{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YKEIOLLMDJGTOU42CSPBUS5P3W","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":"2669cb75a9235a6f31d3baf79645f8b176592b958d9005b6aa55b1ff141ca946","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-27T06:59:46Z","title_canon_sha256":"f0ee6b4c848e6f5deb652b02ee22bdb18053be0ca315f52710920df40586d86a"},"schema_version":"1.0","source":{"id":"1405.6813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6813","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6813v1","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6813","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"YKEIOLLMDJGT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YKEIOLLMDJGTOU42","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YKEIOLLM","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:dee4b97965cfd64d998e50c5cec3278e2ebdc5d3ae4dda306a18136636fe2c05","target":"graph","created_at":"2026-05-18T02:51:00Z","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 consider smooth solutions to the biharmonic heat equation on Euclidean space for which the square of the Laplacian at time t is globally bounded from above by k/t for some k in R, for all t in [0,T]. We prove local, in space and time, estimates for such solutions. We explain how these estimates imply uniqueness of smooth solutions in this class.","authors_text":"Glen Wheeler, Miles Simon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-27T06:59:46Z","title":"Some local estimates and a uniqueness result for the entire biharmonic heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6813","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:da6cc63d39895ef44ceeb38658a631a8e51b6e593e3058cef80771ebdc5f682f","target":"record","created_at":"2026-05-18T02:51:00Z","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":"2669cb75a9235a6f31d3baf79645f8b176592b958d9005b6aa55b1ff141ca946","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-27T06:59:46Z","title_canon_sha256":"f0ee6b4c848e6f5deb652b02ee22bdb18053be0ca315f52710920df40586d86a"},"schema_version":"1.0","source":{"id":"1405.6813","kind":"arxiv","version":1}},"canonical_sha256":"c288872d6c1a4d37539a149e1a4bafddbcaba81b27ad93c5f4a81a539147d229","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c288872d6c1a4d37539a149e1a4bafddbcaba81b27ad93c5f4a81a539147d229","first_computed_at":"2026-05-18T02:51:00.290799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:00.290799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aXORvbluP3VRSKPKBkO6eMPNyFDF2kWCCg5GNH90ck5dV4rNeUb2Yjxv7P4iMW6UpaOrlIg0V7DfR3PBrWUyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:00.291215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da6cc63d39895ef44ceeb38658a631a8e51b6e593e3058cef80771ebdc5f682f","sha256:dee4b97965cfd64d998e50c5cec3278e2ebdc5d3ae4dda306a18136636fe2c05"],"state_sha256":"ccc412d2bed261a553e69dff64d51ee1e220a71e581d3bc3c69fabb154ffab0d"}