{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:C4S4ON7RR3TOHLB7ASXV4DE6NO","short_pith_number":"pith:C4S4ON7R","schema_version":"1.0","canonical_sha256":"1725c737f18ee6e3ac3f04af5e0c9e6b9badf3371e0c21f1b682b7c915fc80dd","source":{"kind":"arxiv","id":"1609.04077","version":2},"attestation_state":"computed","paper":{"title":"From skein theory to presentations for Thompson group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Yunxiang Ren","submitted_at":"2016-09-14T00:24:30Z","abstract_excerpt":"Jones introduced unitary representations of Thompson group $F$ starting from a given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these representations. Moreover, all oriented links arise as matrix coefficients of a subgroup $\\vec{F}$ which is the stabilizer of a certain vector. Later Golan and Sapir determined the subgroup $\\vec{F}$ and showed many interesting properties. In this paper, we investigate into a large class of groups which arises as subgroups of Thompson group $F$ and reveal the relation between the skein theory of the subfactor planar algebr"},"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":"1609.04077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-09-14T00:24:30Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"2c43a5a1e4a6e23b547f082703e9e466a9656ce0393a5d2a541206d4ac4a8d61","abstract_canon_sha256":"2e3a879089d499882d0cadd6dd8d041ae9c797e0922a613f0cf26ad96087e1ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:40.387626Z","signature_b64":"S3YgWqrHMA3UkGrAvR/GbIaBKFz/AHkrkMul9ODL5/SCY6EkF8rK7XmVzxLSzyjVU682K+nfLRhjPwEX1+7oCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1725c737f18ee6e3ac3f04af5e0c9e6b9badf3371e0c21f1b682b7c915fc80dd","last_reissued_at":"2026-05-18T01:03:40.387165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:40.387165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From skein theory to presentations for Thompson group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Yunxiang Ren","submitted_at":"2016-09-14T00:24:30Z","abstract_excerpt":"Jones introduced unitary representations of Thompson group $F$ starting from a given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these representations. Moreover, all oriented links arise as matrix coefficients of a subgroup $\\vec{F}$ which is the stabilizer of a certain vector. Later Golan and Sapir determined the subgroup $\\vec{F}$ and showed many interesting properties. In this paper, we investigate into a large class of groups which arises as subgroups of Thompson group $F$ and reveal the relation between the skein theory of the subfactor planar algebr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04077","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":"1609.04077","created_at":"2026-05-18T01:03:40.387239+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04077v2","created_at":"2026-05-18T01:03:40.387239+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04077","created_at":"2026-05-18T01:03:40.387239+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4S4ON7RR3TO","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4S4ON7RR3TOHLB7","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4S4ON7R","created_at":"2026-05-18T12:30:09.641336+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/C4S4ON7RR3TOHLB7ASXV4DE6NO","json":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO.json","graph_json":"https://pith.science/api/pith-number/C4S4ON7RR3TOHLB7ASXV4DE6NO/graph.json","events_json":"https://pith.science/api/pith-number/C4S4ON7RR3TOHLB7ASXV4DE6NO/events.json","paper":"https://pith.science/paper/C4S4ON7R"},"agent_actions":{"view_html":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO","download_json":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO.json","view_paper":"https://pith.science/paper/C4S4ON7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04077&json=true","fetch_graph":"https://pith.science/api/pith-number/C4S4ON7RR3TOHLB7ASXV4DE6NO/graph.json","fetch_events":"https://pith.science/api/pith-number/C4S4ON7RR3TOHLB7ASXV4DE6NO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/action/storage_attestation","attest_author":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/action/author_attestation","sign_citation":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/action/citation_signature","submit_replication":"https://pith.science/pith/C4S4ON7RR3TOHLB7ASXV4DE6NO/action/replication_record"}},"created_at":"2026-05-18T01:03:40.387239+00:00","updated_at":"2026-05-18T01:03:40.387239+00:00"}