{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2MMTQCBGGOFZAEBSPIUJQFQTQZ","short_pith_number":"pith:2MMTQCBG","canonical_record":{"source":{"id":"1101.2633","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-13T19:02:03Z","cross_cats_sorted":[],"title_canon_sha256":"3dc113d8a10cf884736d88668ce748635454b6128c1744016bad9357e5f652d4","abstract_canon_sha256":"61880ee11e2ed89a5ad0ddbd2ce848d8c6e90e326e0ca79e5e5f7f07947b7867"},"schema_version":"1.0"},"canonical_sha256":"d319380826338b9010327a28981613864ae3ad4d14cd51cd4369f51cfd485afb","source":{"kind":"arxiv","id":"1101.2633","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2633","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2633v3","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2633","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"2MMTQCBGGOFZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2MMTQCBGGOFZAEBS","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2MMTQCBG","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2MMTQCBGGOFZAEBSPIUJQFQTQZ","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2633","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-13T19:02:03Z","cross_cats_sorted":[],"title_canon_sha256":"3dc113d8a10cf884736d88668ce748635454b6128c1744016bad9357e5f652d4","abstract_canon_sha256":"61880ee11e2ed89a5ad0ddbd2ce848d8c6e90e326e0ca79e5e5f7f07947b7867"},"schema_version":"1.0"},"canonical_sha256":"d319380826338b9010327a28981613864ae3ad4d14cd51cd4369f51cfd485afb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:47.108023Z","signature_b64":"3eHSWUSF6j8oonUWO3L3eXAydM2cLYnaDQOtT0DUaVqAiobVvR5zFDdgKyCPc4WdXvnWJfYtybIy6cIJlyV1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d319380826338b9010327a28981613864ae3ad4d14cd51cd4369f51cfd485afb","last_reissued_at":"2026-05-18T04:10:47.107497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:47.107497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2633","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPXSsoVZSQKP2fz5ocsSWU6C3RXH64LHkUBMlCa8gyo+dC7nMXMdoXNQ2pGSsGuoe589WR+w7Ek2LcGQi2VQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:01:24.668988Z"},"content_sha256":"1e7ff228c47e8f904c775b08b9232f886ee51883ba8cd7f0403b0573eea926ce","schema_version":"1.0","event_id":"sha256:1e7ff228c47e8f904c775b08b9232f886ee51883ba8cd7f0403b0573eea926ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2MMTQCBGGOFZAEBSPIUJQFQTQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Seven dimensional flat manifolds with cyclic holonomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Rafa{\\l} Lutowski","submitted_at":"2011-01-13T19:02:03Z","abstract_excerpt":"We classify (up to affine equivalence) all 7-dimensional flat manifolds with a cyclic holonomy group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2633","kind":"arxiv","version":3},"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":"2026-05-18T04:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TIiyLD6ybbA7Keb+MzMKp+3dDAyhVZhkbnjTqmPVY+xBgKbXSoSWQhWGiL+RAXzqKhQD5RdU98Tslss6sKdsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:01:24.669338Z"},"content_sha256":"8b9e0e2c9291352035d402072b38a991ea5ef792781685fb948c1e977aa7f5b2","schema_version":"1.0","event_id":"sha256:8b9e0e2c9291352035d402072b38a991ea5ef792781685fb948c1e977aa7f5b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2MMTQCBGGOFZAEBSPIUJQFQTQZ/bundle.json","state_url":"https://pith.science/pith/2MMTQCBGGOFZAEBSPIUJQFQTQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2MMTQCBGGOFZAEBSPIUJQFQTQZ/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":"2026-07-01T21:01:24Z","links":{"resolver":"https://pith.science/pith/2MMTQCBGGOFZAEBSPIUJQFQTQZ","bundle":"https://pith.science/pith/2MMTQCBGGOFZAEBSPIUJQFQTQZ/bundle.json","state":"https://pith.science/pith/2MMTQCBGGOFZAEBSPIUJQFQTQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2MMTQCBGGOFZAEBSPIUJQFQTQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2MMTQCBGGOFZAEBSPIUJQFQTQZ","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":"61880ee11e2ed89a5ad0ddbd2ce848d8c6e90e326e0ca79e5e5f7f07947b7867","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-13T19:02:03Z","title_canon_sha256":"3dc113d8a10cf884736d88668ce748635454b6128c1744016bad9357e5f652d4"},"schema_version":"1.0","source":{"id":"1101.2633","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2633","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2633v3","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2633","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"2MMTQCBGGOFZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2MMTQCBGGOFZAEBS","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2MMTQCBG","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:8b9e0e2c9291352035d402072b38a991ea5ef792781685fb948c1e977aa7f5b2","target":"graph","created_at":"2026-05-18T04:10:47Z","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":"We classify (up to affine equivalence) all 7-dimensional flat manifolds with a cyclic holonomy group.","authors_text":"Rafa{\\l} Lutowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-13T19:02:03Z","title":"Seven dimensional flat manifolds with cyclic holonomy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2633","kind":"arxiv","version":3},"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":"sha256:1e7ff228c47e8f904c775b08b9232f886ee51883ba8cd7f0403b0573eea926ce","target":"record","created_at":"2026-05-18T04:10:47Z","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":"61880ee11e2ed89a5ad0ddbd2ce848d8c6e90e326e0ca79e5e5f7f07947b7867","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-01-13T19:02:03Z","title_canon_sha256":"3dc113d8a10cf884736d88668ce748635454b6128c1744016bad9357e5f652d4"},"schema_version":"1.0","source":{"id":"1101.2633","kind":"arxiv","version":3}},"canonical_sha256":"d319380826338b9010327a28981613864ae3ad4d14cd51cd4369f51cfd485afb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d319380826338b9010327a28981613864ae3ad4d14cd51cd4369f51cfd485afb","first_computed_at":"2026-05-18T04:10:47.107497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:47.107497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3eHSWUSF6j8oonUWO3L3eXAydM2cLYnaDQOtT0DUaVqAiobVvR5zFDdgKyCPc4WdXvnWJfYtybIy6cIJlyV1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:47.108023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2633","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e7ff228c47e8f904c775b08b9232f886ee51883ba8cd7f0403b0573eea926ce","sha256:8b9e0e2c9291352035d402072b38a991ea5ef792781685fb948c1e977aa7f5b2"],"state_sha256":"7feadce17623b7cda938e39da44e00366d0465283a5cbf2ed8678d1a5eb3e62f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NduYWU1g/xsUMjlYy9XlolmwpU5dAamlWFVbnV2UNAzudWjBKgnlcu2lvYWQeh3pfR44y/+lBdQcgX5b22/SBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:01:24.671305Z","bundle_sha256":"90f6eb79eced7494bafa6bf9aebf0b541ea14a58b461920126c6633ab89f424f"}}