{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2OXOHDBO2AFT4AGVL2RYWOU2N6","short_pith_number":"pith:2OXOHDBO","schema_version":"1.0","canonical_sha256":"d3aee38c2ed00b3e00d55ea38b3a9a6fab07c98daba48af46c74bf94920538a7","source":{"kind":"arxiv","id":"2501.08556","version":1},"attestation_state":"computed","paper":{"title":"Lyapunov stability and uniqueness problems for Hamilton-Jacobi equations without monotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Jun Yan, Kaizhi Wang, Yuqi Ruan","submitted_at":"2025-01-15T03:47:52Z","abstract_excerpt":"We consider the evolutionary Hamilton-Jacobi equation\n  \\begin{align*}\n  w_t(x,t)+H(x,Dw(x,t),w(x,t))=0, \\quad(x,t)\\in M\\times [0,+\\infty),\n  \\end{align*}\n  where $M$ is a compact manifold, $H:T^*M\\times R\\to R$, $H=H(x,p,u)$ satisfies Tonelli conditions in $p$ and the Lipschitz condition in $u$.\n  This work mainly concerns with the Lyapunov stability (including asymptotic stability, and instability) and uniqueness of stationary viscosity solutions of the equation. A criterion for stability and a criterion for instability are given. We do not utilize auxiliary functions and thus our method is "},"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":"2501.08556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-15T03:47:52Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"64bb4d8202677740213fd1c9fc83867bd6976879a34c59eee9276f547ff04757","abstract_canon_sha256":"c2b46f0a5c1f8b383eb4079273933a7e1740f70d2826ce96382136f7cd4f1d5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:21.172153Z","signature_b64":"fw3wZkOh7pvc/tePtzzeVmhe4UFq9555HrrTueMYEsggOgCNn8PbQtrB0S77gAfFLscVM4GdwypIP4jofcB8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3aee38c2ed00b3e00d55ea38b3a9a6fab07c98daba48af46c74bf94920538a7","last_reissued_at":"2026-07-05T10:01:21.171745Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:21.171745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lyapunov stability and uniqueness problems for Hamilton-Jacobi equations without monotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Jun Yan, Kaizhi Wang, Yuqi Ruan","submitted_at":"2025-01-15T03:47:52Z","abstract_excerpt":"We consider the evolutionary Hamilton-Jacobi equation\n  \\begin{align*}\n  w_t(x,t)+H(x,Dw(x,t),w(x,t))=0, \\quad(x,t)\\in M\\times [0,+\\infty),\n  \\end{align*}\n  where $M$ is a compact manifold, $H:T^*M\\times R\\to R$, $H=H(x,p,u)$ satisfies Tonelli conditions in $p$ and the Lipschitz condition in $u$.\n  This work mainly concerns with the Lyapunov stability (including asymptotic stability, and instability) and uniqueness of stationary viscosity solutions of the equation. A criterion for stability and a criterion for instability are given. We do not utilize auxiliary functions and thus our method is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08556","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.08556/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2501.08556","created_at":"2026-07-05T10:01:21.171801+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.08556v1","created_at":"2026-07-05T10:01:21.171801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08556","created_at":"2026-07-05T10:01:21.171801+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OXOHDBO2AFT","created_at":"2026-07-05T10:01:21.171801+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OXOHDBO2AFT4AGV","created_at":"2026-07-05T10:01:21.171801+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OXOHDBO","created_at":"2026-07-05T10:01:21.171801+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/2OXOHDBO2AFT4AGVL2RYWOU2N6","json":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6.json","graph_json":"https://pith.science/api/pith-number/2OXOHDBO2AFT4AGVL2RYWOU2N6/graph.json","events_json":"https://pith.science/api/pith-number/2OXOHDBO2AFT4AGVL2RYWOU2N6/events.json","paper":"https://pith.science/paper/2OXOHDBO"},"agent_actions":{"view_html":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6","download_json":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6.json","view_paper":"https://pith.science/paper/2OXOHDBO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.08556&json=true","fetch_graph":"https://pith.science/api/pith-number/2OXOHDBO2AFT4AGVL2RYWOU2N6/graph.json","fetch_events":"https://pith.science/api/pith-number/2OXOHDBO2AFT4AGVL2RYWOU2N6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6/action/storage_attestation","attest_author":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6/action/author_attestation","sign_citation":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6/action/citation_signature","submit_replication":"https://pith.science/pith/2OXOHDBO2AFT4AGVL2RYWOU2N6/action/replication_record"}},"created_at":"2026-07-05T10:01:21.171801+00:00","updated_at":"2026-07-05T10:01:21.171801+00:00"}