{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:GGZXDVJEJGYRXALXUZQ4VFKKMJ","short_pith_number":"pith:GGZXDVJE","canonical_record":{"source":{"id":"math/0603548","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2006-03-22T23:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"fe1cabb8dc7ecf7bf35dc9238a64ad6de5bb675b3d5e6a0c2287c3a45734dce3","abstract_canon_sha256":"8eb4ac05c498a26864de4f7adbc8c6e55a57c5c00cb03a98bbe8c020142ce935"},"schema_version":"1.0"},"canonical_sha256":"31b371d52449b11b8177a661ca954a62456f79d15f0a201a584cf86c64912c21","source":{"kind":"arxiv","id":"math/0603548","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603548","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603548v2","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603548","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"GGZXDVJEJGYR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GGZXDVJEJGYRXALX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GGZXDVJE","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:GGZXDVJEJGYRXALXUZQ4VFKKMJ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0603548","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2006-03-22T23:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"fe1cabb8dc7ecf7bf35dc9238a64ad6de5bb675b3d5e6a0c2287c3a45734dce3","abstract_canon_sha256":"8eb4ac05c498a26864de4f7adbc8c6e55a57c5c00cb03a98bbe8c020142ce935"},"schema_version":"1.0"},"canonical_sha256":"31b371d52449b11b8177a661ca954a62456f79d15f0a201a584cf86c64912c21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:49.679218Z","signature_b64":"zcJWshyLRHJMAaUVQPSS52lK85LmlF8LroxUYODQDEjIr9b6XBhllO29NWvivSwObeSIkz4W1Ya5q2Xqo6OvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31b371d52449b11b8177a661ca954a62456f79d15f0a201a584cf86c64912c21","last_reissued_at":"2026-05-18T00:20:49.678498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:49.678498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0603548","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7J8v3SXAnfsbxYpreGlmMbKYwOLtrTgNpb1MXDyLgRypmZb2WGmHZRMOfKiZOWHnMk60/OtwYlZnsiiLZOGmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T09:19:49.291308Z"},"content_sha256":"8e3e22a6b3da4a8d9077fc4cb45bfab34ca3aa0ec286359dba0f8e38e94e80a1","schema_version":"1.0","event_id":"sha256:8e3e22a6b3da4a8d9077fc4cb45bfab34ca3aa0ec286359dba0f8e38e94e80a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:GGZXDVJEJGYRXALXUZQ4VFKKMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pure braid subgroups of braided Thompson's groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jose Burillo, Melanie Stein, Sean Cleary, Thomas Brady","submitted_at":"2006-03-22T23:36:59Z","abstract_excerpt":"We describe pure braided versions of Thompson's group F. These groups, $BF$ and $\\hat{BF}$, are subgroups of the braided versions of Thompson's group V, introduced by Brin and Dehornoy. Unlike V, elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe infinite and finite presentations of these groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603548","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AT0U+BNNA4RjtgjKk/Tm2QTch9ZNuXfnkdMeGFRH+A7Xvxlej3r9nhIrI4Zx+Wb0mBLnQdV1L7F/GA8Av9yADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T09:19:49.292043Z"},"content_sha256":"e29254628267e4737439db082e90f8a8fcd61a05ddcddd16b214ab3e6ee99894","schema_version":"1.0","event_id":"sha256:e29254628267e4737439db082e90f8a8fcd61a05ddcddd16b214ab3e6ee99894"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGZXDVJEJGYRXALXUZQ4VFKKMJ/bundle.json","state_url":"https://pith.science/pith/GGZXDVJEJGYRXALXUZQ4VFKKMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGZXDVJEJGYRXALXUZQ4VFKKMJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T09:19:49Z","links":{"resolver":"https://pith.science/pith/GGZXDVJEJGYRXALXUZQ4VFKKMJ","bundle":"https://pith.science/pith/GGZXDVJEJGYRXALXUZQ4VFKKMJ/bundle.json","state":"https://pith.science/pith/GGZXDVJEJGYRXALXUZQ4VFKKMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGZXDVJEJGYRXALXUZQ4VFKKMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:GGZXDVJEJGYRXALXUZQ4VFKKMJ","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":"8eb4ac05c498a26864de4f7adbc8c6e55a57c5c00cb03a98bbe8c020142ce935","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2006-03-22T23:36:59Z","title_canon_sha256":"fe1cabb8dc7ecf7bf35dc9238a64ad6de5bb675b3d5e6a0c2287c3a45734dce3"},"schema_version":"1.0","source":{"id":"math/0603548","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0603548","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0603548v2","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603548","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"GGZXDVJEJGYR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GGZXDVJEJGYRXALX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GGZXDVJE","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:e29254628267e4737439db082e90f8a8fcd61a05ddcddd16b214ab3e6ee99894","target":"graph","created_at":"2026-05-18T00:20:49Z","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 describe pure braided versions of Thompson's group F. These groups, $BF$ and $\\hat{BF}$, are subgroups of the braided versions of Thompson's group V, introduced by Brin and Dehornoy. Unlike V, elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe infinite and finite presentations of these groups.","authors_text":"Jose Burillo, Melanie Stein, Sean Cleary, Thomas Brady","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2006-03-22T23:36:59Z","title":"Pure braid subgroups of braided Thompson's groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603548","kind":"arxiv","version":2},"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":"sha256:8e3e22a6b3da4a8d9077fc4cb45bfab34ca3aa0ec286359dba0f8e38e94e80a1","target":"record","created_at":"2026-05-18T00:20:49Z","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":"8eb4ac05c498a26864de4f7adbc8c6e55a57c5c00cb03a98bbe8c020142ce935","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2006-03-22T23:36:59Z","title_canon_sha256":"fe1cabb8dc7ecf7bf35dc9238a64ad6de5bb675b3d5e6a0c2287c3a45734dce3"},"schema_version":"1.0","source":{"id":"math/0603548","kind":"arxiv","version":2}},"canonical_sha256":"31b371d52449b11b8177a661ca954a62456f79d15f0a201a584cf86c64912c21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31b371d52449b11b8177a661ca954a62456f79d15f0a201a584cf86c64912c21","first_computed_at":"2026-05-18T00:20:49.678498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:49.678498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zcJWshyLRHJMAaUVQPSS52lK85LmlF8LroxUYODQDEjIr9b6XBhllO29NWvivSwObeSIkz4W1Ya5q2Xqo6OvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:49.679218Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0603548","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e3e22a6b3da4a8d9077fc4cb45bfab34ca3aa0ec286359dba0f8e38e94e80a1","sha256:e29254628267e4737439db082e90f8a8fcd61a05ddcddd16b214ab3e6ee99894"],"state_sha256":"5fa7c78080481d34a2766d4f773b411deee2c384ef8e4a6b1099a5b2fe9cc7c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j9B1SFCKRnol2ZcdPRNM7FSF0r3/GCMhMFe6IlNIsRk8aT1OaeRcUpnChpXaELo0ZU6wtFCL/TCHLXEH452zBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T09:19:49.296071Z","bundle_sha256":"8d3a52fe86764e2db7ca7263b217ef93d2222d3f66d5dad8e4ad1571e840b9b1"}}