{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DLBACUYWYHTNRJPIGJ5JFNQBMR","short_pith_number":"pith:DLBACUYW","canonical_record":{"source":{"id":"1110.6080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-27T13:44:33Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"082eeaa29a268e016306a1c86bbd9717993ccd5e9044e723b4bcf05ec1fe5175","abstract_canon_sha256":"c6ac32fa8f1e82652e7dc5f6c731f058e773d277e9a08f88c01f836767582546"},"schema_version":"1.0"},"canonical_sha256":"1ac2015316c1e6d8a5e8327a92b601645f05148b61c4696de51cb70ff2ce5f15","source":{"kind":"arxiv","id":"1110.6080","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6080","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6080v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6080","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"DLBACUYWYHTN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DLBACUYWYHTNRJPI","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DLBACUYW","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DLBACUYWYHTNRJPIGJ5JFNQBMR","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-27T13:44:33Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"082eeaa29a268e016306a1c86bbd9717993ccd5e9044e723b4bcf05ec1fe5175","abstract_canon_sha256":"c6ac32fa8f1e82652e7dc5f6c731f058e773d277e9a08f88c01f836767582546"},"schema_version":"1.0"},"canonical_sha256":"1ac2015316c1e6d8a5e8327a92b601645f05148b61c4696de51cb70ff2ce5f15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:09.723230Z","signature_b64":"Li0UJHDK7lxlyFi3qZ+X3b7Tjo8ixl3sjl28HsMs805vew2tIqSgE+n2ooCObbfT55hDqGjxLjE0BrtnUmQSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ac2015316c1e6d8a5e8327a92b601645f05148b61c4696de51cb70ff2ce5f15","last_reissued_at":"2026-05-18T04:10:09.722586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:09.722586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6080","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":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItYKUe50A9XQ1dEm36vXCrhut3593cYZbctqdS059f+UkcvKO9aYm1QEFwGkgFbAspjc5zVTRW87vc4p1uHMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:06:35.935769Z"},"content_sha256":"376765a04879eb3c7fb400c2b5ce2ce815bc13d644bdec6abb65d0c61b5eeb84","schema_version":"1.0","event_id":"sha256:376765a04879eb3c7fb400c2b5ce2ce815bc13d644bdec6abb65d0c61b5eeb84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DLBACUYWYHTNRJPIGJ5JFNQBMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.GT","authors_text":"Benjamin A. Burton","submitted_at":"2011-10-27T13:44:33Z","abstract_excerpt":"It is important to have effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can make it smaller than its original size. Here we present experimental work that suggests the reality is far different: for an exhaustive census of 81,800,394 one-vertex triangulations that span 1,901 distinct closed orientable 3-manifolds, we never need to add more than two extra tetrahedra, we never need more than a handful of Pachner moves (or bistellar f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6080","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":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQjDYEWv6gy5SB0kgVO4ABeYJtPvZDePLc99kbPXIWGQ1lo/dklE6iWcxc3s9wEDgrNv9xn2fRtCUjnz5JxZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:06:35.936436Z"},"content_sha256":"e02526cf63ac77fa27bbeee1c8e24605cf691c90fc23785ccbd1c5d8de9c10b9","schema_version":"1.0","event_id":"sha256:e02526cf63ac77fa27bbeee1c8e24605cf691c90fc23785ccbd1c5d8de9c10b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DLBACUYWYHTNRJPIGJ5JFNQBMR/bundle.json","state_url":"https://pith.science/pith/DLBACUYWYHTNRJPIGJ5JFNQBMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DLBACUYWYHTNRJPIGJ5JFNQBMR/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":"2026-06-11T22:06:35Z","links":{"resolver":"https://pith.science/pith/DLBACUYWYHTNRJPIGJ5JFNQBMR","bundle":"https://pith.science/pith/DLBACUYWYHTNRJPIGJ5JFNQBMR/bundle.json","state":"https://pith.science/pith/DLBACUYWYHTNRJPIGJ5JFNQBMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DLBACUYWYHTNRJPIGJ5JFNQBMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DLBACUYWYHTNRJPIGJ5JFNQBMR","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":"c6ac32fa8f1e82652e7dc5f6c731f058e773d277e9a08f88c01f836767582546","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-27T13:44:33Z","title_canon_sha256":"082eeaa29a268e016306a1c86bbd9717993ccd5e9044e723b4bcf05ec1fe5175"},"schema_version":"1.0","source":{"id":"1110.6080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6080","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6080v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6080","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"DLBACUYWYHTN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DLBACUYWYHTNRJPI","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DLBACUYW","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:e02526cf63ac77fa27bbeee1c8e24605cf691c90fc23785ccbd1c5d8de9c10b9","target":"graph","created_at":"2026-05-18T04:10:09Z","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":"It is important to have effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can make it smaller than its original size. Here we present experimental work that suggests the reality is far different: for an exhaustive census of 81,800,394 one-vertex triangulations that span 1,901 distinct closed orientable 3-manifolds, we never need to add more than two extra tetrahedra, we never need more than a handful of Pachner moves (or bistellar f","authors_text":"Benjamin A. Burton","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-27T13:44:33Z","title":"Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6080","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":"sha256:376765a04879eb3c7fb400c2b5ce2ce815bc13d644bdec6abb65d0c61b5eeb84","target":"record","created_at":"2026-05-18T04:10:09Z","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":"c6ac32fa8f1e82652e7dc5f6c731f058e773d277e9a08f88c01f836767582546","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-27T13:44:33Z","title_canon_sha256":"082eeaa29a268e016306a1c86bbd9717993ccd5e9044e723b4bcf05ec1fe5175"},"schema_version":"1.0","source":{"id":"1110.6080","kind":"arxiv","version":1}},"canonical_sha256":"1ac2015316c1e6d8a5e8327a92b601645f05148b61c4696de51cb70ff2ce5f15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ac2015316c1e6d8a5e8327a92b601645f05148b61c4696de51cb70ff2ce5f15","first_computed_at":"2026-05-18T04:10:09.722586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.722586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Li0UJHDK7lxlyFi3qZ+X3b7Tjo8ixl3sjl28HsMs805vew2tIqSgE+n2ooCObbfT55hDqGjxLjE0BrtnUmQSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.723230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:376765a04879eb3c7fb400c2b5ce2ce815bc13d644bdec6abb65d0c61b5eeb84","sha256:e02526cf63ac77fa27bbeee1c8e24605cf691c90fc23785ccbd1c5d8de9c10b9"],"state_sha256":"4ae0bd07b3abcdabee41a4ed03425d7c3ec73d40204653e363df025101cdecb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmLKwD7hSoh9iu4ZSlyVEVaKpCQqJcYABPwG1Pme+tyd6wvTb9J0Qt6nYqeLGIUqv2eVGb4iT3K0iF2wOWziCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:06:35.939983Z","bundle_sha256":"96b912986dc784177060f60feaeed6419d08dc3bfd7e779a5c219ee82b8a3005"}}