{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CAVDFYN7FWWZOCVOBOQC6OTJUA","short_pith_number":"pith:CAVDFYN7","schema_version":"1.0","canonical_sha256":"102a32e1bf2dad970aae0ba02f3a69a039b6d1c130074576a6bdb5090ce6914f","source":{"kind":"arxiv","id":"2608.04584","version":1},"attestation_state":"computed","paper":{"title":"Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Farid Najar (UVSQ)","submitted_at":"2026-08-05T08:49:16Z","abstract_excerpt":"We propose MELMO (Moreau Envelope Smoothing with Linear Minimization Oracles), an algorithm for composite optimization problems of the form min x f (x) + g(T x), where f is smooth and g may be non-smooth. The method leverages the Moreau envelope to smooth the non-smooth component while adapting to problem geometry through linear minimization oracles. Assuming g is $\\rho$-weakly convex, we establish a family of convergence bounds parameterized by the step-size and smoothing schedules, thereby making explicit the trade-off between optimizing the smoothed objective and recovering stationarity for"},"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":"2608.04584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-08-05T08:49:16Z","cross_cats_sorted":[],"title_canon_sha256":"e2820625337fc81a37768040bd1d0bf9788d1aac49af8cfe46dd4977ba3989f2","abstract_canon_sha256":"b3b83736391d457aa922c7fc9615278fea5ce50f830932ebec55ade61c913961"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:36:12.563917Z","signature_b64":"ELfPH4LcEMUFb67D0Sijkuq206V6XtEG9zZ6oEd1Zg+GZHHhnGeGdcQsnGQQkSwqvA5/H9pS4Is3mlPtp7+iBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"102a32e1bf2dad970aae0ba02f3a69a039b6d1c130074576a6bdb5090ce6914f","last_reissued_at":"2026-08-06T01:36:12.562506Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:36:12.562506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Farid Najar (UVSQ)","submitted_at":"2026-08-05T08:49:16Z","abstract_excerpt":"We propose MELMO (Moreau Envelope Smoothing with Linear Minimization Oracles), an algorithm for composite optimization problems of the form min x f (x) + g(T x), where f is smooth and g may be non-smooth. The method leverages the Moreau envelope to smooth the non-smooth component while adapting to problem geometry through linear minimization oracles. Assuming g is $\\rho$-weakly convex, we establish a family of convergence bounds parameterized by the step-size and smoothing schedules, thereby making explicit the trade-off between optimizing the smoothed objective and recovering stationarity for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04584","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/2608.04584/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":"2608.04584","created_at":"2026-08-06T01:36:12.564291+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04584v1","created_at":"2026-08-06T01:36:12.564291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04584","created_at":"2026-08-06T01:36:12.564291+00:00"},{"alias_kind":"pith_short_12","alias_value":"CAVDFYN7FWWZ","created_at":"2026-08-06T01:36:12.564291+00:00"},{"alias_kind":"pith_short_16","alias_value":"CAVDFYN7FWWZOCVO","created_at":"2026-08-06T01:36:12.564291+00:00"},{"alias_kind":"pith_short_8","alias_value":"CAVDFYN7","created_at":"2026-08-06T01:36:12.564291+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/CAVDFYN7FWWZOCVOBOQC6OTJUA","json":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA.json","graph_json":"https://pith.science/api/pith-number/CAVDFYN7FWWZOCVOBOQC6OTJUA/graph.json","events_json":"https://pith.science/api/pith-number/CAVDFYN7FWWZOCVOBOQC6OTJUA/events.json","paper":"https://pith.science/paper/CAVDFYN7"},"agent_actions":{"view_html":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA","download_json":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA.json","view_paper":"https://pith.science/paper/CAVDFYN7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04584&json=true","fetch_graph":"https://pith.science/api/pith-number/CAVDFYN7FWWZOCVOBOQC6OTJUA/graph.json","fetch_events":"https://pith.science/api/pith-number/CAVDFYN7FWWZOCVOBOQC6OTJUA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA/action/storage_attestation","attest_author":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA/action/author_attestation","sign_citation":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA/action/citation_signature","submit_replication":"https://pith.science/pith/CAVDFYN7FWWZOCVOBOQC6OTJUA/action/replication_record"}},"created_at":"2026-08-06T01:36:12.564291+00:00","updated_at":"2026-08-06T01:36:12.564291+00:00"}