{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:YNGQDGCMEOA7CB2ACRLDZJKXN7","short_pith_number":"pith:YNGQDGCM","canonical_record":{"source":{"id":"math/0210231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-10-16T19:01:50Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c2ac38a6b4e1237bcb7b9d1749ea1e210f520a82809475c95f96177f98cb7a40","abstract_canon_sha256":"b1b3e45bd2ff98d6a5ff438dc910af2bf5944fc77c9eea9955942e44f4046db5"},"schema_version":"1.0"},"canonical_sha256":"c34d01984c2381f1074014563ca5576fda5ed9c08877c2471d58896dc92a2be2","source":{"kind":"arxiv","id":"math/0210231","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210231","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210231v2","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210231","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"YNGQDGCMEOA7","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"YNGQDGCMEOA7CB2A","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"YNGQDGCM","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:YNGQDGCMEOA7CB2ACRLDZJKXN7","target":"record","payload":{"canonical_record":{"source":{"id":"math/0210231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-10-16T19:01:50Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c2ac38a6b4e1237bcb7b9d1749ea1e210f520a82809475c95f96177f98cb7a40","abstract_canon_sha256":"b1b3e45bd2ff98d6a5ff438dc910af2bf5944fc77c9eea9955942e44f4046db5"},"schema_version":"1.0"},"canonical_sha256":"c34d01984c2381f1074014563ca5576fda5ed9c08877c2471d58896dc92a2be2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:42.433070Z","signature_b64":"wrDkZLGkksSWHo9f0kYVOQHD8CW1d51Mh84s/PwI1VOlCGVZnxVfOgASaCPCYOgFMaXuW5dW0NUqqSEWeARdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c34d01984c2381f1074014563ca5576fda5ed9c08877c2471d58896dc92a2be2","last_reissued_at":"2026-05-18T00:41:42.432377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:42.432377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0210231","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":"2026-05-18T00:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMOtYylgqWIQn+ngbNl7Rqoy0dK469YchAlPdvwlAf08wGAy/mv841v+NjDQ6cvckeApGPMEZ2iTfy+aqaacAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:41:05.247867Z"},"content_sha256":"1c389c0ff4b2bf07d02c5ba1632446e773b0cc674d05ca1393a9b081b4d8024b","schema_version":"1.0","event_id":"sha256:1c389c0ff4b2bf07d02c5ba1632446e773b0cc674d05ca1393a9b081b4d8024b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:YNGQDGCMEOA7CB2ACRLDZJKXN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Biquotients with singly generated rational cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Vitali Kapovitch, Wolfgang Ziller","submitted_at":"2002-10-16T19:01:50Z","abstract_excerpt":"We classify all biquotients whose rational cohomology rings are generated by one element. As a consequence we show that the Gromoll-Meyer 7-sphere is the only exotic sphere which can be written as a biquotient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210231","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":"2026-05-18T00:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"73ceKu6ao4WABS+Z9fvEcz202I3d9Cz7yJXj8Lc9SlSMInlv2reRlH1JEfTi0p1DyQ0AHWNK4GCk3tygqxeoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:41:05.248201Z"},"content_sha256":"2605f82462633e58a82eb64388b670430180ab0027fc20e80d1e31696a39289b","schema_version":"1.0","event_id":"sha256:2605f82462633e58a82eb64388b670430180ab0027fc20e80d1e31696a39289b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNGQDGCMEOA7CB2ACRLDZJKXN7/bundle.json","state_url":"https://pith.science/pith/YNGQDGCMEOA7CB2ACRLDZJKXN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNGQDGCMEOA7CB2ACRLDZJKXN7/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":"2026-06-21T21:41:05Z","links":{"resolver":"https://pith.science/pith/YNGQDGCMEOA7CB2ACRLDZJKXN7","bundle":"https://pith.science/pith/YNGQDGCMEOA7CB2ACRLDZJKXN7/bundle.json","state":"https://pith.science/pith/YNGQDGCMEOA7CB2ACRLDZJKXN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNGQDGCMEOA7CB2ACRLDZJKXN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:YNGQDGCMEOA7CB2ACRLDZJKXN7","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":"b1b3e45bd2ff98d6a5ff438dc910af2bf5944fc77c9eea9955942e44f4046db5","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-10-16T19:01:50Z","title_canon_sha256":"c2ac38a6b4e1237bcb7b9d1749ea1e210f520a82809475c95f96177f98cb7a40"},"schema_version":"1.0","source":{"id":"math/0210231","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210231","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210231v2","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210231","created_at":"2026-05-18T00:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"YNGQDGCMEOA7","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"YNGQDGCMEOA7CB2A","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"YNGQDGCM","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:2605f82462633e58a82eb64388b670430180ab0027fc20e80d1e31696a39289b","target":"graph","created_at":"2026-05-18T00:41:42Z","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 all biquotients whose rational cohomology rings are generated by one element. As a consequence we show that the Gromoll-Meyer 7-sphere is the only exotic sphere which can be written as a biquotient.","authors_text":"Vitali Kapovitch, Wolfgang Ziller","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-10-16T19:01:50Z","title":"Biquotients with singly generated rational cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210231","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":"sha256:1c389c0ff4b2bf07d02c5ba1632446e773b0cc674d05ca1393a9b081b4d8024b","target":"record","created_at":"2026-05-18T00:41:42Z","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":"b1b3e45bd2ff98d6a5ff438dc910af2bf5944fc77c9eea9955942e44f4046db5","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-10-16T19:01:50Z","title_canon_sha256":"c2ac38a6b4e1237bcb7b9d1749ea1e210f520a82809475c95f96177f98cb7a40"},"schema_version":"1.0","source":{"id":"math/0210231","kind":"arxiv","version":2}},"canonical_sha256":"c34d01984c2381f1074014563ca5576fda5ed9c08877c2471d58896dc92a2be2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c34d01984c2381f1074014563ca5576fda5ed9c08877c2471d58896dc92a2be2","first_computed_at":"2026-05-18T00:41:42.432377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:42.432377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wrDkZLGkksSWHo9f0kYVOQHD8CW1d51Mh84s/PwI1VOlCGVZnxVfOgASaCPCYOgFMaXuW5dW0NUqqSEWeARdAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:42.433070Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0210231","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c389c0ff4b2bf07d02c5ba1632446e773b0cc674d05ca1393a9b081b4d8024b","sha256:2605f82462633e58a82eb64388b670430180ab0027fc20e80d1e31696a39289b"],"state_sha256":"175c174bd2e582d0c962fb4380ed036a9b08d5907faa5d919e0a89290e703d95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEVoI28wbjeSkacnIV6fLHb4qjMbcZfqEuMOgc+mmZNgFtvi5PtnmP77M/uHSFaLQJETdYDDI11TX2EWbL0FAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:41:05.250188Z","bundle_sha256":"97be55e3406aaec29501207ee067005e85420ecd62e0906cd8b3da9aeb57914c"}}