{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:PQB37CR3TG4BW2O4BWEQ4J24FA","short_pith_number":"pith:PQB37CR3","schema_version":"1.0","canonical_sha256":"7c03bf8a3b99b81b69dc0d890e275c2806f9c378520a84e75df6a6d6b59da7b5","source":{"kind":"arxiv","id":"2309.00515","version":2},"attestation_state":"computed","paper":{"title":"A New Notion of Tykhonov Well-Posedness for Optimization Problems","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"J. S. Chen, V. K. Hoang, V. S. T. Long","submitted_at":"2023-09-01T15:06:42Z","abstract_excerpt":"Building upon the minimal time function, we propose and study a novel notion of Tykhonov well-posedness with respect to a set of directions for optimization problems. This concept generalizes the classical Tykhonov well-posedness by focusing on existence, stability and convergence along specific directions, rather than over the entire space. We first establish several characterizations of Tykhonov well-posedness with respect to a set of directions, formulated in terms of the diameter of level sets and admissible functions. We then investigate relationships between these level sets and admissib"},"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":"2309.00515","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2023-09-01T15:06:42Z","cross_cats_sorted":[],"title_canon_sha256":"448019ee6dac54b9a0ad50e2a78a82b79f3ef5b64b401daad9a1a24ed30e2fb3","abstract_canon_sha256":"a283570c68570e115f4e1e097e3ae45260120e32a3aec098cec8d32e46ddb625"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:14.454129Z","signature_b64":"7Q3prmylv41dV+hOP2nWGaQ6rL+EEI8FKUixv+fmwiLNx2DWgNTWMuhUHnez+t/GDrJf+yuMxdS3MrPveDSmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c03bf8a3b99b81b69dc0d890e275c2806f9c378520a84e75df6a6d6b59da7b5","last_reissued_at":"2026-05-20T00:00:14.452975Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:14.452975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Notion of Tykhonov Well-Posedness for Optimization Problems","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"J. S. Chen, V. K. Hoang, V. S. T. Long","submitted_at":"2023-09-01T15:06:42Z","abstract_excerpt":"Building upon the minimal time function, we propose and study a novel notion of Tykhonov well-posedness with respect to a set of directions for optimization problems. This concept generalizes the classical Tykhonov well-posedness by focusing on existence, stability and convergence along specific directions, rather than over the entire space. We first establish several characterizations of Tykhonov well-posedness with respect to a set of directions, formulated in terms of the diameter of level sets and admissible functions. We then investigate relationships between these level sets and admissib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.00515","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.00515/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":"2309.00515","created_at":"2026-05-20T00:00:14.453151+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.00515v2","created_at":"2026-05-20T00:00:14.453151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.00515","created_at":"2026-05-20T00:00:14.453151+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQB37CR3TG4B","created_at":"2026-05-20T00:00:14.453151+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQB37CR3TG4BW2O4","created_at":"2026-05-20T00:00:14.453151+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQB37CR3","created_at":"2026-05-20T00:00:14.453151+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/PQB37CR3TG4BW2O4BWEQ4J24FA","json":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA.json","graph_json":"https://pith.science/api/pith-number/PQB37CR3TG4BW2O4BWEQ4J24FA/graph.json","events_json":"https://pith.science/api/pith-number/PQB37CR3TG4BW2O4BWEQ4J24FA/events.json","paper":"https://pith.science/paper/PQB37CR3"},"agent_actions":{"view_html":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA","download_json":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA.json","view_paper":"https://pith.science/paper/PQB37CR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.00515&json=true","fetch_graph":"https://pith.science/api/pith-number/PQB37CR3TG4BW2O4BWEQ4J24FA/graph.json","fetch_events":"https://pith.science/api/pith-number/PQB37CR3TG4BW2O4BWEQ4J24FA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA/action/storage_attestation","attest_author":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA/action/author_attestation","sign_citation":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA/action/citation_signature","submit_replication":"https://pith.science/pith/PQB37CR3TG4BW2O4BWEQ4J24FA/action/replication_record"}},"created_at":"2026-05-20T00:00:14.453151+00:00","updated_at":"2026-05-20T00:00:14.453151+00:00"}