{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:F3ZVMPJKM7G5VGQL7TZR4OOO7K","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":"91f73c074e40914390dcf5a3dedd209c3430ce82331826c6607a44798fb2c2e7","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.GT","submitted_at":"2005-06-20T13:50:48Z","title_canon_sha256":"5ac21c719618589840799533f88c94c48bcc6da19b4c7e06ee4d45535a691ee5"},"schema_version":"1.0","source":{"id":"math/0506397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506397","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506397v1","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506397","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"F3ZVMPJKM7G5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"F3ZVMPJKM7G5VGQL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"F3ZVMPJK","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:904bb29236ff4a41d2270b47c1941cca4b2ea6f11fba0fd930134781310a009e","target":"graph","created_at":"2026-05-18T02:37:59Z","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":"Pursueing our investigations on the relations between Thompson groups and mapping class groups, we introduce the group $T^*$ (and its further generalizations) which is an extension of the Ptolemy-Thompson group $T$ by means of the full braid group $B_{\\infty}$ on infinitely many strands. We prove that it is a finitely presented group with solvable word problem, and give an explicit presentation of it.","authors_text":"Christophe Kapoudjian, Louis Funar","cross_cats":["math.GR"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2005-06-20T13:50:48Z","title":"The braided Ptolemy-Thompson group is finitely presented"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506397","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":"sha256:928af16c05b0a9449a70629d0a8cd33ad4021721f3a5a52fbdaa8048c59335ba","target":"record","created_at":"2026-05-18T02:37:59Z","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":"91f73c074e40914390dcf5a3dedd209c3430ce82331826c6607a44798fb2c2e7","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.GT","submitted_at":"2005-06-20T13:50:48Z","title_canon_sha256":"5ac21c719618589840799533f88c94c48bcc6da19b4c7e06ee4d45535a691ee5"},"schema_version":"1.0","source":{"id":"math/0506397","kind":"arxiv","version":1}},"canonical_sha256":"2ef3563d2a67cdda9a0bfcf31e39cefabaf0e79557fec0d2785555370700642f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ef3563d2a67cdda9a0bfcf31e39cefabaf0e79557fec0d2785555370700642f","first_computed_at":"2026-05-18T02:37:59.759942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.759942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ASd+qnisOa1N82ITk1lup8zQKEGgpcCy2XJrwmuDyZelXsCyeUewL8zknQTIydcjy8x5KlhK8KIdFAKYG6WTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.760433Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:928af16c05b0a9449a70629d0a8cd33ad4021721f3a5a52fbdaa8048c59335ba","sha256:904bb29236ff4a41d2270b47c1941cca4b2ea6f11fba0fd930134781310a009e"],"state_sha256":"533adcaa37387f232d540eef8efc2324d799007d1bb66d8d5ce15fc0b1d3f7a3"}