{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:OYWKHDR3ZW4HDZU4AR4VFIJVNI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4bb64de8685e332ebdc136e04bd83acba1a8809a1af5614db9b2f0268997ff81","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GT","submitted_at":"2000-12-21T13:06:04Z","title_canon_sha256":"f3383b56a0b8c6cd812cd230be5c4d616b8c89e34647cefe8fade92c4b295024"},"schema_version":"1.0","source":{"id":"math/0012216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0012216","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0012216v1","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0012216","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"OYWKHDR3ZW4H","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"OYWKHDR3ZW4HDZU4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"OYWKHDR3","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:273540a5890f6b23292ef3f649c7b0d133742fce55197ef21f63a4c8cfb8016c","target":"graph","created_at":"2026-05-18T02:41:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Yasushi Kasahara","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2000-12-21T13:06:04Z","title":"An expansion of the Jones representation of genus 2 and the Torelli group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0012216","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4016e8cba5a92bda7c0999328cefc92c9016c262da53c77b91f98fda861af015","target":"record","created_at":"2026-05-18T02:41:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4bb64de8685e332ebdc136e04bd83acba1a8809a1af5614db9b2f0268997ff81","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GT","submitted_at":"2000-12-21T13:06:04Z","title_canon_sha256":"f3383b56a0b8c6cd812cd230be5c4d616b8c89e34647cefe8fade92c4b295024"},"schema_version":"1.0","source":{"id":"math/0012216","kind":"arxiv","version":1}},"canonical_sha256":"762ca38e3bcdb871e69c047952a1356a15ab2c17cdb4e792fef8441e20e69231","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"762ca38e3bcdb871e69c047952a1356a15ab2c17cdb4e792fef8441e20e69231","first_computed_at":"2026-05-18T02:41:33.359392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:33.359392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uz6643QiRjkNyw23lGl1H5waCa3+tXtf+19P57ks/bCti0I3qt4+V70im0if9qKN8Q7d5M4P7LzBJCe1hudQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:33.359878Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0012216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4016e8cba5a92bda7c0999328cefc92c9016c262da53c77b91f98fda861af015","sha256:273540a5890f6b23292ef3f649c7b0d133742fce55197ef21f63a4c8cfb8016c"],"state_sha256":"b3365cae3033b22db14e31987d676b8727e1cb83746ce61a7eb34520ea235fc5"}