{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LXO2TL7A6RZBJ4WAHOGR5AKJXH","short_pith_number":"pith:LXO2TL7A","canonical_record":{"source":{"id":"1002.4087","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-22T09:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"f2a05cbcd4f3e9b1549e689f4ddeda9d0afd2253ce89404bc48a44815637d909","abstract_canon_sha256":"db8ea14844b145d095d79507cb77fb76ee2f20db9dd3fd4161fd44b9bd6ff9fb"},"schema_version":"1.0"},"canonical_sha256":"5ddda9afe0f47214f2c03b8d1e8149b9c1ad6f669649bf90b733d4bcdf4541b3","source":{"kind":"arxiv","id":"1002.4087","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4087","created_at":"2026-05-18T02:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4087v2","created_at":"2026-05-18T02:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4087","created_at":"2026-05-18T02:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"LXO2TL7A6RZB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LXO2TL7A6RZBJ4WA","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LXO2TL7A","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LXO2TL7A6RZBJ4WAHOGR5AKJXH","target":"record","payload":{"canonical_record":{"source":{"id":"1002.4087","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-22T09:48:55Z","cross_cats_sorted":[],"title_canon_sha256":"f2a05cbcd4f3e9b1549e689f4ddeda9d0afd2253ce89404bc48a44815637d909","abstract_canon_sha256":"db8ea14844b145d095d79507cb77fb76ee2f20db9dd3fd4161fd44b9bd6ff9fb"},"schema_version":"1.0"},"canonical_sha256":"5ddda9afe0f47214f2c03b8d1e8149b9c1ad6f669649bf90b733d4bcdf4541b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:58.234456Z","signature_b64":"+2l8nf55oueF9mkbxyCN16Ja8wB1kNDjrgHJwQQELAxaRv9Bp0MKx81xsotcXfw7/tvxwwPzjC4GBRfWCToLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ddda9afe0f47214f2c03b8d1e8149b9c1ad6f669649bf90b733d4bcdf4541b3","last_reissued_at":"2026-05-18T02:08:58.233818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:58.233818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.4087","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xjaots9MKm7Rs3aIl7gUEspOHPmIM2askjVDZhXhukDl3flFEN5j74MtgDw/f8o4rF07tJKoX3i0usEbAML1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:48:17.250043Z"},"content_sha256":"3f05bf2dd66d7de202383817a861c2eee61f0f3ea8afa7d43385f3ebc31ff20e","schema_version":"1.0","event_id":"sha256:3f05bf2dd66d7de202383817a861c2eee61f0f3ea8afa7d43385f3ebc31ff20e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LXO2TL7A6RZBJ4WAHOGR5AKJXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SBV regularity for Hamilton-Jacobi equations in $\\mathbb R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Camillo De Lellis, Roger Robyr, Stefano Bianchini","submitted_at":"2010-02-22T09:48:55Z","abstract_excerpt":"In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \\partial_t u + H(D_{x} u)=0 \\qquad \\textrm{in} \\Omega\\subset \\mathbb R\\times \\mathbb R^{n} . $$ In particular, under the assumption that the Hamiltonian $H\\in C^2(\\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\\partial_t u$ belong to the class $SBV_{loc}(\\Omega)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4087","kind":"arxiv","version":2},"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":"2026-05-18T02:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gER+Sz8zTolMrAEVPmfBuE3GSQpI0oyCItacZeTIgRYiYkurcRRSgy/3AvcSjuHl+INBegpGNMIzIA+AvK8IAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:48:17.250401Z"},"content_sha256":"a14c4bcda89ae9e81c4dbbe29a8f12ace3d2d248632e302e8fcddf8b7c0b5cbb","schema_version":"1.0","event_id":"sha256:a14c4bcda89ae9e81c4dbbe29a8f12ace3d2d248632e302e8fcddf8b7c0b5cbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXO2TL7A6RZBJ4WAHOGR5AKJXH/bundle.json","state_url":"https://pith.science/pith/LXO2TL7A6RZBJ4WAHOGR5AKJXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXO2TL7A6RZBJ4WAHOGR5AKJXH/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":"2026-06-01T17:48:17Z","links":{"resolver":"https://pith.science/pith/LXO2TL7A6RZBJ4WAHOGR5AKJXH","bundle":"https://pith.science/pith/LXO2TL7A6RZBJ4WAHOGR5AKJXH/bundle.json","state":"https://pith.science/pith/LXO2TL7A6RZBJ4WAHOGR5AKJXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXO2TL7A6RZBJ4WAHOGR5AKJXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LXO2TL7A6RZBJ4WAHOGR5AKJXH","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":"db8ea14844b145d095d79507cb77fb76ee2f20db9dd3fd4161fd44b9bd6ff9fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-22T09:48:55Z","title_canon_sha256":"f2a05cbcd4f3e9b1549e689f4ddeda9d0afd2253ce89404bc48a44815637d909"},"schema_version":"1.0","source":{"id":"1002.4087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4087","created_at":"2026-05-18T02:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4087v2","created_at":"2026-05-18T02:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4087","created_at":"2026-05-18T02:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"LXO2TL7A6RZB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LXO2TL7A6RZBJ4WA","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LXO2TL7A","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:a14c4bcda89ae9e81c4dbbe29a8f12ace3d2d248632e302e8fcddf8b7c0b5cbb","target":"graph","created_at":"2026-05-18T02:08:58Z","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":"In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \\partial_t u + H(D_{x} u)=0 \\qquad \\textrm{in} \\Omega\\subset \\mathbb R\\times \\mathbb R^{n} . $$ In particular, under the assumption that the Hamiltonian $H\\in C^2(\\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\\partial_t u$ belong to the class $SBV_{loc}(\\Omega)$.","authors_text":"Camillo De Lellis, Roger Robyr, Stefano Bianchini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-22T09:48:55Z","title":"SBV regularity for Hamilton-Jacobi equations in $\\mathbb R^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4087","kind":"arxiv","version":2},"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":"sha256:3f05bf2dd66d7de202383817a861c2eee61f0f3ea8afa7d43385f3ebc31ff20e","target":"record","created_at":"2026-05-18T02:08:58Z","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":"db8ea14844b145d095d79507cb77fb76ee2f20db9dd3fd4161fd44b9bd6ff9fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-02-22T09:48:55Z","title_canon_sha256":"f2a05cbcd4f3e9b1549e689f4ddeda9d0afd2253ce89404bc48a44815637d909"},"schema_version":"1.0","source":{"id":"1002.4087","kind":"arxiv","version":2}},"canonical_sha256":"5ddda9afe0f47214f2c03b8d1e8149b9c1ad6f669649bf90b733d4bcdf4541b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ddda9afe0f47214f2c03b8d1e8149b9c1ad6f669649bf90b733d4bcdf4541b3","first_computed_at":"2026-05-18T02:08:58.233818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:58.233818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+2l8nf55oueF9mkbxyCN16Ja8wB1kNDjrgHJwQQELAxaRv9Bp0MKx81xsotcXfw7/tvxwwPzjC4GBRfWCToLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:58.234456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f05bf2dd66d7de202383817a861c2eee61f0f3ea8afa7d43385f3ebc31ff20e","sha256:a14c4bcda89ae9e81c4dbbe29a8f12ace3d2d248632e302e8fcddf8b7c0b5cbb"],"state_sha256":"92813a1cf3224a3031084f7309542ffcc1f7d895efea62eee1930222c5ab1728"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptpK/uYG5I7q3qjRsekAWE9UzvnulaP5KbNp4bFDWDV0h2PPsXdpG/3YO+T78qjwSKOHpCX/Vay3LBXoaEa7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:48:17.252255Z","bundle_sha256":"497b16bd85c12bc535de81bbf3b5e82b97ebcb5c1b1055e7125e663415f29b0c"}}