{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NM5OBTDYOQIIUTQ3FJ7CYMPZ3O","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":"3fcfe1158a5235ff7e64d1e98e1c0965e9bf621f5023e91918675ba164ce604e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T07:45:47Z","title_canon_sha256":"33e2cd75b9500143d360375a2c3163bc1bc152fa6429a77c07a03beaa57f2406"},"schema_version":"1.0","source":{"id":"2508.18764","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.18764","created_at":"2026-07-05T12:00:29Z"},{"alias_kind":"arxiv_version","alias_value":"2508.18764v2","created_at":"2026-07-05T12:00:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18764","created_at":"2026-07-05T12:00:29Z"},{"alias_kind":"pith_short_12","alias_value":"NM5OBTDYOQII","created_at":"2026-07-05T12:00:29Z"},{"alias_kind":"pith_short_16","alias_value":"NM5OBTDYOQIIUTQ3","created_at":"2026-07-05T12:00:29Z"},{"alias_kind":"pith_short_8","alias_value":"NM5OBTDY","created_at":"2026-07-05T12:00:29Z"}],"graph_snapshots":[{"event_id":"sha256:edf50a7d0effec04796f0d337784ea098ef43be9f90669a843d5d61654698a51","target":"graph","created_at":"2026-07-05T12:00:29Z","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/2508.18764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gradient-flow (GF) viewpoints unify and illuminate optimization algorithms, yet most GF analyses focus on unconstrained settings. We develop a geometry-respecting framework for constrained problems by (i) reparameterizing feasible sets with maps whose Jacobians vanish on the boundary (orthant/box) or have rank $n-1$ on the simplex (the Fisher--Shahshahani operator), (ii) deriving flows in parameter space that induce feasible primal dynamics, (iii) discretizing with A-stable implicit schemes (backward Euler on vector domains; feasible Cayley on Stiefel) solved by robust inner loops (modified Ga","authors_text":"Valentin Leplat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T07:45:47Z","title":"The Geometry of Constrained Optimization: Constrained Gradient Flows via Reparameterization: A-Stable Implicit Schemes, KKT from Stationarity, and Geometry-Respecting Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18764","kind":"arxiv","version":2},"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:a6caec9a8e3587e6f5a4c875fc65182d01a01f1b55d5d434acfe5202ca85946d","target":"record","created_at":"2026-07-05T12:00:29Z","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":"3fcfe1158a5235ff7e64d1e98e1c0965e9bf621f5023e91918675ba164ce604e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T07:45:47Z","title_canon_sha256":"33e2cd75b9500143d360375a2c3163bc1bc152fa6429a77c07a03beaa57f2406"},"schema_version":"1.0","source":{"id":"2508.18764","kind":"arxiv","version":2}},"canonical_sha256":"6b3ae0cc7874108a4e1b2a7e2c31f9db8798f3f94930825a7cf203fb851166a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b3ae0cc7874108a4e1b2a7e2c31f9db8798f3f94930825a7cf203fb851166a3","first_computed_at":"2026-07-05T12:00:29.217877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:00:29.217877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6C/vzzbeKsdLWyV86OLcj3I1MRUV8om7CmDTwq11L/EwST73TTBjJQiZ9b1p+jMhobJX/HV9ZRTM5uym1Dq2Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:00:29.218390Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.18764","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6caec9a8e3587e6f5a4c875fc65182d01a01f1b55d5d434acfe5202ca85946d","sha256:edf50a7d0effec04796f0d337784ea098ef43be9f90669a843d5d61654698a51"],"state_sha256":"3fa351f7955de239886b9e3b1445ccb3e4d93019fcaa65c03c397875c3598136"}