{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5BARHQBMWOLLJNBO2RAHA44SKG","short_pith_number":"pith:5BARHQBM","canonical_record":{"source":{"id":"2410.17778","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-10-23T11:30:33Z","cross_cats_sorted":[],"title_canon_sha256":"e1214acebe9b8767728a557008fbefef6091ff1dfbddccf35a557a518b992d9f","abstract_canon_sha256":"6f3001885d9b0eeb97544ef3ea5a48e5fc569c64266b8846f6b52617a2755626"},"schema_version":"1.0"},"canonical_sha256":"e84113c02cb396b4b42ed440707392518fdcd559cec8b3b492ee9bb89c8cbb88","source":{"kind":"arxiv","id":"2410.17778","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17778","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17778v2","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17778","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"5BARHQBMWOLL","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"pith_short_16","alias_value":"5BARHQBMWOLLJNBO","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"pith_short_8","alias_value":"5BARHQBM","created_at":"2026-07-05T09:31:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5BARHQBMWOLLJNBO2RAHA44SKG","target":"record","payload":{"canonical_record":{"source":{"id":"2410.17778","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-10-23T11:30:33Z","cross_cats_sorted":[],"title_canon_sha256":"e1214acebe9b8767728a557008fbefef6091ff1dfbddccf35a557a518b992d9f","abstract_canon_sha256":"6f3001885d9b0eeb97544ef3ea5a48e5fc569c64266b8846f6b52617a2755626"},"schema_version":"1.0"},"canonical_sha256":"e84113c02cb396b4b42ed440707392518fdcd559cec8b3b492ee9bb89c8cbb88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:31:09.652628Z","signature_b64":"CM9byBmwzF1o8TZLBnj+CConk7rlAKWw8YYPlCuwuJuBHm7HC+yFv3Q8JALVidcR3IDhUIGIsTByr5D5Q6ZpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e84113c02cb396b4b42ed440707392518fdcd559cec8b3b492ee9bb89c8cbb88","last_reissued_at":"2026-07-05T09:31:09.652100Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:31:09.652100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.17778","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":"2026-07-05T09:31:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YkCuOIHFw+YsUABjoUCkwRn6piGmIL3ZUKTHa7Q79LO0cGUrOXTZIJ1Dl5WRrN2O39bK4ryUfpeD4qR5TFAmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:47:09.039872Z"},"content_sha256":"823c6fadf862caf9f6cf6438dd65289a865c8dc648788bf45b33aaa4dc0eddea","schema_version":"1.0","event_id":"sha256:823c6fadf862caf9f6cf6438dd65289a865c8dc648788bf45b33aaa4dc0eddea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5BARHQBMWOLLJNBO2RAHA44SKG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determinant of the OU matrix of a braid diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ayaka Shimizu, Yoshiro Yaguchi","submitted_at":"2024-10-23T11:30:33Z","abstract_excerpt":"In this paper, we define the OU matrix of a braid diagram and discuss how the OU matrix reflects the warping degree or the layeredness of the braid diagram, and show that the determinant of the OU matrix of a layered braid diagram is the product of the determinants of the layers. We also introduce invariants of positive braids which are derived from the OU matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17778","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/2410.17778/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":"2026-07-05T09:31:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1WkwmzcV8/OkDakMzNPHG1PctJCri8aN2f6uwWBTcT1mugFUvRSYdSbe9QW7ie9MhNWHHEgCEDmYiALk0ZLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:47:09.040444Z"},"content_sha256":"f64b6849eabfe5120e695f5343aeb924c23d28e1a20531e89b134f9ec02437bb","schema_version":"1.0","event_id":"sha256:f64b6849eabfe5120e695f5343aeb924c23d28e1a20531e89b134f9ec02437bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5BARHQBMWOLLJNBO2RAHA44SKG/bundle.json","state_url":"https://pith.science/pith/5BARHQBMWOLLJNBO2RAHA44SKG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5BARHQBMWOLLJNBO2RAHA44SKG/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":"2026-08-16T14:47:09Z","links":{"resolver":"https://pith.science/pith/5BARHQBMWOLLJNBO2RAHA44SKG","bundle":"https://pith.science/pith/5BARHQBMWOLLJNBO2RAHA44SKG/bundle.json","state":"https://pith.science/pith/5BARHQBMWOLLJNBO2RAHA44SKG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5BARHQBMWOLLJNBO2RAHA44SKG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5BARHQBMWOLLJNBO2RAHA44SKG","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":"6f3001885d9b0eeb97544ef3ea5a48e5fc569c64266b8846f6b52617a2755626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-10-23T11:30:33Z","title_canon_sha256":"e1214acebe9b8767728a557008fbefef6091ff1dfbddccf35a557a518b992d9f"},"schema_version":"1.0","source":{"id":"2410.17778","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17778","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17778v2","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17778","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"5BARHQBMWOLL","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"pith_short_16","alias_value":"5BARHQBMWOLLJNBO","created_at":"2026-07-05T09:31:09Z"},{"alias_kind":"pith_short_8","alias_value":"5BARHQBM","created_at":"2026-07-05T09:31:09Z"}],"graph_snapshots":[{"event_id":"sha256:f64b6849eabfe5120e695f5343aeb924c23d28e1a20531e89b134f9ec02437bb","target":"graph","created_at":"2026-07-05T09:31:09Z","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/2410.17778/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we define the OU matrix of a braid diagram and discuss how the OU matrix reflects the warping degree or the layeredness of the braid diagram, and show that the determinant of the OU matrix of a layered braid diagram is the product of the determinants of the layers. We also introduce invariants of positive braids which are derived from the OU matrix.","authors_text":"Ayaka Shimizu, Yoshiro Yaguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-10-23T11:30:33Z","title":"Determinant of the OU matrix of a braid diagram"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17778","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":"sha256:823c6fadf862caf9f6cf6438dd65289a865c8dc648788bf45b33aaa4dc0eddea","target":"record","created_at":"2026-07-05T09:31:09Z","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":"6f3001885d9b0eeb97544ef3ea5a48e5fc569c64266b8846f6b52617a2755626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-10-23T11:30:33Z","title_canon_sha256":"e1214acebe9b8767728a557008fbefef6091ff1dfbddccf35a557a518b992d9f"},"schema_version":"1.0","source":{"id":"2410.17778","kind":"arxiv","version":2}},"canonical_sha256":"e84113c02cb396b4b42ed440707392518fdcd559cec8b3b492ee9bb89c8cbb88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e84113c02cb396b4b42ed440707392518fdcd559cec8b3b492ee9bb89c8cbb88","first_computed_at":"2026-07-05T09:31:09.652100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:31:09.652100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CM9byBmwzF1o8TZLBnj+CConk7rlAKWw8YYPlCuwuJuBHm7HC+yFv3Q8JALVidcR3IDhUIGIsTByr5D5Q6ZpDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:31:09.652628Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.17778","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:823c6fadf862caf9f6cf6438dd65289a865c8dc648788bf45b33aaa4dc0eddea","sha256:f64b6849eabfe5120e695f5343aeb924c23d28e1a20531e89b134f9ec02437bb"],"state_sha256":"7960394497191c323b6ab917dab202e8824fe71250c86aaabd561392ed7078d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTHuJQfSjlh1CCjASUXykTpaeQKsOJRk+HU74mQr6mKRDPi6hBBaYpiylvXyve9oQfCbCQNOqciB6W3C5WFxBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:47:09.045624Z","bundle_sha256":"f95fd9c184965d499ab807dfe0323c096542b4d1a1a3dbe8e4358173a3dd4edf"}}