{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6LAEBPOFZRTP7KMXWVYFJPKSDD","short_pith_number":"pith:6LAEBPOF","canonical_record":{"source":{"id":"1201.1774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-09T14:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"ade4d82d8bd6430e08512bdabfe45e1611ce50f125cfa81f590b4b46d16516a2","abstract_canon_sha256":"7665474b8c23084383d7b93661d51361e1faf657dae0cc4bf5b5d81023d9e75b"},"schema_version":"1.0"},"canonical_sha256":"f2c040bdc5cc66ffa997b57054bd5218ca794840750bd173d9fd3636fc7bb1ac","source":{"kind":"arxiv","id":"1201.1774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1774","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1774v1","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1774","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"6LAEBPOFZRTP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LAEBPOFZRTP7KMX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LAEBPOF","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6LAEBPOFZRTP7KMXWVYFJPKSDD","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-09T14:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"ade4d82d8bd6430e08512bdabfe45e1611ce50f125cfa81f590b4b46d16516a2","abstract_canon_sha256":"7665474b8c23084383d7b93661d51361e1faf657dae0cc4bf5b5d81023d9e75b"},"schema_version":"1.0"},"canonical_sha256":"f2c040bdc5cc66ffa997b57054bd5218ca794840750bd173d9fd3636fc7bb1ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:55.758706Z","signature_b64":"BRHbTAlpRj4MT5NyDIP8dOnvTc4f6xZtq96rPj09NyvwmjA3zBGp2PQy5E+eDzCTlfmk1IhvCOUsmnpuObN5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2c040bdc5cc66ffa997b57054bd5218ca794840750bd173d9fd3636fc7bb1ac","last_reissued_at":"2026-05-18T04:04:55.758091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:55.758091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1774","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GWdXfLf4A3ZwmrROEC/RMHrOAe8rJE09D1tx2PRa89UIma1+WdpEU49mvSSB5+aqwXw771yvQwWOGamaO+pICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:32:21.679765Z"},"content_sha256":"955be223775bb1afe60a17509be40bf3f78a70146f8f209a394d19d0e5da925d","schema_version":"1.0","event_id":"sha256:955be223775bb1afe60a17509be40bf3f78a70146f8f209a394d19d0e5da925d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6LAEBPOFZRTP7KMXWVYFJPKSDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isolated initial singularities for the viscous Hamilton-Jacobi equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Nguyen Anh Dao (LMPT)","submitted_at":"2012-01-09T14:18:18Z","abstract_excerpt":"Here we study the nonnegative solutions of the viscous Hamilton-Jacobi equation [u_{t}-\\Delta u+|\\nabla u|^{q}=0] in $Q_{\\Omega,T}=\\Omega\\times(0,T),$ where $q>1,T\\in(0,\\infty] ,$ and $\\Omega$ is a smooth bounded domain of $\\mathbb{R}% ^{N}$ containing $0,$ or $\\Omega=\\mathbb{R}^{N}.$ We consider solutions with a possible singularity at point $(x,t)=(0,0).$ We show that if $q\\geq q_{\\ast}=(N+2)/(N+1)$ the singularity is removable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1774","kind":"arxiv","version":1},"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":"2026-05-18T04:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jbXZuA8nKZTtq5eGIaWqd/+z0ZU7qGrKvI8QaPGC4/eumtocNnOtsxjbwj8XkHMeTxxWdR7smEM2BBruR+PDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:32:21.680113Z"},"content_sha256":"2cff968e4b569b8de1aa5de49c943a96510af97fd0e764684605213a72176731","schema_version":"1.0","event_id":"sha256:2cff968e4b569b8de1aa5de49c943a96510af97fd0e764684605213a72176731"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LAEBPOFZRTP7KMXWVYFJPKSDD/bundle.json","state_url":"https://pith.science/pith/6LAEBPOFZRTP7KMXWVYFJPKSDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LAEBPOFZRTP7KMXWVYFJPKSDD/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":"2026-06-26T14:32:21Z","links":{"resolver":"https://pith.science/pith/6LAEBPOFZRTP7KMXWVYFJPKSDD","bundle":"https://pith.science/pith/6LAEBPOFZRTP7KMXWVYFJPKSDD/bundle.json","state":"https://pith.science/pith/6LAEBPOFZRTP7KMXWVYFJPKSDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LAEBPOFZRTP7KMXWVYFJPKSDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6LAEBPOFZRTP7KMXWVYFJPKSDD","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":"7665474b8c23084383d7b93661d51361e1faf657dae0cc4bf5b5d81023d9e75b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-09T14:18:18Z","title_canon_sha256":"ade4d82d8bd6430e08512bdabfe45e1611ce50f125cfa81f590b4b46d16516a2"},"schema_version":"1.0","source":{"id":"1201.1774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1774","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1774v1","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1774","created_at":"2026-05-18T04:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"6LAEBPOFZRTP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6LAEBPOFZRTP7KMX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6LAEBPOF","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:2cff968e4b569b8de1aa5de49c943a96510af97fd0e764684605213a72176731","target":"graph","created_at":"2026-05-18T04:04:55Z","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":"Here we study the nonnegative solutions of the viscous Hamilton-Jacobi equation [u_{t}-\\Delta u+|\\nabla u|^{q}=0] in $Q_{\\Omega,T}=\\Omega\\times(0,T),$ where $q>1,T\\in(0,\\infty] ,$ and $\\Omega$ is a smooth bounded domain of $\\mathbb{R}% ^{N}$ containing $0,$ or $\\Omega=\\mathbb{R}^{N}.$ We consider solutions with a possible singularity at point $(x,t)=(0,0).$ We show that if $q\\geq q_{\\ast}=(N+2)/(N+1)$ the singularity is removable.","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Nguyen Anh Dao (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-09T14:18:18Z","title":"Isolated initial singularities for the viscous Hamilton-Jacobi equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1774","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":"sha256:955be223775bb1afe60a17509be40bf3f78a70146f8f209a394d19d0e5da925d","target":"record","created_at":"2026-05-18T04:04:55Z","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":"7665474b8c23084383d7b93661d51361e1faf657dae0cc4bf5b5d81023d9e75b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-09T14:18:18Z","title_canon_sha256":"ade4d82d8bd6430e08512bdabfe45e1611ce50f125cfa81f590b4b46d16516a2"},"schema_version":"1.0","source":{"id":"1201.1774","kind":"arxiv","version":1}},"canonical_sha256":"f2c040bdc5cc66ffa997b57054bd5218ca794840750bd173d9fd3636fc7bb1ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2c040bdc5cc66ffa997b57054bd5218ca794840750bd173d9fd3636fc7bb1ac","first_computed_at":"2026-05-18T04:04:55.758091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:55.758091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BRHbTAlpRj4MT5NyDIP8dOnvTc4f6xZtq96rPj09NyvwmjA3zBGp2PQy5E+eDzCTlfmk1IhvCOUsmnpuObN5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:55.758706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:955be223775bb1afe60a17509be40bf3f78a70146f8f209a394d19d0e5da925d","sha256:2cff968e4b569b8de1aa5de49c943a96510af97fd0e764684605213a72176731"],"state_sha256":"4e90bb4aecac4af67c3712927467c57a216410c7687a500523ddbdecaa5c1cab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RILW+G20kmnb/j1QE9NtFL8LNL/AjM3yX2miCeFvqtdYOvrm5YVtsTbH5x1r1ZkYUYLJiRUTl5M83xq39XiTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:32:21.684946Z","bundle_sha256":"11b30d67392612b5150ab0bc930188264c31a8ed96bd30233095a09f6a8243c0"}}