{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:5DV7FHWIFWGMRCW3DOK5KA3MY6","short_pith_number":"pith:5DV7FHWI","canonical_record":{"source":{"id":"0706.4368","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-06-29T08:24:05Z","cross_cats_sorted":[],"title_canon_sha256":"d90c6d9d95e36c22452b05dfcb0ac70f0b3728ec10e15466df2e6652948e9a15","abstract_canon_sha256":"2123cd91d6d8cce65f7d00c088e04a3d31d90adab9fba2c12c7bd66c4c4d560a"},"schema_version":"1.0"},"canonical_sha256":"e8ebf29ec82d8cc88adb1b95d5036cc7ab1249e46e610e985edaa2b7152b5c7d","source":{"kind":"arxiv","id":"0706.4368","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.4368","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"0706.4368v1","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.4368","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"5DV7FHWIFWGM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5DV7FHWIFWGMRCW3","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5DV7FHWI","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:5DV7FHWIFWGMRCW3DOK5KA3MY6","target":"record","payload":{"canonical_record":{"source":{"id":"0706.4368","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-06-29T08:24:05Z","cross_cats_sorted":[],"title_canon_sha256":"d90c6d9d95e36c22452b05dfcb0ac70f0b3728ec10e15466df2e6652948e9a15","abstract_canon_sha256":"2123cd91d6d8cce65f7d00c088e04a3d31d90adab9fba2c12c7bd66c4c4d560a"},"schema_version":"1.0"},"canonical_sha256":"e8ebf29ec82d8cc88adb1b95d5036cc7ab1249e46e610e985edaa2b7152b5c7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:31.508904Z","signature_b64":"LhZfbYwD1/ydoiD/KNXCesm1Cp2C+HDquewqmIL0SUYKEvVDyb4qyUG/R4h+uIRaA+OCvTdp88H4FdU/9TYcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8ebf29ec82d8cc88adb1b95d5036cc7ab1249e46e610e985edaa2b7152b5c7d","last_reissued_at":"2026-05-18T04:31:31.508338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:31.508338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.4368","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":"2026-05-18T04:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvwXHCF9LK0psNXZzVaaZjIfcfMuoQPQNx8xfJ+3EIJ4VRBadk2FipogccVQNbJGvBFoVsa191Uj0LjrQQJ4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:21:57.406208Z"},"content_sha256":"563759abf7f9dc31a2587a404d9af6946d8431a031fb8f16e22c585c42118a24","schema_version":"1.0","event_id":"sha256:563759abf7f9dc31a2587a404d9af6946d8431a031fb8f16e22c585c42118a24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:5DV7FHWIFWGMRCW3DOK5KA3MY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial and geometric methods in topology","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Carlo Petronio, Damian Heard, Ekaterina Pervova","submitted_at":"2007-06-29T08:24:05Z","abstract_excerpt":"Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry within three-dimensional topology. We will also point out the striking difference with the two-dimensional case, and we will review some of the results of the combinatorial and computational approach to three-manifolds developed by different mathematicians over the last several years."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4368","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":"2026-05-18T04:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dv7/ycZ/ElLYLBaUzSFO28V59Gq6l1u+GFn4bgu4sxsZGLqLvlUZkLydSV78XLE9qA6yybMbRoLRF1Fi7496BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:21:57.406933Z"},"content_sha256":"4498ea26db2479b1853b9cc4abf878eda3caea1563d596fe1a7ec56b625d8e1d","schema_version":"1.0","event_id":"sha256:4498ea26db2479b1853b9cc4abf878eda3caea1563d596fe1a7ec56b625d8e1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DV7FHWIFWGMRCW3DOK5KA3MY6/bundle.json","state_url":"https://pith.science/pith/5DV7FHWIFWGMRCW3DOK5KA3MY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DV7FHWIFWGMRCW3DOK5KA3MY6/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":"2026-06-08T18:21:57Z","links":{"resolver":"https://pith.science/pith/5DV7FHWIFWGMRCW3DOK5KA3MY6","bundle":"https://pith.science/pith/5DV7FHWIFWGMRCW3DOK5KA3MY6/bundle.json","state":"https://pith.science/pith/5DV7FHWIFWGMRCW3DOK5KA3MY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DV7FHWIFWGMRCW3DOK5KA3MY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:5DV7FHWIFWGMRCW3DOK5KA3MY6","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":"2123cd91d6d8cce65f7d00c088e04a3d31d90adab9fba2c12c7bd66c4c4d560a","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2007-06-29T08:24:05Z","title_canon_sha256":"d90c6d9d95e36c22452b05dfcb0ac70f0b3728ec10e15466df2e6652948e9a15"},"schema_version":"1.0","source":{"id":"0706.4368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.4368","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"0706.4368v1","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.4368","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"5DV7FHWIFWGM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5DV7FHWIFWGMRCW3","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5DV7FHWI","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:4498ea26db2479b1853b9cc4abf878eda3caea1563d596fe1a7ec56b625d8e1d","target":"graph","created_at":"2026-05-18T04:31:31Z","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":"Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry within three-dimensional topology. We will also point out the striking difference with the two-dimensional case, and we will review some of the results of the combinatorial and computational approach to three-manifolds developed by different mathematicians over the last several years.","authors_text":"Carlo Petronio, Damian Heard, Ekaterina Pervova","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-06-29T08:24:05Z","title":"Combinatorial and geometric methods in topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4368","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":"sha256:563759abf7f9dc31a2587a404d9af6946d8431a031fb8f16e22c585c42118a24","target":"record","created_at":"2026-05-18T04:31:31Z","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":"2123cd91d6d8cce65f7d00c088e04a3d31d90adab9fba2c12c7bd66c4c4d560a","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2007-06-29T08:24:05Z","title_canon_sha256":"d90c6d9d95e36c22452b05dfcb0ac70f0b3728ec10e15466df2e6652948e9a15"},"schema_version":"1.0","source":{"id":"0706.4368","kind":"arxiv","version":1}},"canonical_sha256":"e8ebf29ec82d8cc88adb1b95d5036cc7ab1249e46e610e985edaa2b7152b5c7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8ebf29ec82d8cc88adb1b95d5036cc7ab1249e46e610e985edaa2b7152b5c7d","first_computed_at":"2026-05-18T04:31:31.508338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:31.508338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LhZfbYwD1/ydoiD/KNXCesm1Cp2C+HDquewqmIL0SUYKEvVDyb4qyUG/R4h+uIRaA+OCvTdp88H4FdU/9TYcDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:31.508904Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.4368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:563759abf7f9dc31a2587a404d9af6946d8431a031fb8f16e22c585c42118a24","sha256:4498ea26db2479b1853b9cc4abf878eda3caea1563d596fe1a7ec56b625d8e1d"],"state_sha256":"3a001450f714a55be0ff21ea634df34f2a291d708a6b4e498b1fa57e93891c54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8j2XbzEJsBXy6Mf4F21cA6TN5f7akkiO4c94x1UexptqHWQ7LcgxuHpkYiyvSLS5UAQHTDMSbCdDuKFzCbTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:21:57.411281Z","bundle_sha256":"1e5570871049f42ee2f29afa3d6de257b1b61b7cb07a1551d54e48ab8118f70f"}}