{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WMGK7X6N23UOU3OQU5SA2EVKSN","short_pith_number":"pith:WMGK7X6N","schema_version":"1.0","canonical_sha256":"b30cafdfcdd6e8ea6dd0a7640d12aa93746319ff2e018fec11e3e47e86eefe68","source":{"kind":"arxiv","id":"1605.07532","version":1},"attestation_state":"computed","paper":{"title":"The Selection problem for discounted Hamilton-Jacobi equations: some non-convex cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diogo A. Gomes, Hiroyoshi Mitake, Hung V. Tran","submitted_at":"2016-05-24T16:31:13Z","abstract_excerpt":"Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton-Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton-Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton-Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not dire"},"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":"1605.07532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-24T16:31:13Z","cross_cats_sorted":[],"title_canon_sha256":"ec9ec83747bb7d5dd6f13196510f895f6d0b04e714ca642afa144c0b0c010367","abstract_canon_sha256":"0c0860127547ca32e26583da413021f3ea70058488ea850821c308611367460f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:45.812293Z","signature_b64":"ozuVAvuARqGLVAajl0+YDhiOhBofiP1KJu7gsxU5H0ljwb6UGYMFhYCHaREAR5hkLrSm//50d7mfMP8pG1hUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b30cafdfcdd6e8ea6dd0a7640d12aa93746319ff2e018fec11e3e47e86eefe68","last_reissued_at":"2026-05-18T01:13:45.811773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:45.811773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Selection problem for discounted Hamilton-Jacobi equations: some non-convex cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diogo A. Gomes, Hiroyoshi Mitake, Hung V. Tran","submitted_at":"2016-05-24T16:31:13Z","abstract_excerpt":"Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton-Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton-Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton-Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not dire"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07532","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.07532","created_at":"2026-05-18T01:13:45.811852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.07532v1","created_at":"2026-05-18T01:13:45.811852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07532","created_at":"2026-05-18T01:13:45.811852+00:00"},{"alias_kind":"pith_short_12","alias_value":"WMGK7X6N23UO","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"WMGK7X6N23UOU3OQ","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"WMGK7X6N","created_at":"2026-05-18T12:30:48.956258+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/WMGK7X6N23UOU3OQU5SA2EVKSN","json":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN.json","graph_json":"https://pith.science/api/pith-number/WMGK7X6N23UOU3OQU5SA2EVKSN/graph.json","events_json":"https://pith.science/api/pith-number/WMGK7X6N23UOU3OQU5SA2EVKSN/events.json","paper":"https://pith.science/paper/WMGK7X6N"},"agent_actions":{"view_html":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN","download_json":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN.json","view_paper":"https://pith.science/paper/WMGK7X6N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.07532&json=true","fetch_graph":"https://pith.science/api/pith-number/WMGK7X6N23UOU3OQU5SA2EVKSN/graph.json","fetch_events":"https://pith.science/api/pith-number/WMGK7X6N23UOU3OQU5SA2EVKSN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN/action/storage_attestation","attest_author":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN/action/author_attestation","sign_citation":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN/action/citation_signature","submit_replication":"https://pith.science/pith/WMGK7X6N23UOU3OQU5SA2EVKSN/action/replication_record"}},"created_at":"2026-05-18T01:13:45.811852+00:00","updated_at":"2026-05-18T01:13:45.811852+00:00"}