{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NAFMLRCGTMRC2IM52NSUZKFR56","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1ceedf8dbabfd22f367a141fc00bee786945591234e514f090d026f74afe5c3b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-12-05T21:38:54Z","title_canon_sha256":"53f36a52c0b9e0b3a613e51492a57449bc399b6736ecda6f8cc4a4bf1495530c"},"schema_version":"1.0","source":{"id":"2412.04625","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.04625","created_at":"2026-07-05T09:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"2412.04625v1","created_at":"2026-07-05T09:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.04625","created_at":"2026-07-05T09:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"NAFMLRCGTMRC","created_at":"2026-07-05T09:45:20Z"},{"alias_kind":"pith_short_16","alias_value":"NAFMLRCGTMRC2IM5","created_at":"2026-07-05T09:45:20Z"},{"alias_kind":"pith_short_8","alias_value":"NAFMLRCG","created_at":"2026-07-05T09:45:20Z"}],"graph_snapshots":[{"event_id":"sha256:ee8ae2b88d827c2a28e781e904fbb1be4b8df84ef648e8ca2d22efb48fc155fb","target":"graph","created_at":"2026-07-05T09:45:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.04625/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the global minimization of a particular type of minimum structured optimization problems wherein the variables must belong to some basic set, the feasible domain is described by the intersection of a large number of functional constraints and the objective stems as the pointwise minimum of a collection of functional pieces. Among others, this setting includes all non-convex piecewise linear problems. The global minimum of a minimum structured problem can be computed using a simple enumeration scheme by solving a sequence of individual problems involving each a single piece and then","authors_text":"Fran\\c{c}ois Glineur, Guillaume Van Dessel","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-12-05T21:38:54Z","title":"Global minimization of a minimum of a finite collection of functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.04625","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e2d129c5b232a3bddb495a305dc6c43b1bc902cc7ccbb21f75d4415b7fa1dc0a","target":"record","created_at":"2026-07-05T09:45:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1ceedf8dbabfd22f367a141fc00bee786945591234e514f090d026f74afe5c3b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-12-05T21:38:54Z","title_canon_sha256":"53f36a52c0b9e0b3a613e51492a57449bc399b6736ecda6f8cc4a4bf1495530c"},"schema_version":"1.0","source":{"id":"2412.04625","kind":"arxiv","version":1}},"canonical_sha256":"680ac5c4469b222d219dd3654ca8b1efb1bc57db25ba1607ff6b177ec7a8e5da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"680ac5c4469b222d219dd3654ca8b1efb1bc57db25ba1607ff6b177ec7a8e5da","first_computed_at":"2026-07-05T09:45:20.913050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:45:20.913050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZQT9Z6c/EP7kzuHoNk/e2hypXMOL4X8O5JQLeETFeI3VGULnF1G17yTlyk290UIryg5xKM8sbW2fWJktfsoBBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:45:20.913631Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.04625","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2d129c5b232a3bddb495a305dc6c43b1bc902cc7ccbb21f75d4415b7fa1dc0a","sha256:ee8ae2b88d827c2a28e781e904fbb1be4b8df84ef648e8ca2d22efb48fc155fb"],"state_sha256":"d62d5e67736470eeaf0e190704d36ec3f708940553624d086e307779224ca3be"}