{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:A2TZUD4LP73W3LSVVUSOWF3ZWJ","short_pith_number":"pith:A2TZUD4L","schema_version":"1.0","canonical_sha256":"06a79a0f8b7ff76dae55ad24eb1779b2506f11ee053093e40f1c7040a60d375b","source":{"kind":"arxiv","id":"1208.3288","version":2},"attestation_state":"computed","paper":{"title":"Regularity of viscosity solutions defined by Hopf-type formula for Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nguyen Hoang","submitted_at":"2012-08-16T04:48:44Z","abstract_excerpt":"Some properties of characteristic curves in connection with viscosity solutions of Hamilton-Jacobi equations defined by Hopf-type formula are studied. We investigate the points where the Hopf-type formula $u(t,x)$ is differentiable, and the strip of the form $(0,t_0)\\times \\R^n$ of the domain $\\Omega$ where the viscosity solution $u(t,x)$ is continuously differentiable. Moreover, we present the propagation of singularity in forward of $u(t,x).$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.3288","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-16T04:48:44Z","cross_cats_sorted":[],"title_canon_sha256":"fc40e498b28afa48274957b39d25e1edab730fd1429c43e9edf5138cc3d24366","abstract_canon_sha256":"82c5c17f63fd3035b0c2e15f387836fb042b52dd9317548d3a99d5a0999b33db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:55.016807Z","signature_b64":"upZeFy4+eO09zpLPp3O9VmWimwfYdRKQSHae3rIdF8rfOIfyF9YEM84ap/JI8E+AdPuO8FmJzgPyhwmaAZgIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06a79a0f8b7ff76dae55ad24eb1779b2506f11ee053093e40f1c7040a60d375b","last_reissued_at":"2026-05-18T03:05:55.015974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:55.015974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of viscosity solutions defined by Hopf-type formula for Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nguyen Hoang","submitted_at":"2012-08-16T04:48:44Z","abstract_excerpt":"Some properties of characteristic curves in connection with viscosity solutions of Hamilton-Jacobi equations defined by Hopf-type formula are studied. We investigate the points where the Hopf-type formula $u(t,x)$ is differentiable, and the strip of the form $(0,t_0)\\times \\R^n$ of the domain $\\Omega$ where the viscosity solution $u(t,x)$ is continuously differentiable. Moreover, we present the propagation of singularity in forward of $u(t,x).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3288","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.3288","created_at":"2026-05-18T03:05:55.016118+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3288v2","created_at":"2026-05-18T03:05:55.016118+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3288","created_at":"2026-05-18T03:05:55.016118+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2TZUD4LP73W","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2TZUD4LP73W3LSV","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2TZUD4L","created_at":"2026-05-18T12:26:58.693483+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ","json":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ.json","graph_json":"https://pith.science/api/pith-number/A2TZUD4LP73W3LSVVUSOWF3ZWJ/graph.json","events_json":"https://pith.science/api/pith-number/A2TZUD4LP73W3LSVVUSOWF3ZWJ/events.json","paper":"https://pith.science/paper/A2TZUD4L"},"agent_actions":{"view_html":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ","download_json":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ.json","view_paper":"https://pith.science/paper/A2TZUD4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3288&json=true","fetch_graph":"https://pith.science/api/pith-number/A2TZUD4LP73W3LSVVUSOWF3ZWJ/graph.json","fetch_events":"https://pith.science/api/pith-number/A2TZUD4LP73W3LSVVUSOWF3ZWJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ/action/storage_attestation","attest_author":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ/action/author_attestation","sign_citation":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ/action/citation_signature","submit_replication":"https://pith.science/pith/A2TZUD4LP73W3LSVVUSOWF3ZWJ/action/replication_record"}},"created_at":"2026-05-18T03:05:55.016118+00:00","updated_at":"2026-05-18T03:05:55.016118+00:00"}