{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7W226AQC4KDTWD6KYQKXCEMKOK","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":"2934d890e017e6e0d9c0dd2d1befa159e654325ad58a3b20378b564b1f3df7ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-02T08:47:38Z","title_canon_sha256":"c29c6710ea9de5cd7c71f6fb64c267f42a50ef04a91e37a2a38d7e22e29837e9"},"schema_version":"1.0","source":{"id":"1411.0227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0227","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0227v1","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0227","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"7W226AQC4KDT","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7W226AQC4KDTWD6K","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7W226AQC","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:5a48a60152beb9291d62c3953edcb00076d594909bfccd1fbeea257e6841619f","target":"graph","created_at":"2026-05-18T02:38:52Z","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 provide Sobolev estimates for solutions of first order Hamilton-Jacobi equations with Hamiltonians which are superlinear in the gradient variable. We also show that the solutions are differentiable almost everywhere. The proof relies on an inverse H\\\"older inequality. Applications to mean field games are discussed.","authors_text":"Alessio Porretta, Daniela Tonon, Pierre Cardaliaguet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-02T08:47:38Z","title":"Sobolev regularity for the first order Hamilton-Jacobi equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0227","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:cfa5699d36ad07d4ec6ac4f1b6e786f1bad9f3b3311cc9ca211458567a539a22","target":"record","created_at":"2026-05-18T02:38:52Z","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":"2934d890e017e6e0d9c0dd2d1befa159e654325ad58a3b20378b564b1f3df7ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-02T08:47:38Z","title_canon_sha256":"c29c6710ea9de5cd7c71f6fb64c267f42a50ef04a91e37a2a38d7e22e29837e9"},"schema_version":"1.0","source":{"id":"1411.0227","kind":"arxiv","version":1}},"canonical_sha256":"fdb5af0202e2873b0fcac41571118a72b2b596332af4ad485cd2ebfc5fda64c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdb5af0202e2873b0fcac41571118a72b2b596332af4ad485cd2ebfc5fda64c5","first_computed_at":"2026-05-18T02:38:52.236875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:52.236875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0mH3hFMDs26zoW7vFE3LN+Pj4aPYyzvALzS9gwdES4pnr0aAqKrpxzUtPpkBHnc3oOwYgSddiKEOoL4Uj9dCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:52.237413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfa5699d36ad07d4ec6ac4f1b6e786f1bad9f3b3311cc9ca211458567a539a22","sha256:5a48a60152beb9291d62c3953edcb00076d594909bfccd1fbeea257e6841619f"],"state_sha256":"2de3dca573a5a5bd1830465f597e7a50afe5a3f57d9f644df047dd5ebe5918d2"}