{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YYSCELE2RNUKBKXVKQQ4DLSXUB","short_pith_number":"pith:YYSCELE2","canonical_record":{"source":{"id":"1703.09322","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-27T22:03:35Z","cross_cats_sorted":[],"title_canon_sha256":"1c57e0777cc5e59ddfc3860111184e930c7314df31278ede379dab875ca2ed42","abstract_canon_sha256":"430ad69c9b7390687d7f686d3649213a621defb7e9e9f201c7fa39fbf1e181de"},"schema_version":"1.0"},"canonical_sha256":"c624222c9a8b68a0aaf55421c1ae57a04b3fa411587390ceaab5fc9652ec8f78","source":{"kind":"arxiv","id":"1703.09322","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09322","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09322v4","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09322","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"YYSCELE2RNUK","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YYSCELE2RNUKBKXV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YYSCELE2","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YYSCELE2RNUKBKXVKQQ4DLSXUB","target":"record","payload":{"canonical_record":{"source":{"id":"1703.09322","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-27T22:03:35Z","cross_cats_sorted":[],"title_canon_sha256":"1c57e0777cc5e59ddfc3860111184e930c7314df31278ede379dab875ca2ed42","abstract_canon_sha256":"430ad69c9b7390687d7f686d3649213a621defb7e9e9f201c7fa39fbf1e181de"},"schema_version":"1.0"},"canonical_sha256":"c624222c9a8b68a0aaf55421c1ae57a04b3fa411587390ceaab5fc9652ec8f78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:32.558660Z","signature_b64":"vhd1idNRUfJiAYio1dmUzthjUzr67NdXuXwubXC8F8tgjcEgS+TW+c3JiSGOQQPuI+h28WxbOgpGszwlkgrzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c624222c9a8b68a0aaf55421c1ae57a04b3fa411587390ceaab5fc9652ec8f78","last_reissued_at":"2026-05-18T00:32:32.557904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:32.557904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.09322","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZki8ALSHeJpi+NXWAdXA6t5H3o6nI9LM7M4no1FBwdxWbcg0bUkjQW7YNXzHZRFmmhveth1VbWxBOrb34vlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:45:32.812286Z"},"content_sha256":"9c36bbabf825e5b67d99feb5a85f5fc2a4a87d8e25ebad89fc799e458ac0441f","schema_version":"1.0","event_id":"sha256:9c36bbabf825e5b67d99feb5a85f5fc2a4a87d8e25ebad89fc799e458ac0441f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YYSCELE2RNUKBKXVKQQ4DLSXUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The defect of Bennequin-Eliashberg inequality and Bennequin surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Keiko Kawamuro, Tetsuya Ito","submitted_at":"2017-03-27T22:03:35Z","abstract_excerpt":"For a null-homologous transverse link $\\mathcal T$ in a general contact manifold with an open book, we explore strongly quasipositive braids and Bennequin surfaces. We define the defect $\\delta(\\mathcal T)$ of the Bennequin-Eliashberg inequality.\n  We study relations between $\\delta(\\mathcal T)$ and minimal genus Bennequin surfaces of $\\mathcal T$. In particular, in the disk open book case, under some large fractional Dehn twist coefficient assumption, we show that $\\delta(\\mathcal T)=N$ if and only if $\\mathcal T$ is the boundary of a Bennequin surface with exactly $N$ negatively twisted band"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09322","kind":"arxiv","version":4},"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":"2026-05-18T00:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzHIq5X34P9B03Dyac3hFUM4xJclPQfOkl01opRKCqiE/jhpXJ+2bGYmz+sCdnubmodcwnvmVeuOHgvIMQmKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:45:32.812646Z"},"content_sha256":"34a4741a3ac60df7b66cd654450b595f07d11555cf06f7ca9c8527fea3ea349b","schema_version":"1.0","event_id":"sha256:34a4741a3ac60df7b66cd654450b595f07d11555cf06f7ca9c8527fea3ea349b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYSCELE2RNUKBKXVKQQ4DLSXUB/bundle.json","state_url":"https://pith.science/pith/YYSCELE2RNUKBKXVKQQ4DLSXUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYSCELE2RNUKBKXVKQQ4DLSXUB/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":"2026-06-05T15:45:32Z","links":{"resolver":"https://pith.science/pith/YYSCELE2RNUKBKXVKQQ4DLSXUB","bundle":"https://pith.science/pith/YYSCELE2RNUKBKXVKQQ4DLSXUB/bundle.json","state":"https://pith.science/pith/YYSCELE2RNUKBKXVKQQ4DLSXUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYSCELE2RNUKBKXVKQQ4DLSXUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YYSCELE2RNUKBKXVKQQ4DLSXUB","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":"430ad69c9b7390687d7f686d3649213a621defb7e9e9f201c7fa39fbf1e181de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-27T22:03:35Z","title_canon_sha256":"1c57e0777cc5e59ddfc3860111184e930c7314df31278ede379dab875ca2ed42"},"schema_version":"1.0","source":{"id":"1703.09322","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09322","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09322v4","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09322","created_at":"2026-05-18T00:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"YYSCELE2RNUK","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YYSCELE2RNUKBKXV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YYSCELE2","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:34a4741a3ac60df7b66cd654450b595f07d11555cf06f7ca9c8527fea3ea349b","target":"graph","created_at":"2026-05-18T00:32:32Z","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":"For a null-homologous transverse link $\\mathcal T$ in a general contact manifold with an open book, we explore strongly quasipositive braids and Bennequin surfaces. We define the defect $\\delta(\\mathcal T)$ of the Bennequin-Eliashberg inequality.\n  We study relations between $\\delta(\\mathcal T)$ and minimal genus Bennequin surfaces of $\\mathcal T$. In particular, in the disk open book case, under some large fractional Dehn twist coefficient assumption, we show that $\\delta(\\mathcal T)=N$ if and only if $\\mathcal T$ is the boundary of a Bennequin surface with exactly $N$ negatively twisted band","authors_text":"Keiko Kawamuro, Tetsuya Ito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-27T22:03:35Z","title":"The defect of Bennequin-Eliashberg inequality and Bennequin surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09322","kind":"arxiv","version":4},"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":"sha256:9c36bbabf825e5b67d99feb5a85f5fc2a4a87d8e25ebad89fc799e458ac0441f","target":"record","created_at":"2026-05-18T00:32:32Z","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":"430ad69c9b7390687d7f686d3649213a621defb7e9e9f201c7fa39fbf1e181de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-27T22:03:35Z","title_canon_sha256":"1c57e0777cc5e59ddfc3860111184e930c7314df31278ede379dab875ca2ed42"},"schema_version":"1.0","source":{"id":"1703.09322","kind":"arxiv","version":4}},"canonical_sha256":"c624222c9a8b68a0aaf55421c1ae57a04b3fa411587390ceaab5fc9652ec8f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c624222c9a8b68a0aaf55421c1ae57a04b3fa411587390ceaab5fc9652ec8f78","first_computed_at":"2026-05-18T00:32:32.557904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:32.557904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhd1idNRUfJiAYio1dmUzthjUzr67NdXuXwubXC8F8tgjcEgS+TW+c3JiSGOQQPuI+h28WxbOgpGszwlkgrzAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:32.558660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09322","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c36bbabf825e5b67d99feb5a85f5fc2a4a87d8e25ebad89fc799e458ac0441f","sha256:34a4741a3ac60df7b66cd654450b595f07d11555cf06f7ca9c8527fea3ea349b"],"state_sha256":"3d302517ad6410fd9aae8b1dcf3012b67b1bda0e7aa7e3f745585283ed79a096"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LczUgnV+7U3g5HXdFLpA8GWYEBKRDHiagSkb3m7BaQwur9+/FgQ0pRL7jimo2OqGUAQrLryqVupJSqjSDsc2Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:45:32.814584Z","bundle_sha256":"906ccbac18cad779415dec672e5e812b2469a8d11a3f11c0cf223e0a6d9c16a3"}}