2026-05-18T01:59:11.607217+00:00"}