{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:EINQZNBQ2GCJ2DSN6AVC4NR64L","short_pith_number":"pith:EINQZNBQ","canonical_record":{"source":{"id":"math/0509345","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-09-15T08:18:16Z","cross_cats_sorted":[],"title_canon_sha256":"135ce6f2f57a6bc00136f87ceac36461d670128cddad6cc72010afff02200ade","abstract_canon_sha256":"07efd9bb2b46665a1609bbb0e7e9c5bebe1d0f0e3a89987cb0bd25057b1c62c9"},"schema_version":"1.0"},"canonical_sha256":"221b0cb430d1849d0e4df02a2e363ee2da0af1400ad439dfb9f30a4fee462d59","source":{"kind":"arxiv","id":"math/0509345","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509345","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509345v1","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509345","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"EINQZNBQ2GCJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EINQZNBQ2GCJ2DSN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EINQZNBQ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:EINQZNBQ2GCJ2DSN6AVC4NR64L","target":"record","payload":{"canonical_record":{"source":{"id":"math/0509345","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-09-15T08:18:16Z","cross_cats_sorted":[],"title_canon_sha256":"135ce6f2f57a6bc00136f87ceac36461d670128cddad6cc72010afff02200ade","abstract_canon_sha256":"07efd9bb2b46665a1609bbb0e7e9c5bebe1d0f0e3a89987cb0bd25057b1c62c9"},"schema_version":"1.0"},"canonical_sha256":"221b0cb430d1849d0e4df02a2e363ee2da0af1400ad439dfb9f30a4fee462d59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:54.746521Z","signature_b64":"uVzP2BKN5Glt24LsT2lby+MXBJrziNhdD9gVqcUm/2c9MjAwM4ReDzezHSbVNG+PTk9FuOA6RmzT7DJd9up6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"221b0cb430d1849d0e4df02a2e363ee2da0af1400ad439dfb9f30a4fee462d59","last_reissued_at":"2026-05-18T04:32:54.746088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:54.746088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0509345","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":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UwTE7P5r64NZJtRms9BLOgPFZcbLpf7RxUIbomo4A1REhwgNpETFblsb7M4NdNn23Nq8dtP0up07/4odnNhtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:08:43.629800Z"},"content_sha256":"8e4266665a01f72fa719f40bb2c8d0a2c0a797ed268e3b4f0bacac0ade5912db","schema_version":"1.0","event_id":"sha256:8e4266665a01f72fa719f40bb2c8d0a2c0a797ed268e3b4f0bacac0ade5912db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:EINQZNBQ2GCJ2DSN6AVC4NR64L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Observations from the 8-tetrahedron non-orientable census","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Benjamin A. Burton","submitted_at":"2005-09-15T08:18:16Z","abstract_excerpt":"Through computer enumeration with the aid of topological results, we catalogue all 18 closed non-orientable P^2-irreducible 3-manifolds that can be formed from at most eight tetrahedra. In addition we give an overview as to how the 100 resulting minimal triangulations are constructed. Observations and conjectures are drawn from the census data, and future potential for the non-orientable census is discussed. Some preliminary nine-tetrahedron results are also included."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509345","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":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dl+LJtpmqPFbkBI1dUVfSKXdH/IsGggN5kYQzh4TZEL6NAmaUDZHmb2tohLWgtsJmzzX7kwTum32vs+qy388Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:08:43.630465Z"},"content_sha256":"431855f3b1d80370a722fabd3535ae60e0c589bca3697200911411a99210c290","schema_version":"1.0","event_id":"sha256:431855f3b1d80370a722fabd3535ae60e0c589bca3697200911411a99210c290"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EINQZNBQ2GCJ2DSN6AVC4NR64L/bundle.json","state_url":"https://pith.science/pith/EINQZNBQ2GCJ2DSN6AVC4NR64L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EINQZNBQ2GCJ2DSN6AVC4NR64L/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":"2026-06-11T22:08:43Z","links":{"resolver":"https://pith.science/pith/EINQZNBQ2GCJ2DSN6AVC4NR64L","bundle":"https://pith.science/pith/EINQZNBQ2GCJ2DSN6AVC4NR64L/bundle.json","state":"https://pith.science/pith/EINQZNBQ2GCJ2DSN6AVC4NR64L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EINQZNBQ2GCJ2DSN6AVC4NR64L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:EINQZNBQ2GCJ2DSN6AVC4NR64L","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":"07efd9bb2b46665a1609bbb0e7e9c5bebe1d0f0e3a89987cb0bd25057b1c62c9","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2005-09-15T08:18:16Z","title_canon_sha256":"135ce6f2f57a6bc00136f87ceac36461d670128cddad6cc72010afff02200ade"},"schema_version":"1.0","source":{"id":"math/0509345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509345","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509345v1","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509345","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"EINQZNBQ2GCJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EINQZNBQ2GCJ2DSN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EINQZNBQ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:431855f3b1d80370a722fabd3535ae60e0c589bca3697200911411a99210c290","target":"graph","created_at":"2026-05-18T04:32:54Z","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":"Through computer enumeration with the aid of topological results, we catalogue all 18 closed non-orientable P^2-irreducible 3-manifolds that can be formed from at most eight tetrahedra. In addition we give an overview as to how the 100 resulting minimal triangulations are constructed. Observations and conjectures are drawn from the census data, and future potential for the non-orientable census is discussed. Some preliminary nine-tetrahedron results are also included.","authors_text":"Benjamin A. Burton","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2005-09-15T08:18:16Z","title":"Observations from the 8-tetrahedron non-orientable census"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509345","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":"sha256:8e4266665a01f72fa719f40bb2c8d0a2c0a797ed268e3b4f0bacac0ade5912db","target":"record","created_at":"2026-05-18T04:32:54Z","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":"07efd9bb2b46665a1609bbb0e7e9c5bebe1d0f0e3a89987cb0bd25057b1c62c9","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2005-09-15T08:18:16Z","title_canon_sha256":"135ce6f2f57a6bc00136f87ceac36461d670128cddad6cc72010afff02200ade"},"schema_version":"1.0","source":{"id":"math/0509345","kind":"arxiv","version":1}},"canonical_sha256":"221b0cb430d1849d0e4df02a2e363ee2da0af1400ad439dfb9f30a4fee462d59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"221b0cb430d1849d0e4df02a2e363ee2da0af1400ad439dfb9f30a4fee462d59","first_computed_at":"2026-05-18T04:32:54.746088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:54.746088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uVzP2BKN5Glt24LsT2lby+MXBJrziNhdD9gVqcUm/2c9MjAwM4ReDzezHSbVNG+PTk9FuOA6RmzT7DJd9up6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:54.746521Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0509345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e4266665a01f72fa719f40bb2c8d0a2c0a797ed268e3b4f0bacac0ade5912db","sha256:431855f3b1d80370a722fabd3535ae60e0c589bca3697200911411a99210c290"],"state_sha256":"f14fa5a36322c785a8faaeb4894255ae1ff2d89b738df60ae337429c4a1adb83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G1F1snEf2mzJLrAkGbuFoaFiz+MxL34XEtAtQsp1lwyXl8n+dBoezHRJXt1bQXasydmj6xnl/WP7ZTCnGebTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:08:43.633771Z","bundle_sha256":"fb93eb1d46fe0d3128143603d24d9cbc034cd954680a2efc573ef30581218412"}}