{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:OYWKHDR3ZW4HDZU4AR4VFIJVNI","short_pith_number":"pith:OYWKHDR3","schema_version":"1.0","canonical_sha256":"762ca38e3bcdb871e69c047952a1356a15ab2c17cdb4e792fef8441e20e69231","source":{"kind":"arxiv","id":"math/0012216","version":1},"attestation_state":"computed","paper":{"title":"An expansion of the Jones representation of genus 2 and the Torelli group","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Yasushi Kasahara","submitted_at":"2000-12-21T13:06:04Z","abstract_excerpt":"We study the algebraic property of the representation of the mapping class group of a closed oriented surface of genus 2 constructed by VFR Jones [Annals of Math. 126 (1987) 335-388]. It arises from the Iwahori-Hecke algebra representations of Artin's braid group of 6 strings, and is defined over integral Laurent polynomials Z[t, t^{-1}]. We substitute the parameter t with -e^{h}, and then expand the powers e^h in their Taylor series. This expansion naturally induces a filtration on the Torelli group which is coarser than its lower central series. We present some results on the structure of th"},"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/0012216","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2000-12-21T13:06:04Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f3383b56a0b8c6cd812cd230be5c4d616b8c89e34647cefe8fade92c4b295024","abstract_canon_sha256":"4bb64de8685e332ebdc136e04bd83acba1a8809a1af5614db9b2f0268997ff81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:33.359878Z","signature_b64":"Uz6643QiRjkNyw23lGl1H5waCa3+tXtf+19P57ks/bCti0I3qt4+V70im0if9qKN8Q7d5M4P7LzBJCe1hudQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"762ca38e3bcdb871e69c047952a1356a15ab2c17cdb4e792fef8441e20e69231","last_reissued_at":"2026-05-18T02:41:33.359392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:33.359392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An expansion of the Jones representation of genus 2 and the Torelli group","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Yasushi Kasahara","submitted_at":"2000-12-21T13:06:04Z","abstract_excerpt":"We study the algebraic property of the representation of the mapping class group of a closed oriented surface of genus 2 constructed by VFR Jones [Annals of Math. 126 (1987) 335-388]. It arises from the Iwahori-Hecke algebra representations of Artin's braid group of 6 strings, and is defined over integral Laurent polynomials Z[t, t^{-1}]. We substitute the parameter t with -e^{h}, and then expand the powers e^h in their Taylor series. This expansion naturally induces a filtration on the Torelli group which is coarser than its lower central series. We present some results on the structure of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0012216","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":"math/0012216","created_at":"2026-05-18T02:41:33.359447+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0012216v1","created_at":"2026-05-18T02:41:33.359447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0012216","created_at":"2026-05-18T02:41:33.359447+00:00"},{"alias_kind":"pith_short_12","alias_value":"OYWKHDR3ZW4H","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"OYWKHDR3ZW4HDZU4","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"OYWKHDR3","created_at":"2026-05-18T12:25:50.254431+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/OYWKHDR3ZW4HDZU4AR4VFIJVNI","json":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI.json","graph_json":"https://pith.science/api/pith-number/OYWKHDR3ZW4HDZU4AR4VFIJVNI/graph.json","events_json":"https://pith.science/api/pith-number/OYWKHDR3ZW4HDZU4AR4VFIJVNI/events.json","paper":"https://pith.science/paper/OYWKHDR3"},"agent_actions":{"view_html":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI","download_json":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI.json","view_paper":"https://pith.science/paper/OYWKHDR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0012216&json=true","fetch_graph":"https://pith.science/api/pith-number/OYWKHDR3ZW4HDZU4AR4VFIJVNI/graph.json","fetch_events":"https://pith.science/api/pith-number/OYWKHDR3ZW4HDZU4AR4VFIJVNI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI/action/storage_attestation","attest_author":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI/action/author_attestation","sign_citation":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI/action/citation_signature","submit_replication":"https://pith.science/pith/OYWKHDR3ZW4HDZU4AR4VFIJVNI/action/replication_record"}},"created_at":"2026-05-18T02:41:33.359447+00:00","updated_at":"2026-05-18T02:41:33.359447+00:00"}