{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SUZM367BDN4K2DEU5FYMBE4E6X","short_pith_number":"pith:SUZM367B","canonical_record":{"source":{"id":"1503.08521","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-30T01:56:23Z","cross_cats_sorted":[],"title_canon_sha256":"e9658c51542f86808f1f00e562b03c3e311f9c3ad9dfde1f3029727b4634c6e8","abstract_canon_sha256":"96945a8777e1da7c84f89b1ecef103f58a40e52eb52f70d8b0e08f7cfab39d0d"},"schema_version":"1.0"},"canonical_sha256":"9532cdfbe11b78ad0c94e970c09384f5de18d0efda0a2656dc1ff2a6d2141bef","source":{"kind":"arxiv","id":"1503.08521","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08521","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08521v2","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08521","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"SUZM367BDN4K","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUZM367BDN4K2DEU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUZM367B","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SUZM367BDN4K2DEU5FYMBE4E6X","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08521","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-30T01:56:23Z","cross_cats_sorted":[],"title_canon_sha256":"e9658c51542f86808f1f00e562b03c3e311f9c3ad9dfde1f3029727b4634c6e8","abstract_canon_sha256":"96945a8777e1da7c84f89b1ecef103f58a40e52eb52f70d8b0e08f7cfab39d0d"},"schema_version":"1.0"},"canonical_sha256":"9532cdfbe11b78ad0c94e970c09384f5de18d0efda0a2656dc1ff2a6d2141bef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:36.672100Z","signature_b64":"onrx64YNbxjaF1OlCLssij0cS5fqynhOocFD0hJtg7cPQl6cc1SRcCnuwgsCG5R9O99yKFHopW0hP7b5EedFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9532cdfbe11b78ad0c94e970c09384f5de18d0efda0a2656dc1ff2a6d2141bef","last_reissued_at":"2026-05-18T01:20:36.671347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:36.671347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08521","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":"2026-05-18T01:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tdNzu5JqPud1p9XpN/BeonS9hVjj7vKNk1a1XcHVR1wF/ZLCy2iDOLTB+1n2Wk0lU3cCW1MHf0e9BhRwq7ZyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:37:13.375792Z"},"content_sha256":"79dcc7e6ef3c977057956b7694aa3d28b61b58e056deff23c696b69ff107b485","schema_version":"1.0","event_id":"sha256:79dcc7e6ef3c977057956b7694aa3d28b61b58e056deff23c696b69ff107b485"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SUZM367BDN4K2DEU5FYMBE4E6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Morse area and Scharlemann-Thompson width for hyperbolic 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Diane Hoffoss, Joseph Maher","submitted_at":"2015-03-30T01:56:23Z","abstract_excerpt":"Scharlemann and Thompson define a numerical complexity for a 3-manifold using handle decompositions of the manifold. We show that for compact hyperbolic 3-manifolds this is linearly related to a definition of metric complexity in terms of the areas of level sets of Morse functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08521","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":"2026-05-18T01:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OO1vR2rygqw8WEj8wwmyZFZqYMhGEDhzYSjeWZ6wyXbvz1/nG0tZZbSStr0EQ8aH2XmlmoA3B8mwcwQQasTMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:37:13.376521Z"},"content_sha256":"335fe1d0e35e2bb5c211577109f18626ed8c2781bad4ed0779b583bb2062d19a","schema_version":"1.0","event_id":"sha256:335fe1d0e35e2bb5c211577109f18626ed8c2781bad4ed0779b583bb2062d19a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUZM367BDN4K2DEU5FYMBE4E6X/bundle.json","state_url":"https://pith.science/pith/SUZM367BDN4K2DEU5FYMBE4E6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUZM367BDN4K2DEU5FYMBE4E6X/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":"2026-06-05T20:37:13Z","links":{"resolver":"https://pith.science/pith/SUZM367BDN4K2DEU5FYMBE4E6X","bundle":"https://pith.science/pith/SUZM367BDN4K2DEU5FYMBE4E6X/bundle.json","state":"https://pith.science/pith/SUZM367BDN4K2DEU5FYMBE4E6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUZM367BDN4K2DEU5FYMBE4E6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SUZM367BDN4K2DEU5FYMBE4E6X","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":"96945a8777e1da7c84f89b1ecef103f58a40e52eb52f70d8b0e08f7cfab39d0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-30T01:56:23Z","title_canon_sha256":"e9658c51542f86808f1f00e562b03c3e311f9c3ad9dfde1f3029727b4634c6e8"},"schema_version":"1.0","source":{"id":"1503.08521","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08521","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08521v2","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08521","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"SUZM367BDN4K","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUZM367BDN4K2DEU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUZM367B","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:335fe1d0e35e2bb5c211577109f18626ed8c2781bad4ed0779b583bb2062d19a","target":"graph","created_at":"2026-05-18T01:20:36Z","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":"Scharlemann and Thompson define a numerical complexity for a 3-manifold using handle decompositions of the manifold. We show that for compact hyperbolic 3-manifolds this is linearly related to a definition of metric complexity in terms of the areas of level sets of Morse functions.","authors_text":"Diane Hoffoss, Joseph Maher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-30T01:56:23Z","title":"Morse area and Scharlemann-Thompson width for hyperbolic 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08521","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":"sha256:79dcc7e6ef3c977057956b7694aa3d28b61b58e056deff23c696b69ff107b485","target":"record","created_at":"2026-05-18T01:20:36Z","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":"96945a8777e1da7c84f89b1ecef103f58a40e52eb52f70d8b0e08f7cfab39d0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-30T01:56:23Z","title_canon_sha256":"e9658c51542f86808f1f00e562b03c3e311f9c3ad9dfde1f3029727b4634c6e8"},"schema_version":"1.0","source":{"id":"1503.08521","kind":"arxiv","version":2}},"canonical_sha256":"9532cdfbe11b78ad0c94e970c09384f5de18d0efda0a2656dc1ff2a6d2141bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9532cdfbe11b78ad0c94e970c09384f5de18d0efda0a2656dc1ff2a6d2141bef","first_computed_at":"2026-05-18T01:20:36.671347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:36.671347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"onrx64YNbxjaF1OlCLssij0cS5fqynhOocFD0hJtg7cPQl6cc1SRcCnuwgsCG5R9O99yKFHopW0hP7b5EedFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:36.672100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08521","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79dcc7e6ef3c977057956b7694aa3d28b61b58e056deff23c696b69ff107b485","sha256:335fe1d0e35e2bb5c211577109f18626ed8c2781bad4ed0779b583bb2062d19a"],"state_sha256":"8097e7e25f9a39552740152f69381b7339f3be98822b45a41d20b54d922a8132"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0RyfVxPMVp1PQA5lWLkRpkeVAWfhLT+wiotfZRD8Ve0z+/t/gA7ykubVeafLYI14oB/KIm4rwNunwX4O7NH7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:37:13.380178Z","bundle_sha256":"d84d73ef700917c4e4e44b5b247aa94dc7f5a7a12cc56e5d5a37551961a0e9fe"}}