{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VVUZLBWN2CLOTI6TRSI5EF6GZX","short_pith_number":"pith:VVUZLBWN","canonical_record":{"source":{"id":"1205.4455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-20T20:22:34Z","cross_cats_sorted":[],"title_canon_sha256":"5a5481be5e639721f36f7f69b0c55483c8ffd1d75530278fcbdcee59b2bf4757","abstract_canon_sha256":"365ee56385da9b18dbc54fd5811f3c203349305952968f753d6b5242df648e84"},"schema_version":"1.0"},"canonical_sha256":"ad699586cdd096e9a3d38c91d217c6cdf0091d0a444ba2caa441ff76aaa2f1a3","source":{"kind":"arxiv","id":"1205.4455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4455","created_at":"2026-05-18T03:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4455v1","created_at":"2026-05-18T03:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4455","created_at":"2026-05-18T03:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"VVUZLBWN2CLO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VVUZLBWN2CLOTI6T","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VVUZLBWN","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VVUZLBWN2CLOTI6TRSI5EF6GZX","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-20T20:22:34Z","cross_cats_sorted":[],"title_canon_sha256":"5a5481be5e639721f36f7f69b0c55483c8ffd1d75530278fcbdcee59b2bf4757","abstract_canon_sha256":"365ee56385da9b18dbc54fd5811f3c203349305952968f753d6b5242df648e84"},"schema_version":"1.0"},"canonical_sha256":"ad699586cdd096e9a3d38c91d217c6cdf0091d0a444ba2caa441ff76aaa2f1a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:13.163648Z","signature_b64":"sAVKFG5QBtvluvPjvadIjctpRnEHrXjTnoUsEtg3ENGy+61d+EONJzk502QkWr4ZcLPqrMd/4s51ls/v5L0jBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad699586cdd096e9a3d38c91d217c6cdf0091d0a444ba2caa441ff76aaa2f1a3","last_reissued_at":"2026-05-18T03:55:13.163173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:13.163173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4455","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":"2026-05-18T03:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLkqlbt8WKt+yxzwFaoEqRSkVZyJ/hioy5kTT8DCcLT7o1NC/6PEfKGCkj6Dl8pA4CPkbq7RcF2aEIWfFjKxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:35:54.962260Z"},"content_sha256":"66550bb2320953d2fc44459e58779f4a1a5ad63aadf96ba47470f7b665736bf8","schema_version":"1.0","event_id":"sha256:66550bb2320953d2fc44459e58779f4a1a5ad63aadf96ba47470f7b665736bf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VVUZLBWN2CLOTI6TRSI5EF6GZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Manifolds without conjugate points and their fundamental groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Sergei Ivanov, Vitali Kapovitch","submitted_at":"2012-05-20T20:22:34Z","abstract_excerpt":"We show that in the fundamental groups of closed manifolds without conjugate points centralizers of all elements virtually split."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4455","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":"2026-05-18T03:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mD+0+3R1kjGdMrU3RYKFlzJDsnSG6OTUiNmi/+N0973e50rZmkG7+Fd0AM25cuMFkl8QXd9PRvZauysq8hAUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:35:54.962626Z"},"content_sha256":"47ee6395e5d4e75fae444593767b1ef9739e929e288a1188142cd64e799bb178","schema_version":"1.0","event_id":"sha256:47ee6395e5d4e75fae444593767b1ef9739e929e288a1188142cd64e799bb178"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVUZLBWN2CLOTI6TRSI5EF6GZX/bundle.json","state_url":"https://pith.science/pith/VVUZLBWN2CLOTI6TRSI5EF6GZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVUZLBWN2CLOTI6TRSI5EF6GZX/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":"2026-06-23T19:35:54Z","links":{"resolver":"https://pith.science/pith/VVUZLBWN2CLOTI6TRSI5EF6GZX","bundle":"https://pith.science/pith/VVUZLBWN2CLOTI6TRSI5EF6GZX/bundle.json","state":"https://pith.science/pith/VVUZLBWN2CLOTI6TRSI5EF6GZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVUZLBWN2CLOTI6TRSI5EF6GZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VVUZLBWN2CLOTI6TRSI5EF6GZX","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":"365ee56385da9b18dbc54fd5811f3c203349305952968f753d6b5242df648e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-20T20:22:34Z","title_canon_sha256":"5a5481be5e639721f36f7f69b0c55483c8ffd1d75530278fcbdcee59b2bf4757"},"schema_version":"1.0","source":{"id":"1205.4455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4455","created_at":"2026-05-18T03:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4455v1","created_at":"2026-05-18T03:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4455","created_at":"2026-05-18T03:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"VVUZLBWN2CLO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VVUZLBWN2CLOTI6T","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VVUZLBWN","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:47ee6395e5d4e75fae444593767b1ef9739e929e288a1188142cd64e799bb178","target":"graph","created_at":"2026-05-18T03:55:13Z","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 show that in the fundamental groups of closed manifolds without conjugate points centralizers of all elements virtually split.","authors_text":"Sergei Ivanov, Vitali Kapovitch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-20T20:22:34Z","title":"Manifolds without conjugate points and their fundamental groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4455","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":"sha256:66550bb2320953d2fc44459e58779f4a1a5ad63aadf96ba47470f7b665736bf8","target":"record","created_at":"2026-05-18T03:55:13Z","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":"365ee56385da9b18dbc54fd5811f3c203349305952968f753d6b5242df648e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-20T20:22:34Z","title_canon_sha256":"5a5481be5e639721f36f7f69b0c55483c8ffd1d75530278fcbdcee59b2bf4757"},"schema_version":"1.0","source":{"id":"1205.4455","kind":"arxiv","version":1}},"canonical_sha256":"ad699586cdd096e9a3d38c91d217c6cdf0091d0a444ba2caa441ff76aaa2f1a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad699586cdd096e9a3d38c91d217c6cdf0091d0a444ba2caa441ff76aaa2f1a3","first_computed_at":"2026-05-18T03:55:13.163173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:13.163173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sAVKFG5QBtvluvPjvadIjctpRnEHrXjTnoUsEtg3ENGy+61d+EONJzk502QkWr4ZcLPqrMd/4s51ls/v5L0jBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:13.163648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66550bb2320953d2fc44459e58779f4a1a5ad63aadf96ba47470f7b665736bf8","sha256:47ee6395e5d4e75fae444593767b1ef9739e929e288a1188142cd64e799bb178"],"state_sha256":"cd81ad9b534c8ceb3f52c3fd2d4012a14fff5564123c6d9075121a030e9a948a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Js+G5/6QKgICTJdHahfrSIi7MADAYdz4balV/t9c20+T3AG5UImvzX+9DT4GIkRg/5OR1k4W8346+iUG0oMsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:35:54.964502Z","bundle_sha256":"4a039885cecb488394cde16c704a2eb5a8e67efb79efb3318a52debf33aa93f6"}}