{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PSGVIPKPDSBXJJYYVHG2G2ELA4","short_pith_number":"pith:PSGVIPKP","canonical_record":{"source":{"id":"1108.5748","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-08-29T20:40:54Z","cross_cats_sorted":[],"title_canon_sha256":"85fe0ea15027752a3a0572923faf239855fa2063a58a162fc499ebfac19c8936","abstract_canon_sha256":"a3977ce033a1b6252aae5c61eb97025d4c4c07a08578a358b2d3294223ca0d4e"},"schema_version":"1.0"},"canonical_sha256":"7c8d543d4f1c8374a718a9cda3688b0703a0da07e8b24e603d5c79b367a035f5","source":{"kind":"arxiv","id":"1108.5748","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5748","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5748v2","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5748","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"PSGVIPKPDSBX","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PSGVIPKPDSBXJJYY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PSGVIPKP","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PSGVIPKPDSBXJJYYVHG2G2ELA4","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5748","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-08-29T20:40:54Z","cross_cats_sorted":[],"title_canon_sha256":"85fe0ea15027752a3a0572923faf239855fa2063a58a162fc499ebfac19c8936","abstract_canon_sha256":"a3977ce033a1b6252aae5c61eb97025d4c4c07a08578a358b2d3294223ca0d4e"},"schema_version":"1.0"},"canonical_sha256":"7c8d543d4f1c8374a718a9cda3688b0703a0da07e8b24e603d5c79b367a035f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:18.823452Z","signature_b64":"npgsrKwrJcsoQRTMqew9G6dct+kwCLMUblvhRm9Xdkviv4vvqhxpgFbIQ5Gv7eWK9ifLQa5y+ejtMro7pJkYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c8d543d4f1c8374a718a9cda3688b0703a0da07e8b24e603d5c79b367a035f5","last_reissued_at":"2026-05-18T02:55:18.822998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:18.822998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5748","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":"2026-05-18T02:55:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZSsf+qEQ/cQQygGA5pvGnzeJDtCrnJmEQOSK990iwSKy5Bvd0jMgIqs6n7NvelI/qENrmvhPVFmmptwu3U44Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T15:55:29.785834Z"},"content_sha256":"6553e6f63118915f875ed8e689920be09246cb20996687fefacfd373735b520c","schema_version":"1.0","event_id":"sha256:6553e6f63118915f875ed8e689920be09246cb20996687fefacfd373735b520c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PSGVIPKPDSBXJJYYVHG2G2ELA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cusp geometry of fibered 3-manifolds","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Futer, Saul Schleimer","submitted_at":"2011-08-29T20:40:54Z","abstract_excerpt":"Let F be a surface and suppose that \\phi: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_\\phi is hyperbolic and contains a maximal cusp C about the puncture p.\n  We show that the area (and height) of the cusp torus bounding C is equal to the stable translation distance of \\phi acting on the arc complex A(F,p), up to an explicitly bounded multiplicative error. Our proof relies on elementary facts about the hyperbolic geometry of pleated surfaces. In particular, the proof of this theorem does not use any deep results in Teichmueller theory, Kleinian gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5748","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":""},"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":"2026-05-18T02:55:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xzQT46vujfDFkRRkYkXkS9ghsPMdhvIWIO6r30GQTrEJlWjWjS/rdODHtHwDjLyT5pLHEp9j7mIq1VeRwq7rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T15:55:29.786399Z"},"content_sha256":"68af780a98ff0eddb41514037212214f608ad18a98397b30982e738b5793776a","schema_version":"1.0","event_id":"sha256:68af780a98ff0eddb41514037212214f608ad18a98397b30982e738b5793776a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSGVIPKPDSBXJJYYVHG2G2ELA4/bundle.json","state_url":"https://pith.science/pith/PSGVIPKPDSBXJJYYVHG2G2ELA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSGVIPKPDSBXJJYYVHG2G2ELA4/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":"2026-05-21T15:55:29Z","links":{"resolver":"https://pith.science/pith/PSGVIPKPDSBXJJYYVHG2G2ELA4","bundle":"https://pith.science/pith/PSGVIPKPDSBXJJYYVHG2G2ELA4/bundle.json","state":"https://pith.science/pith/PSGVIPKPDSBXJJYYVHG2G2ELA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSGVIPKPDSBXJJYYVHG2G2ELA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PSGVIPKPDSBXJJYYVHG2G2ELA4","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":"a3977ce033a1b6252aae5c61eb97025d4c4c07a08578a358b2d3294223ca0d4e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-08-29T20:40:54Z","title_canon_sha256":"85fe0ea15027752a3a0572923faf239855fa2063a58a162fc499ebfac19c8936"},"schema_version":"1.0","source":{"id":"1108.5748","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5748","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5748v2","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5748","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"PSGVIPKPDSBX","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PSGVIPKPDSBXJJYY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PSGVIPKP","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:68af780a98ff0eddb41514037212214f608ad18a98397b30982e738b5793776a","target":"graph","created_at":"2026-05-18T02:55:18Z","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":"Let F be a surface and suppose that \\phi: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_\\phi is hyperbolic and contains a maximal cusp C about the puncture p.\n  We show that the area (and height) of the cusp torus bounding C is equal to the stable translation distance of \\phi acting on the arc complex A(F,p), up to an explicitly bounded multiplicative error. Our proof relies on elementary facts about the hyperbolic geometry of pleated surfaces. In particular, the proof of this theorem does not use any deep results in Teichmueller theory, Kleinian gro","authors_text":"David Futer, Saul Schleimer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-08-29T20:40:54Z","title":"Cusp geometry of fibered 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5748","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":"sha256:6553e6f63118915f875ed8e689920be09246cb20996687fefacfd373735b520c","target":"record","created_at":"2026-05-18T02:55:18Z","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":"a3977ce033a1b6252aae5c61eb97025d4c4c07a08578a358b2d3294223ca0d4e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.GT","submitted_at":"2011-08-29T20:40:54Z","title_canon_sha256":"85fe0ea15027752a3a0572923faf239855fa2063a58a162fc499ebfac19c8936"},"schema_version":"1.0","source":{"id":"1108.5748","kind":"arxiv","version":2}},"canonical_sha256":"7c8d543d4f1c8374a718a9cda3688b0703a0da07e8b24e603d5c79b367a035f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c8d543d4f1c8374a718a9cda3688b0703a0da07e8b24e603d5c79b367a035f5","first_computed_at":"2026-05-18T02:55:18.822998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:18.822998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"npgsrKwrJcsoQRTMqew9G6dct+kwCLMUblvhRm9Xdkviv4vvqhxpgFbIQ5Gv7eWK9ifLQa5y+ejtMro7pJkYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:18.823452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5748","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6553e6f63118915f875ed8e689920be09246cb20996687fefacfd373735b520c","sha256:68af780a98ff0eddb41514037212214f608ad18a98397b30982e738b5793776a"],"state_sha256":"c6ad22599178993c849b7e74b9df99bb198e11071b75121b68bf6b66b3d2bc10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2mjeCxD0yz5fpDpYTQpuC4sPNhy07C+D3PdrFFE43d0j+weLCsc8erta4EjwiEwiqx8VPA8/1CPS+Nh6MzjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T15:55:29.789582Z","bundle_sha256":"726e07d252a3e8733315d3e5255d2d8646d345f828fa0f801b6db3f689c84012"}}