{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KPLWIKPYRWLVOVPVJF3F4ZPHHM","short_pith_number":"pith:KPLWIKPY","schema_version":"1.0","canonical_sha256":"53d76429f88d975755f549765e65e73b1946b0d9b998e830c039bc8d16fadce8","source":{"kind":"arxiv","id":"1709.10332","version":5},"attestation_state":"computed","paper":{"title":"Knot polynomials from 1-cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Thomas Fiedler","submitted_at":"2017-09-28T17:41:53Z","abstract_excerpt":"Let $M_n$ be the topological moduli space of all parallel n-cables of long framed oriented knots in 3-space. We construct in a combinatorial way for each natural number $n>1$ a 1-cocycle $R_n$ which represents a non trivial class in $H^1(M_n; \\mathbb{Z} [x_1,x_2,...,x_1^{-1},x_2^{-1},...])$, where the number of variables $x_m$ depends on $n$. To each generic point in $M_n$ we associate in a canonical way an arc {\\em scan} in $M_n$, such that $R_n(scan)$ is already a polynomial knot invariant. We show that $R_3(scan)$ detects the non-invertibility of the knot $8_{17}$ in a very simple way and w"},"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":"1709.10332","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-09-28T17:41:53Z","cross_cats_sorted":[],"title_canon_sha256":"7756300bbc3ccea6c179a7f283c283a51c7d00e8f614666b0b97f8c6d605893d","abstract_canon_sha256":"322daff6d6747948641c12fec9b2f6c48a60cbf10ef5d775000e19e92e2dfd69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:15.461103Z","signature_b64":"Hy63S+Rggow2As4h1maSDztc4KsSukd8fmnqDGOpNPdbGP0M1QAD2Af2iK4iNsBZ+vIKa0FNVAOzOfmgBn33BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53d76429f88d975755f549765e65e73b1946b0d9b998e830c039bc8d16fadce8","last_reissued_at":"2026-05-17T23:56:15.460479Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:15.460479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Knot polynomials from 1-cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Thomas Fiedler","submitted_at":"2017-09-28T17:41:53Z","abstract_excerpt":"Let $M_n$ be the topological moduli space of all parallel n-cables of long framed oriented knots in 3-space. We construct in a combinatorial way for each natural number $n>1$ a 1-cocycle $R_n$ which represents a non trivial class in $H^1(M_n; \\mathbb{Z} [x_1,x_2,...,x_1^{-1},x_2^{-1},...])$, where the number of variables $x_m$ depends on $n$. To each generic point in $M_n$ we associate in a canonical way an arc {\\em scan} in $M_n$, such that $R_n(scan)$ is already a polynomial knot invariant. We show that $R_3(scan)$ detects the non-invertibility of the knot $8_{17}$ in a very simple way and w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10332","kind":"arxiv","version":5},"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":"1709.10332","created_at":"2026-05-17T23:56:15.460603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.10332v5","created_at":"2026-05-17T23:56:15.460603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10332","created_at":"2026-05-17T23:56:15.460603+00:00"},{"alias_kind":"pith_short_12","alias_value":"KPLWIKPYRWLV","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KPLWIKPYRWLVOVPV","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KPLWIKPY","created_at":"2026-05-18T12:31:24.725408+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/KPLWIKPYRWLVOVPVJF3F4ZPHHM","json":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM.json","graph_json":"https://pith.science/api/pith-number/KPLWIKPYRWLVOVPVJF3F4ZPHHM/graph.json","events_json":"https://pith.science/api/pith-number/KPLWIKPYRWLVOVPVJF3F4ZPHHM/events.json","paper":"https://pith.science/paper/KPLWIKPY"},"agent_actions":{"view_html":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM","download_json":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM.json","view_paper":"https://pith.science/paper/KPLWIKPY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.10332&json=true","fetch_graph":"https://pith.science/api/pith-number/KPLWIKPYRWLVOVPVJF3F4ZPHHM/graph.json","fetch_events":"https://pith.science/api/pith-number/KPLWIKPYRWLVOVPVJF3F4ZPHHM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM/action/storage_attestation","attest_author":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM/action/author_attestation","sign_citation":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM/action/citation_signature","submit_replication":"https://pith.science/pith/KPLWIKPYRWLVOVPVJF3F4ZPHHM/action/replication_record"}},"created_at":"2026-05-17T23:56:15.460603+00:00","updated_at":"2026-05-17T23:56:15.460603+00:00"}