{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:FY3DOLL24HGOEJ7U4HJQUVKPFI","short_pith_number":"pith:FY3DOLL2","canonical_record":{"source":{"id":"2302.04964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-02-09T22:42:36Z","cross_cats_sorted":[],"title_canon_sha256":"52c690476dfe0e268d238f3b04be5b540eb19b0a86d1c0cf7a8bc6e38f431218","abstract_canon_sha256":"3aed87a7f1acfddf4b9109650b5bc7b888e2a767af791fd38538bffca9015273"},"schema_version":"1.0"},"canonical_sha256":"2e36372d7ae1cce227f4e1d30a554f2a3d9bbf55874cbe6c41fb891d3eefb559","source":{"kind":"arxiv","id":"2302.04964","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.04964","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"2302.04964v2","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.04964","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"FY3DOLL24HGO","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_16","alias_value":"FY3DOLL24HGOEJ7U","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_8","alias_value":"FY3DOLL2","created_at":"2026-05-20T14:03:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:FY3DOLL24HGOEJ7U4HJQUVKPFI","target":"record","payload":{"canonical_record":{"source":{"id":"2302.04964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-02-09T22:42:36Z","cross_cats_sorted":[],"title_canon_sha256":"52c690476dfe0e268d238f3b04be5b540eb19b0a86d1c0cf7a8bc6e38f431218","abstract_canon_sha256":"3aed87a7f1acfddf4b9109650b5bc7b888e2a767af791fd38538bffca9015273"},"schema_version":"1.0"},"canonical_sha256":"2e36372d7ae1cce227f4e1d30a554f2a3d9bbf55874cbe6c41fb891d3eefb559","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T14:03:16.342214Z","signature_b64":"Ev3EuWHArMB85DPlq/XR66OwGktC8lBXqVCAD1CWE6GjYZuAmisVx2GZHpbzrWh8JVHrslGduMUY2vY6WoyoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e36372d7ae1cce227f4e1d30a554f2a3d9bbf55874cbe6c41fb891d3eefb559","last_reissued_at":"2026-05-20T14:03:16.341834Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T14:03:16.341834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.04964","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":"2026-05-20T14:03:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzVBW8P11OJX5WpoWrvh+RJc7MQ1uqTiJiY0gFM7vkmF4TmBDGQXe3/w7gleg3k7FfkDwE3KrJx9bN01o9J5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:01:41.189390Z"},"content_sha256":"a7d777899bee6b9773b6c955febaa2d56bb33693e06cb52c0fb900ce0582a7e4","schema_version":"1.0","event_id":"sha256:a7d777899bee6b9773b6c955febaa2d56bb33693e06cb52c0fb900ce0582a7e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:FY3DOLL24HGOEJ7U4HJQUVKPFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ancient Ricci flows of bounded girth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mat Langford, Ramiro Lafuente, Theodora Bourni, Timothy Buttsworth","submitted_at":"2023-02-09T22:42:36Z","abstract_excerpt":"For each $n\\ge 3$, we construct a 'pancake-like', $O(2)\\times O(n-1)$-invariant ancient Ricci flow with positive curvature operator and bounded \"girth\", and we determine its asymptotic limits backwards in time. This solution is new even in dimension three. The construction hinges on the Ricci flow invariance of certain conditions on the curvature and its spatial derivatives under this symmetry regime, whose proof does not follow from Hamilton's tensor maximum principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.04964","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.04964/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T14:03:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jGlXpSE2a7pcZOrQX4ur1lL2cHFD2Q68vmylTTflpLEVywoZAIyaRlLn1W3rXvVN/j3/xyyNHb3Jo1R6UQUYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:01:41.190469Z"},"content_sha256":"c532cbd09e708b8f36f21fea9760118ce6b077c533155baae99eb9bfac310f03","schema_version":"1.0","event_id":"sha256:c532cbd09e708b8f36f21fea9760118ce6b077c533155baae99eb9bfac310f03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FY3DOLL24HGOEJ7U4HJQUVKPFI/bundle.json","state_url":"https://pith.science/pith/FY3DOLL24HGOEJ7U4HJQUVKPFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FY3DOLL24HGOEJ7U4HJQUVKPFI/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":"2026-05-30T16:01:41Z","links":{"resolver":"https://pith.science/pith/FY3DOLL24HGOEJ7U4HJQUVKPFI","bundle":"https://pith.science/pith/FY3DOLL24HGOEJ7U4HJQUVKPFI/bundle.json","state":"https://pith.science/pith/FY3DOLL24HGOEJ7U4HJQUVKPFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FY3DOLL24HGOEJ7U4HJQUVKPFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FY3DOLL24HGOEJ7U4HJQUVKPFI","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":"3aed87a7f1acfddf4b9109650b5bc7b888e2a767af791fd38538bffca9015273","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-02-09T22:42:36Z","title_canon_sha256":"52c690476dfe0e268d238f3b04be5b540eb19b0a86d1c0cf7a8bc6e38f431218"},"schema_version":"1.0","source":{"id":"2302.04964","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.04964","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"2302.04964v2","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.04964","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"FY3DOLL24HGO","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_16","alias_value":"FY3DOLL24HGOEJ7U","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_8","alias_value":"FY3DOLL2","created_at":"2026-05-20T14:03:16Z"}],"graph_snapshots":[{"event_id":"sha256:c532cbd09e708b8f36f21fea9760118ce6b077c533155baae99eb9bfac310f03","target":"graph","created_at":"2026-05-20T14:03:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.04964/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For each $n\\ge 3$, we construct a 'pancake-like', $O(2)\\times O(n-1)$-invariant ancient Ricci flow with positive curvature operator and bounded \"girth\", and we determine its asymptotic limits backwards in time. This solution is new even in dimension three. The construction hinges on the Ricci flow invariance of certain conditions on the curvature and its spatial derivatives under this symmetry regime, whose proof does not follow from Hamilton's tensor maximum principle.","authors_text":"Mat Langford, Ramiro Lafuente, Theodora Bourni, Timothy Buttsworth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-02-09T22:42:36Z","title":"Ancient Ricci flows of bounded girth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.04964","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:a7d777899bee6b9773b6c955febaa2d56bb33693e06cb52c0fb900ce0582a7e4","target":"record","created_at":"2026-05-20T14:03:16Z","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":"3aed87a7f1acfddf4b9109650b5bc7b888e2a767af791fd38538bffca9015273","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-02-09T22:42:36Z","title_canon_sha256":"52c690476dfe0e268d238f3b04be5b540eb19b0a86d1c0cf7a8bc6e38f431218"},"schema_version":"1.0","source":{"id":"2302.04964","kind":"arxiv","version":2}},"canonical_sha256":"2e36372d7ae1cce227f4e1d30a554f2a3d9bbf55874cbe6c41fb891d3eefb559","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e36372d7ae1cce227f4e1d30a554f2a3d9bbf55874cbe6c41fb891d3eefb559","first_computed_at":"2026-05-20T14:03:16.341834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T14:03:16.341834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ev3EuWHArMB85DPlq/XR66OwGktC8lBXqVCAD1CWE6GjYZuAmisVx2GZHpbzrWh8JVHrslGduMUY2vY6WoyoAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T14:03:16.342214Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.04964","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7d777899bee6b9773b6c955febaa2d56bb33693e06cb52c0fb900ce0582a7e4","sha256:c532cbd09e708b8f36f21fea9760118ce6b077c533155baae99eb9bfac310f03"],"state_sha256":"c2477faffa8b290489a02830cf01e442636a1fe120f41c4bb1fcd86a897e82d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xatL1gAwCB4vmQe+QzZ3YV1yeBm307h4Fbl/7M+q+Vn5qEbrqabVEB65ubsGndRc4nnaQwN1BvLZlciLZRgBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:01:41.194517Z","bundle_sha256":"04804df40a9cf008e0af5049f3fc2273e26ad037d95e1aba91c1c0d12a4e775c"}}