{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:2GPCLUAMGYAWLZHQRWVTAN4TSD","short_pith_number":"pith:2GPCLUAM","canonical_record":{"source":{"id":"2308.07291","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-08-14T17:27:53Z","cross_cats_sorted":[],"title_canon_sha256":"f24bcae7be71bd7e89c9cbe9e7fabddd1acdd3dd68fd5ab007910c78644e59ba","abstract_canon_sha256":"e7479e6120f639199e079d0fc3d637c4da6d561932b8b16f404af911ca17067e"},"schema_version":"1.0"},"canonical_sha256":"d19e25d00c360165e4f08dab30379390f025f9300b9a008a82e70167ea0e6cc4","source":{"kind":"arxiv","id":"2308.07291","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.07291","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"arxiv_version","alias_value":"2308.07291v2","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.07291","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"pith_short_12","alias_value":"2GPCLUAMGYAW","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"pith_short_16","alias_value":"2GPCLUAMGYAWLZHQ","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"pith_short_8","alias_value":"2GPCLUAM","created_at":"2026-07-05T07:25:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:2GPCLUAMGYAWLZHQRWVTAN4TSD","target":"record","payload":{"canonical_record":{"source":{"id":"2308.07291","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-08-14T17:27:53Z","cross_cats_sorted":[],"title_canon_sha256":"f24bcae7be71bd7e89c9cbe9e7fabddd1acdd3dd68fd5ab007910c78644e59ba","abstract_canon_sha256":"e7479e6120f639199e079d0fc3d637c4da6d561932b8b16f404af911ca17067e"},"schema_version":"1.0"},"canonical_sha256":"d19e25d00c360165e4f08dab30379390f025f9300b9a008a82e70167ea0e6cc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:25:44.113426Z","signature_b64":"4i9qrFdfaMoCbt8UdNtSApJQxuiRlIRXmYOyJkjyssDGOqAqdJHpHR8sKZSTT01cPnMDuIzdzEJHuqZlsyWWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d19e25d00c360165e4f08dab30379390f025f9300b9a008a82e70167ea0e6cc4","last_reissued_at":"2026-07-05T07:25:44.112927Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:25:44.112927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.07291","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":"2026-07-05T07:25:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V7vL4CaLjxW1JtF6bLUWcIcfislrv1Iomor4b1GZdoEKyEWa1wEHyXg2OFXs101bguvsQv1kS4EdUDbQb2/zBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:47:52.822347Z"},"content_sha256":"1a021978ccb0b492bf3827c8292446529860bfa38ca51182f74319a3a6df2563","schema_version":"1.0","event_id":"sha256:1a021978ccb0b492bf3827c8292446529860bfa38ca51182f74319a3a6df2563"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:2GPCLUAMGYAWLZHQRWVTAN4TSD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Passing from plat closure to standard closure of braids in $\\mathbb{R}^3$, in handlebodies and in thickened surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Paolo Cavicchioli, Sofia Lambropoulou","submitted_at":"2023-08-14T17:27:53Z","abstract_excerpt":"Given a knot or link in the form of plat closure of a braid, we describe an algorithm to obtain a braid representing the same knot or link with the standard closure, and vice-versa. We analyze the three cases of knots and links: in \\(\\mathbb{R}^3\\), in handlebodies and in thickened surfaces. We show that the algorithm is quadratic in the number of crossings and loop generators of the braid when passing from plat to standard closure, while it is linear when passing from standard to plat closure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07291","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.07291/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:25:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPktocNu83YvIkc1hxaESDpDdu6NOIN5Wt8jdW6zZa4tJwphK6r5G5arBcbauXKx6pRN9EiI92bZH8A7x5H5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:47:52.822722Z"},"content_sha256":"9bc38c684363d8fbdc18b3fcf2e58cf29b3e46a835648f55595bab1ffb925ac1","schema_version":"1.0","event_id":"sha256:9bc38c684363d8fbdc18b3fcf2e58cf29b3e46a835648f55595bab1ffb925ac1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2GPCLUAMGYAWLZHQRWVTAN4TSD/bundle.json","state_url":"https://pith.science/pith/2GPCLUAMGYAWLZHQRWVTAN4TSD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2GPCLUAMGYAWLZHQRWVTAN4TSD/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":"2026-07-06T21:47:52Z","links":{"resolver":"https://pith.science/pith/2GPCLUAMGYAWLZHQRWVTAN4TSD","bundle":"https://pith.science/pith/2GPCLUAMGYAWLZHQRWVTAN4TSD/bundle.json","state":"https://pith.science/pith/2GPCLUAMGYAWLZHQRWVTAN4TSD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2GPCLUAMGYAWLZHQRWVTAN4TSD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2GPCLUAMGYAWLZHQRWVTAN4TSD","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":"e7479e6120f639199e079d0fc3d637c4da6d561932b8b16f404af911ca17067e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-08-14T17:27:53Z","title_canon_sha256":"f24bcae7be71bd7e89c9cbe9e7fabddd1acdd3dd68fd5ab007910c78644e59ba"},"schema_version":"1.0","source":{"id":"2308.07291","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.07291","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"arxiv_version","alias_value":"2308.07291v2","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.07291","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"pith_short_12","alias_value":"2GPCLUAMGYAW","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"pith_short_16","alias_value":"2GPCLUAMGYAWLZHQ","created_at":"2026-07-05T07:25:44Z"},{"alias_kind":"pith_short_8","alias_value":"2GPCLUAM","created_at":"2026-07-05T07:25:44Z"}],"graph_snapshots":[{"event_id":"sha256:9bc38c684363d8fbdc18b3fcf2e58cf29b3e46a835648f55595bab1ffb925ac1","target":"graph","created_at":"2026-07-05T07:25:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.07291/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a knot or link in the form of plat closure of a braid, we describe an algorithm to obtain a braid representing the same knot or link with the standard closure, and vice-versa. We analyze the three cases of knots and links: in \\(\\mathbb{R}^3\\), in handlebodies and in thickened surfaces. We show that the algorithm is quadratic in the number of crossings and loop generators of the braid when passing from plat to standard closure, while it is linear when passing from standard to plat closure.","authors_text":"Paolo Cavicchioli, Sofia Lambropoulou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-08-14T17:27:53Z","title":"Passing from plat closure to standard closure of braids in $\\mathbb{R}^3$, in handlebodies and in thickened surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07291","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":"sha256:1a021978ccb0b492bf3827c8292446529860bfa38ca51182f74319a3a6df2563","target":"record","created_at":"2026-07-05T07:25:44Z","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":"e7479e6120f639199e079d0fc3d637c4da6d561932b8b16f404af911ca17067e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-08-14T17:27:53Z","title_canon_sha256":"f24bcae7be71bd7e89c9cbe9e7fabddd1acdd3dd68fd5ab007910c78644e59ba"},"schema_version":"1.0","source":{"id":"2308.07291","kind":"arxiv","version":2}},"canonical_sha256":"d19e25d00c360165e4f08dab30379390f025f9300b9a008a82e70167ea0e6cc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d19e25d00c360165e4f08dab30379390f025f9300b9a008a82e70167ea0e6cc4","first_computed_at":"2026-07-05T07:25:44.112927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:25:44.112927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4i9qrFdfaMoCbt8UdNtSApJQxuiRlIRXmYOyJkjyssDGOqAqdJHpHR8sKZSTT01cPnMDuIzdzEJHuqZlsyWWBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:25:44.113426Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.07291","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a021978ccb0b492bf3827c8292446529860bfa38ca51182f74319a3a6df2563","sha256:9bc38c684363d8fbdc18b3fcf2e58cf29b3e46a835648f55595bab1ffb925ac1"],"state_sha256":"517c2d876bcb0ad4026f1222546e0339f6dd60a9f18ab23fbf1a76d631033f05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2uFN6zOUBvBn2HEm/+Pd0tXeYyEJU3hW9B+A/2ONpO4kvpJuB+MIdCxy80gKNrwfEVCoj+AYkkzEjv7hOQwEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T21:47:52.824719Z","bundle_sha256":"6c92e7d9d599e1189cd655364e5cb5823acf614d06de904d0d421ea3c322691c"}}