{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KPJGEF26QL4RHJ74X3AXWLW4KG","short_pith_number":"pith:KPJGEF26","schema_version":"1.0","canonical_sha256":"53d262175e82f913a7fcbec17b2edc51bda70f1dae3660baa216d0e3fef0a503","source":{"kind":"arxiv","id":"1504.06327","version":1},"attestation_state":"computed","paper":{"title":"Knots, BPS states, and algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"hep-th","authors_text":"Piotr Kucharski, Piotr Su{\\l}kowski, Stavros Garoufalidis","submitted_at":"2015-04-23T20:00:51Z","abstract_excerpt":"We analyze relations between BPS degeneracies related to Labastida-Marino-Ooguri-Vafa (LMOV) invariants, and algebraic curves associated to knots. We introduce a new class of such curves that we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the corresponding (extremal) BPS degeneracies. These formulas lead to nontrivial integrality statements in number theory, as well as to an improved integrality conjecture stronger than the known M-theory integrality predictions. Furthermore we determine the BPS degeneracies encoded in augmenta"},"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":"1504.06327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-23T20:00:51Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3c8ed43d69b27da558bfe9d9d2b5f4cefe8dd38767a440fbcea08b3f6a4cc1f1","abstract_canon_sha256":"09ba4e5e4dd1559f8cb0da060d8966f8318e783595f4af8115b809ab20c0e510"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:10.155829Z","signature_b64":"1AispmJH5Qh/jTFnpBvysXOr5KBISTDrk1T3kJHjUhQi5/LGEpYWsfy81LnJyDIjpq5VkvlJyhvxt1V6caUwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53d262175e82f913a7fcbec17b2edc51bda70f1dae3660baa216d0e3fef0a503","last_reissued_at":"2026-05-18T00:44:10.155188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:10.155188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Knots, BPS states, and algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"hep-th","authors_text":"Piotr Kucharski, Piotr Su{\\l}kowski, Stavros Garoufalidis","submitted_at":"2015-04-23T20:00:51Z","abstract_excerpt":"We analyze relations between BPS degeneracies related to Labastida-Marino-Ooguri-Vafa (LMOV) invariants, and algebraic curves associated to knots. We introduce a new class of such curves that we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the corresponding (extremal) BPS degeneracies. These formulas lead to nontrivial integrality statements in number theory, as well as to an improved integrality conjecture stronger than the known M-theory integrality predictions. Furthermore we determine the BPS degeneracies encoded in augmenta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06327","kind":"arxiv","version":1},"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":"1504.06327","created_at":"2026-05-18T00:44:10.155293+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06327v1","created_at":"2026-05-18T00:44:10.155293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06327","created_at":"2026-05-18T00:44:10.155293+00:00"},{"alias_kind":"pith_short_12","alias_value":"KPJGEF26QL4R","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KPJGEF26QL4RHJ74","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KPJGEF26","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG","json":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG.json","graph_json":"https://pith.science/api/pith-number/KPJGEF26QL4RHJ74X3AXWLW4KG/graph.json","events_json":"https://pith.science/api/pith-number/KPJGEF26QL4RHJ74X3AXWLW4KG/events.json","paper":"https://pith.science/paper/KPJGEF26"},"agent_actions":{"view_html":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG","download_json":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG.json","view_paper":"https://pith.science/paper/KPJGEF26","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06327&json=true","fetch_graph":"https://pith.science/api/pith-number/KPJGEF26QL4RHJ74X3AXWLW4KG/graph.json","fetch_events":"https://pith.science/api/pith-number/KPJGEF26QL4RHJ74X3AXWLW4KG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG/action/storage_attestation","attest_author":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG/action/author_attestation","sign_citation":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG/action/citation_signature","submit_replication":"https://pith.science/pith/KPJGEF26QL4RHJ74X3AXWLW4KG/action/replication_record"}},"created_at":"2026-05-18T00:44:10.155293+00:00","updated_at":"2026-05-18T00:44:10.155293+00:00"}