{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:V2VYWFADWCQSFZU6PBK3BSP37H","short_pith_number":"pith:V2VYWFAD","canonical_record":{"source":{"id":"1807.01500","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-04T09:42:46Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f66be8a482090c4b2613e87506ed504486683ae9936e045c8ed5be29c366a40a","abstract_canon_sha256":"8b35af2c831e7c35a9b34adbbcc22ea41fbf762691a90c746f2703a25264914e"},"schema_version":"1.0"},"canonical_sha256":"aeab8b1403b0a122e69e7855b0c9fbf9f1efcf1a1fff1e8d2e0bd037bba39413","source":{"kind":"arxiv","id":"1807.01500","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01500","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01500v3","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01500","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"V2VYWFADWCQS","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V2VYWFADWCQSFZU6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V2VYWFAD","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:V2VYWFADWCQSFZU6PBK3BSP37H","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01500","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-04T09:42:46Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f66be8a482090c4b2613e87506ed504486683ae9936e045c8ed5be29c366a40a","abstract_canon_sha256":"8b35af2c831e7c35a9b34adbbcc22ea41fbf762691a90c746f2703a25264914e"},"schema_version":"1.0"},"canonical_sha256":"aeab8b1403b0a122e69e7855b0c9fbf9f1efcf1a1fff1e8d2e0bd037bba39413","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:33.515674Z","signature_b64":"EajLQfLEHEiGORr0evpbWeWXqhW1gApYcNbABSjfEMEe5uSXDdsfyxm8RNlfCtW0N4vIZM20hE7PnNA+sYymDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeab8b1403b0a122e69e7855b0c9fbf9f1efcf1a1fff1e8d2e0bd037bba39413","last_reissued_at":"2026-05-17T23:49:33.514918Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:33.514918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01500","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M10D2fXXsK6zrKaFEFIDd9UY1goGxCzkv2ANdAwiu+TzwuMnJV4/2Z8O1GvUH1zeQ8Nf03wLWobWWdpCqBVrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:18:31.903130Z"},"content_sha256":"71f546f04d94d1fe81bc18389bdef1cc25bab1da2a4233d2e6757e0a05080326","schema_version":"1.0","event_id":"sha256:71f546f04d94d1fe81bc18389bdef1cc25bab1da2a4233d2e6757e0a05080326"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:V2VYWFADWCQSFZU6PBK3BSP37H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Garside theory and subsurfaces: some examples in braid groups","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Bert Wiest, Saul Schleimer","submitted_at":"2018-07-04T09:42:46Z","abstract_excerpt":"Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomial in the length of the braids. In this paper we suggest a more precise bound: for rigid braids with $N$ strands and of Garside length $L$, the sliding circuit set should have at most $C\\cdot L^{N-2}$ elements, for some constant $C$. We construct a family of braids which realise t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01500","kind":"arxiv","version":3},"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":"2026-05-17T23:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qUKfeIXLB+YZx1JbUdWEn0D5lCDlHCC5iab/uRXsbfDd1fWmIrNX7kV5liYqDJ24wX1LZ43a61e6t2KCf/lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:18:31.903851Z"},"content_sha256":"4f06d6b41e026aa689bf12f98d925a58083a894eff02aa545a56015b396060f7","schema_version":"1.0","event_id":"sha256:4f06d6b41e026aa689bf12f98d925a58083a894eff02aa545a56015b396060f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V2VYWFADWCQSFZU6PBK3BSP37H/bundle.json","state_url":"https://pith.science/pith/V2VYWFADWCQSFZU6PBK3BSP37H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V2VYWFADWCQSFZU6PBK3BSP37H/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":"2026-06-08T05:18:31Z","links":{"resolver":"https://pith.science/pith/V2VYWFADWCQSFZU6PBK3BSP37H","bundle":"https://pith.science/pith/V2VYWFADWCQSFZU6PBK3BSP37H/bundle.json","state":"https://pith.science/pith/V2VYWFADWCQSFZU6PBK3BSP37H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V2VYWFADWCQSFZU6PBK3BSP37H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V2VYWFADWCQSFZU6PBK3BSP37H","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":"8b35af2c831e7c35a9b34adbbcc22ea41fbf762691a90c746f2703a25264914e","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-04T09:42:46Z","title_canon_sha256":"f66be8a482090c4b2613e87506ed504486683ae9936e045c8ed5be29c366a40a"},"schema_version":"1.0","source":{"id":"1807.01500","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01500","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01500v3","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01500","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"V2VYWFADWCQS","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V2VYWFADWCQSFZU6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V2VYWFAD","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:4f06d6b41e026aa689bf12f98d925a58083a894eff02aa545a56015b396060f7","target":"graph","created_at":"2026-05-17T23:49:33Z","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":"Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomial in the length of the braids. In this paper we suggest a more precise bound: for rigid braids with $N$ strands and of Garside length $L$, the sliding circuit set should have at most $C\\cdot L^{N-2}$ elements, for some constant $C$. We construct a family of braids which realise t","authors_text":"Bert Wiest, Saul Schleimer","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-04T09:42:46Z","title":"Garside theory and subsurfaces: some examples in braid groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01500","kind":"arxiv","version":3},"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":"sha256:71f546f04d94d1fe81bc18389bdef1cc25bab1da2a4233d2e6757e0a05080326","target":"record","created_at":"2026-05-17T23:49:33Z","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":"8b35af2c831e7c35a9b34adbbcc22ea41fbf762691a90c746f2703a25264914e","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2018-07-04T09:42:46Z","title_canon_sha256":"f66be8a482090c4b2613e87506ed504486683ae9936e045c8ed5be29c366a40a"},"schema_version":"1.0","source":{"id":"1807.01500","kind":"arxiv","version":3}},"canonical_sha256":"aeab8b1403b0a122e69e7855b0c9fbf9f1efcf1a1fff1e8d2e0bd037bba39413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeab8b1403b0a122e69e7855b0c9fbf9f1efcf1a1fff1e8d2e0bd037bba39413","first_computed_at":"2026-05-17T23:49:33.514918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:33.514918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EajLQfLEHEiGORr0evpbWeWXqhW1gApYcNbABSjfEMEe5uSXDdsfyxm8RNlfCtW0N4vIZM20hE7PnNA+sYymDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:33.515674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01500","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71f546f04d94d1fe81bc18389bdef1cc25bab1da2a4233d2e6757e0a05080326","sha256:4f06d6b41e026aa689bf12f98d925a58083a894eff02aa545a56015b396060f7"],"state_sha256":"17fbbbc10491bcccab7a35d4b628dd195c5c62aaea44adc146e963a06bd0f99d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vUr10runXw/FnRK+fmYyY0190FIG5/64dmzrraHQRW4/VKh/PVJAHFV5eMhjO4zblx/p8R+FkZWThHWvyduWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T05:18:31.907609Z","bundle_sha256":"283fe7753f04b4a1062c7818506364e140c8a1502964fa127b6e907f76489869"}}