{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EEKKADQ5GPPKV6IVJZQ44BRCUL","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":"7894a8a923b2415fc6745ec0cefb86e37387c357d649dbd942ccd5a82cae6546","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-08-05T13:48:07Z","title_canon_sha256":"a1ee2eb7f622ec786698997b1a857070a2cd94dd2e8ca6e121c986855f1908dc"},"schema_version":"1.0","source":{"id":"2608.04855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04855","created_at":"2026-08-06T01:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04855v1","created_at":"2026-08-06T01:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04855","created_at":"2026-08-06T01:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"EEKKADQ5GPPK","created_at":"2026-08-06T01:47:24Z"},{"alias_kind":"pith_short_16","alias_value":"EEKKADQ5GPPKV6IV","created_at":"2026-08-06T01:47:24Z"},{"alias_kind":"pith_short_8","alias_value":"EEKKADQ5","created_at":"2026-08-06T01:47:24Z"}],"graph_snapshots":[{"event_id":"sha256:2ff9589f5064ad4f207409262fd6bb24448e45c71ddca8874e574b4778b71716","target":"graph","created_at":"2026-08-06T01:47:24Z","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/2608.04855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Grayson and Gage proved that an immortal curve shortening flow of simple closed curves on a closed surface converges subsequentially to a closed geodesic, and they asked whether this limiting geodesic is unique. We answer this question negatively by constructing a smooth Riemannian metric on $\\mathbb{S}^2$ and an immortal simple closed curve shortening flow that converges along different sequences of times to every geodesic in a one-parameter family of distinct simple closed geodesics.","authors_text":"Shrey Aryan, Tang-Kai Lee","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-08-05T13:48:07Z","title":"Non-uniqueness of geodesic limits and a question of Grayson and Gage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04855","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":"sha256:4f77004c3dbd6309b0424eba4ab7e7e319a1dec0de7b6b33fba9349445e2b410","target":"record","created_at":"2026-08-06T01:47:24Z","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":"7894a8a923b2415fc6745ec0cefb86e37387c357d649dbd942ccd5a82cae6546","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-08-05T13:48:07Z","title_canon_sha256":"a1ee2eb7f622ec786698997b1a857070a2cd94dd2e8ca6e121c986855f1908dc"},"schema_version":"1.0","source":{"id":"2608.04855","kind":"arxiv","version":1}},"canonical_sha256":"2114a00e1d33deaaf9154e61ce0622a2d8780b78ea91cb7cf7487a237392c5f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2114a00e1d33deaaf9154e61ce0622a2d8780b78ea91cb7cf7487a237392c5f1","first_computed_at":"2026-08-06T01:47:24.421905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:47:24.421905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JINeIlrplr1D113uskH8E1A0rgvr29XRkfaHG162mggvYoL6v2zHtNYw0nQth23R65OM10kyNAaoN/D4yvtLBA==","signature_status":"signed_v1","signed_at":"2026-08-06T01:47:24.423318Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f77004c3dbd6309b0424eba4ab7e7e319a1dec0de7b6b33fba9349445e2b410","sha256:2ff9589f5064ad4f207409262fd6bb24448e45c71ddca8874e574b4778b71716"],"state_sha256":"2cae588d5b7a2532d984a43558086387532810aa9afd6a182f76bed7527b135c"}