{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PVGXXAW3J43XOU373UVGJKF7TD","short_pith_number":"pith:PVGXXAW3","canonical_record":{"source":{"id":"1710.00361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T14:47:53Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"93517782b8763370e31088c5a7827dba67eb36bda261b47e4c5c449ae2b9aa3c","abstract_canon_sha256":"d291f3076d8200244ee89d782454ed88cc01f2b10ce3dce6614a6aa47c43acf7"},"schema_version":"1.0"},"canonical_sha256":"7d4d7b82db4f3777537fdd2a64a8bf98f981b9acb717037f0248d298017180dd","source":{"kind":"arxiv","id":"1710.00361","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00361","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00361v3","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00361","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"PVGXXAW3J43X","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVGXXAW3J43XOU37","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVGXXAW3","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PVGXXAW3J43XOU373UVGJKF7TD","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T14:47:53Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"93517782b8763370e31088c5a7827dba67eb36bda261b47e4c5c449ae2b9aa3c","abstract_canon_sha256":"d291f3076d8200244ee89d782454ed88cc01f2b10ce3dce6614a6aa47c43acf7"},"schema_version":"1.0"},"canonical_sha256":"7d4d7b82db4f3777537fdd2a64a8bf98f981b9acb717037f0248d298017180dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:30.531869Z","signature_b64":"0Hyj9eqzl7t9Wi1Z9M4qzYU+jNn02ADFNxDIp14dcOmBwarPfm2Q+HOsl6jDekRFADByN4jFkePhJi8oARHbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d4d7b82db4f3777537fdd2a64a8bf98f981b9acb717037f0248d298017180dd","last_reissued_at":"2026-05-18T00:15:30.531182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:30.531182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00361","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":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86nYT9lroL1RXEfbxCsY9o0nCyFRg1bsp2/spOky3OhX8xUcrKs88h/bdgDTWquB5F2pqdQwKxYcypF+HVlqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:29:47.828813Z"},"content_sha256":"83ed4a3ed9b506cff20d2e33dc4bcca5bdc8e63a4306e56d36d2502184824f5b","schema_version":"1.0","event_id":"sha256:83ed4a3ed9b506cff20d2e33dc4bcca5bdc8e63a4306e56d36d2502184824f5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PVGXXAW3J43XOU373UVGJKF7TD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ancient solutions of geometric flows with curvature pinching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Carlo Sinestrari, Susanna Risa","submitted_at":"2017-10-01T14:47:53Z","abstract_excerpt":"We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension greater than one, and for some nonlinear curvature flows of hypersurfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00361","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":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGdp3JEQbHuUDuAF+sJQWx80GS8H2rGePFlT6V+7OhScj3FFwypfuKPvu4UR/c6p144fc7kSaLAK/RboeaHxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:29:47.829159Z"},"content_sha256":"5f5d6adc9f5be38b94ab331c315183e2de610acac8e41b0f4f7c8a07144da4bd","schema_version":"1.0","event_id":"sha256:5f5d6adc9f5be38b94ab331c315183e2de610acac8e41b0f4f7c8a07144da4bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVGXXAW3J43XOU373UVGJKF7TD/bundle.json","state_url":"https://pith.science/pith/PVGXXAW3J43XOU373UVGJKF7TD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVGXXAW3J43XOU373UVGJKF7TD/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":"2026-06-30T20:29:47Z","links":{"resolver":"https://pith.science/pith/PVGXXAW3J43XOU373UVGJKF7TD","bundle":"https://pith.science/pith/PVGXXAW3J43XOU373UVGJKF7TD/bundle.json","state":"https://pith.science/pith/PVGXXAW3J43XOU373UVGJKF7TD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVGXXAW3J43XOU373UVGJKF7TD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PVGXXAW3J43XOU373UVGJKF7TD","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":"d291f3076d8200244ee89d782454ed88cc01f2b10ce3dce6614a6aa47c43acf7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T14:47:53Z","title_canon_sha256":"93517782b8763370e31088c5a7827dba67eb36bda261b47e4c5c449ae2b9aa3c"},"schema_version":"1.0","source":{"id":"1710.00361","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00361","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00361v3","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00361","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"PVGXXAW3J43X","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVGXXAW3J43XOU37","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVGXXAW3","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:5f5d6adc9f5be38b94ab331c315183e2de610acac8e41b0f4f7c8a07144da4bd","target":"graph","created_at":"2026-05-18T00:15:30Z","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 prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension greater than one, and for some nonlinear curvature flows of hypersurfaces.","authors_text":"Carlo Sinestrari, Susanna Risa","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T14:47:53Z","title":"Ancient solutions of geometric flows with curvature pinching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00361","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":"sha256:83ed4a3ed9b506cff20d2e33dc4bcca5bdc8e63a4306e56d36d2502184824f5b","target":"record","created_at":"2026-05-18T00:15:30Z","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":"d291f3076d8200244ee89d782454ed88cc01f2b10ce3dce6614a6aa47c43acf7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T14:47:53Z","title_canon_sha256":"93517782b8763370e31088c5a7827dba67eb36bda261b47e4c5c449ae2b9aa3c"},"schema_version":"1.0","source":{"id":"1710.00361","kind":"arxiv","version":3}},"canonical_sha256":"7d4d7b82db4f3777537fdd2a64a8bf98f981b9acb717037f0248d298017180dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d4d7b82db4f3777537fdd2a64a8bf98f981b9acb717037f0248d298017180dd","first_computed_at":"2026-05-18T00:15:30.531182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:30.531182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Hyj9eqzl7t9Wi1Z9M4qzYU+jNn02ADFNxDIp14dcOmBwarPfm2Q+HOsl6jDekRFADByN4jFkePhJi8oARHbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:30.531869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00361","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83ed4a3ed9b506cff20d2e33dc4bcca5bdc8e63a4306e56d36d2502184824f5b","sha256:5f5d6adc9f5be38b94ab331c315183e2de610acac8e41b0f4f7c8a07144da4bd"],"state_sha256":"2101c3ac64bf0d5e879d5cde899616933610000974575633a5776f49a751d9f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FO5zjTOrYcNmP6tkFd59tzYDovmvGAkXgL03paOXwTuKWLgIPlVPGqy00T90YIYI8K5qTPFq+UY0gI0K0IzzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:29:47.831233Z","bundle_sha256":"299aa464d8193175bec4ad05cbda51cb9f80a2a3d19c799cf7d738dfe7118924"}}