{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:O4EY772VTYZ5DTDLQOC54PMYZ2","short_pith_number":"pith:O4EY772V","canonical_record":{"source":{"id":"1010.3174","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2010-10-15T14:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"b92d01322e6006ab46656692b90886e46e3acc1a54a844c96ae9b0e74251f333","abstract_canon_sha256":"dd18c4244a875506f911ea8ed2a2b366486ba7b76bac795973b0ad03e6e1cc7d"},"schema_version":"1.0"},"canonical_sha256":"77098fff559e33d1cc6b8385de3d98ceba03a765da620f2e8bd3d3c74be01f13","source":{"kind":"arxiv","id":"1010.3174","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3174","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3174v1","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3174","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"O4EY772VTYZ5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O4EY772VTYZ5DTDL","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O4EY772V","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:O4EY772VTYZ5DTDLQOC54PMYZ2","target":"record","payload":{"canonical_record":{"source":{"id":"1010.3174","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2010-10-15T14:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"b92d01322e6006ab46656692b90886e46e3acc1a54a844c96ae9b0e74251f333","abstract_canon_sha256":"dd18c4244a875506f911ea8ed2a2b366486ba7b76bac795973b0ad03e6e1cc7d"},"schema_version":"1.0"},"canonical_sha256":"77098fff559e33d1cc6b8385de3d98ceba03a765da620f2e8bd3d3c74be01f13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:17.534110Z","signature_b64":"bDbbR4bNZpv80qa0tkAnagLYd6Go8ZjkyOdrtIGQ/rzUHYpQvJZAnVh0ZO/eV5lYveESuXuNrpaCRA5oRqeHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77098fff559e33d1cc6b8385de3d98ceba03a765da620f2e8bd3d3c74be01f13","last_reissued_at":"2026-05-18T04:39:17.533434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:17.533434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.3174","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcxQTxKz9JKUJOyuH9Jt8KBCv1K6Q9MAhRayq+eFPSwXKViFmEWY4QG61L6tADk2UoEgRQZqN3zSs9ejGQyFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:54:24.466933Z"},"content_sha256":"e4b84acd2c20de15de7fde9fe1537edb8283a77dd426955cecbf5ee4705ec223","schema_version":"1.0","event_id":"sha256:e4b84acd2c20de15de7fde9fe1537edb8283a77dd426955cecbf5ee4705ec223"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:O4EY772VTYZ5DTDLQOC54PMYZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometry of the disk complex","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Howard Masur, Saul Schleimer","submitted_at":"2010-10-15T14:06:44Z","abstract_excerpt":"We give a distance estimate for the metric on the disk complex and show that it is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error depending only on the genus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3174","kind":"arxiv","version":1},"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":"2026-05-18T04:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lr7ys8RS2XQBluJzKCbBZGUsxxvPlPlMi1J9LK+GIcMX9BhvL+UhZQ1cz3ayiHwyj9YgPRumYIifjatmdt7qAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:54:24.467630Z"},"content_sha256":"21a7a1c69fa50748d1a46504c98358fcf1dd4e8c46a1b85bd71c82502b4a6f41","schema_version":"1.0","event_id":"sha256:21a7a1c69fa50748d1a46504c98358fcf1dd4e8c46a1b85bd71c82502b4a6f41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4EY772VTYZ5DTDLQOC54PMYZ2/bundle.json","state_url":"https://pith.science/pith/O4EY772VTYZ5DTDLQOC54PMYZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4EY772VTYZ5DTDLQOC54PMYZ2/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":"2026-05-27T14:54:24Z","links":{"resolver":"https://pith.science/pith/O4EY772VTYZ5DTDLQOC54PMYZ2","bundle":"https://pith.science/pith/O4EY772VTYZ5DTDLQOC54PMYZ2/bundle.json","state":"https://pith.science/pith/O4EY772VTYZ5DTDLQOC54PMYZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4EY772VTYZ5DTDLQOC54PMYZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:O4EY772VTYZ5DTDLQOC54PMYZ2","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":"dd18c4244a875506f911ea8ed2a2b366486ba7b76bac795973b0ad03e6e1cc7d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2010-10-15T14:06:44Z","title_canon_sha256":"b92d01322e6006ab46656692b90886e46e3acc1a54a844c96ae9b0e74251f333"},"schema_version":"1.0","source":{"id":"1010.3174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3174","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3174v1","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3174","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"O4EY772VTYZ5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O4EY772VTYZ5DTDL","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O4EY772V","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:21a7a1c69fa50748d1a46504c98358fcf1dd4e8c46a1b85bd71c82502b4a6f41","target":"graph","created_at":"2026-05-18T04:39:17Z","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 give a distance estimate for the metric on the disk complex and show that it is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error depending only on the genus.","authors_text":"Howard Masur, Saul Schleimer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2010-10-15T14:06:44Z","title":"The geometry of the disk complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3174","kind":"arxiv","version":1},"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:e4b84acd2c20de15de7fde9fe1537edb8283a77dd426955cecbf5ee4705ec223","target":"record","created_at":"2026-05-18T04:39:17Z","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":"dd18c4244a875506f911ea8ed2a2b366486ba7b76bac795973b0ad03e6e1cc7d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2010-10-15T14:06:44Z","title_canon_sha256":"b92d01322e6006ab46656692b90886e46e3acc1a54a844c96ae9b0e74251f333"},"schema_version":"1.0","source":{"id":"1010.3174","kind":"arxiv","version":1}},"canonical_sha256":"77098fff559e33d1cc6b8385de3d98ceba03a765da620f2e8bd3d3c74be01f13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77098fff559e33d1cc6b8385de3d98ceba03a765da620f2e8bd3d3c74be01f13","first_computed_at":"2026-05-18T04:39:17.533434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:17.533434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDbbR4bNZpv80qa0tkAnagLYd6Go8ZjkyOdrtIGQ/rzUHYpQvJZAnVh0ZO/eV5lYveESuXuNrpaCRA5oRqeHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:17.534110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4b84acd2c20de15de7fde9fe1537edb8283a77dd426955cecbf5ee4705ec223","sha256:21a7a1c69fa50748d1a46504c98358fcf1dd4e8c46a1b85bd71c82502b4a6f41"],"state_sha256":"350bab64f58c9c3c54cfb84be907fccb9733cfa881bb0cf41fbe88fddfc5072e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrdDxbLC3WqEJKNax4DJNbqFUwD7OktuLJwokGAcsMreVmCXCeT4n3hrYqqjBPIF/6iUPAcrKl4yEaN2GszECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:54:24.471253Z","bundle_sha256":"0439a65b3c76182c7f690f9ea7ea34ffeb103c036fca70185fe3e2f2cd55d530"}}