{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:PENO5B5ZDYLHQJRES2MFNXJMJ4","short_pith_number":"pith:PENO5B5Z","canonical_record":{"source":{"id":"2211.12639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-11-22T23:55:11Z","cross_cats_sorted":[],"title_canon_sha256":"290a9236ea2cc1ab26c10b3a0c78a8b1b2db4ae2fbfca714e97908e817e7d81c","abstract_canon_sha256":"d71a1960dae10b643078929b34cb88e8a0c0309c4c9ba4434560366285e1e42e"},"schema_version":"1.0"},"canonical_sha256":"791aee87b91e16782624969856dd2c4f2b03f76ea1313a1c0723ce99f690bbda","source":{"kind":"arxiv","id":"2211.12639","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.12639","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"2211.12639v1","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.12639","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"PENO5B5ZDYLH","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"pith_short_16","alias_value":"PENO5B5ZDYLHQJRE","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"pith_short_8","alias_value":"PENO5B5Z","created_at":"2026-07-05T05:18:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:PENO5B5ZDYLHQJRES2MFNXJMJ4","target":"record","payload":{"canonical_record":{"source":{"id":"2211.12639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-11-22T23:55:11Z","cross_cats_sorted":[],"title_canon_sha256":"290a9236ea2cc1ab26c10b3a0c78a8b1b2db4ae2fbfca714e97908e817e7d81c","abstract_canon_sha256":"d71a1960dae10b643078929b34cb88e8a0c0309c4c9ba4434560366285e1e42e"},"schema_version":"1.0"},"canonical_sha256":"791aee87b91e16782624969856dd2c4f2b03f76ea1313a1c0723ce99f690bbda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:18:53.188506Z","signature_b64":"moNzVPXOjK9+Wt1MZ/oa8tAPBN2iA8KTF/QAech58m1m91BSWwbUVG2QTdPA/wj9dcWyD6UgHniLfYnX8dDzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"791aee87b91e16782624969856dd2c4f2b03f76ea1313a1c0723ce99f690bbda","last_reissued_at":"2026-07-05T05:18:53.188134Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:18:53.188134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.12639","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":"2026-07-05T05:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6X+bNryZ03RCjJ9eHcUKK69iaOyGZymlhiHNgkgAo3QkoBujZ8FRa1BXo/YX1O8qTV9e0tJwyoZdpnZFfe9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:16:13.805691Z"},"content_sha256":"345f0f78091eb4b74549529150a7fb87009d46baffe1b82f3916a9dc99bdd86a","schema_version":"1.0","event_id":"sha256:345f0f78091eb4b74549529150a7fb87009d46baffe1b82f3916a9dc99bdd86a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:PENO5B5ZDYLHQJRES2MFNXJMJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamilton's Theorem (on the compactness of pinched hypersurfaces) via mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mat Langford, Stephen Lynch, Theodora Bourni","submitted_at":"2022-11-22T23:55:11Z","abstract_excerpt":"We make rigorous an old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.12639","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.12639/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":"2026-07-05T05:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkTDZE7NAwNHWCgVWf2jNTrAgoP5c+9jFe/5cnFkwD9OMQ0b2J3AWs3KA10SdHotPnlANy+/350WYIjkBhZXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:16:13.806259Z"},"content_sha256":"d777ff31af26f914d45fef383889a402f9df6f522ea2aa3da0f8228eb148d2f0","schema_version":"1.0","event_id":"sha256:d777ff31af26f914d45fef383889a402f9df6f522ea2aa3da0f8228eb148d2f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PENO5B5ZDYLHQJRES2MFNXJMJ4/bundle.json","state_url":"https://pith.science/pith/PENO5B5ZDYLHQJRES2MFNXJMJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PENO5B5ZDYLHQJRES2MFNXJMJ4/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":"2026-08-05T02:16:13Z","links":{"resolver":"https://pith.science/pith/PENO5B5ZDYLHQJRES2MFNXJMJ4","bundle":"https://pith.science/pith/PENO5B5ZDYLHQJRES2MFNXJMJ4/bundle.json","state":"https://pith.science/pith/PENO5B5ZDYLHQJRES2MFNXJMJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PENO5B5ZDYLHQJRES2MFNXJMJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PENO5B5ZDYLHQJRES2MFNXJMJ4","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":"d71a1960dae10b643078929b34cb88e8a0c0309c4c9ba4434560366285e1e42e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-11-22T23:55:11Z","title_canon_sha256":"290a9236ea2cc1ab26c10b3a0c78a8b1b2db4ae2fbfca714e97908e817e7d81c"},"schema_version":"1.0","source":{"id":"2211.12639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.12639","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"2211.12639v1","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.12639","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"PENO5B5ZDYLH","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"pith_short_16","alias_value":"PENO5B5ZDYLHQJRE","created_at":"2026-07-05T05:18:53Z"},{"alias_kind":"pith_short_8","alias_value":"PENO5B5Z","created_at":"2026-07-05T05:18:53Z"}],"graph_snapshots":[{"event_id":"sha256:d777ff31af26f914d45fef383889a402f9df6f522ea2aa3da0f8228eb148d2f0","target":"graph","created_at":"2026-07-05T05:18:53Z","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/2211.12639/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We make rigorous an old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature.","authors_text":"Mat Langford, Stephen Lynch, Theodora Bourni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-11-22T23:55:11Z","title":"Hamilton's Theorem (on the compactness of pinched hypersurfaces) via mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.12639","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":"sha256:345f0f78091eb4b74549529150a7fb87009d46baffe1b82f3916a9dc99bdd86a","target":"record","created_at":"2026-07-05T05:18:53Z","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":"d71a1960dae10b643078929b34cb88e8a0c0309c4c9ba4434560366285e1e42e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-11-22T23:55:11Z","title_canon_sha256":"290a9236ea2cc1ab26c10b3a0c78a8b1b2db4ae2fbfca714e97908e817e7d81c"},"schema_version":"1.0","source":{"id":"2211.12639","kind":"arxiv","version":1}},"canonical_sha256":"791aee87b91e16782624969856dd2c4f2b03f76ea1313a1c0723ce99f690bbda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"791aee87b91e16782624969856dd2c4f2b03f76ea1313a1c0723ce99f690bbda","first_computed_at":"2026-07-05T05:18:53.188134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:18:53.188134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"moNzVPXOjK9+Wt1MZ/oa8tAPBN2iA8KTF/QAech58m1m91BSWwbUVG2QTdPA/wj9dcWyD6UgHniLfYnX8dDzBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:18:53.188506Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.12639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:345f0f78091eb4b74549529150a7fb87009d46baffe1b82f3916a9dc99bdd86a","sha256:d777ff31af26f914d45fef383889a402f9df6f522ea2aa3da0f8228eb148d2f0"],"state_sha256":"49985adb94d824614c5c2a399946780a30c413bb9f6c1c9aa0c951484115bf0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2+eZpAw+BXo/snixpTokwx1brKycr7E+VDrcWCYRCmKwuG7HeEX+HPmJ2imlCazxMUYmZj1N7ffJIo9XdbLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:16:13.812227Z","bundle_sha256":"a8f96c2660450c8c75ef811598e035399761696150a94c1ee7859b9d51085656"}}