{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NM5OBTDYOQIIUTQ3FJ7CYMPZ3O","short_pith_number":"pith:NM5OBTDY","canonical_record":{"source":{"id":"2508.18764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T07:45:47Z","cross_cats_sorted":[],"title_canon_sha256":"33e2cd75b9500143d360375a2c3163bc1bc152fa6429a77c07a03beaa57f2406","abstract_canon_sha256":"3fcfe1158a5235ff7e64d1e98e1c0965e9bf621f5023e91918675ba164ce604e"},"schema_version":"1.0"},"canonical_sha256":"6b3ae0cc7874108a4e1b2a7e2c31f9db8798f3f94930825a7cf203fb851166a3","source":{"kind":"arxiv","id":"2508.18764","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NM5OBTDYOQIIUTQ3FJ7CYMPZ3O","target":"record","payload":{"canonical_record":{"source":{"id":"2508.18764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T07:45:47Z","cross_cats_sorted":[],"title_canon_sha256":"33e2cd75b9500143d360375a2c3163bc1bc152fa6429a77c07a03beaa57f2406","abstract_canon_sha256":"3fcfe1158a5235ff7e64d1e98e1c0965e9bf621f5023e91918675ba164ce604e"},"schema_version":"1.0"},"canonical_sha256":"6b3ae0cc7874108a4e1b2a7e2c31f9db8798f3f94930825a7cf203fb851166a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:00:29.218390Z","signature_b64":"6C/vzzbeKsdLWyV86OLcj3I1MRUV8om7CmDTwq11L/EwST73TTBjJQiZ9b1p+jMhobJX/HV9ZRTM5uym1Dq2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b3ae0cc7874108a4e1b2a7e2c31f9db8798f3f94930825a7cf203fb851166a3","last_reissued_at":"2026-07-05T12:00:29.217877Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:00:29.217877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.18764","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:00:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYom3fGz96SW53Aa6RnCBfFT4BE5rOs1Zx3EZI9hM9VY4Sj6EoRg3JAobgV2/JtZCWshy6lUxhIgwMq40JK7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:33:41.905709Z"},"content_sha256":"a6caec9a8e3587e6f5a4c875fc65182d01a01f1b55d5d434acfe5202ca85946d","schema_version":"1.0","event_id":"sha256:a6caec9a8e3587e6f5a4c875fc65182d01a01f1b55d5d434acfe5202ca85946d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NM5OBTDYOQIIUTQ3FJ7CYMPZ3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Constrained Optimization: Constrained Gradient Flows via Reparameterization: A-Stable Implicit Schemes, KKT from Stationarity, and Geometry-Respecting Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Valentin Leplat","submitted_at":"2025-08-26T07:45:47Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18764","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/2508.18764/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:00:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENR43DRwb33Env7UXKm3ipXAZxtoN+g97eKpHq4dGachwm9Ua6hXDPOQWnGksMZc6zGqEFsVaBZzzN8bslwyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:33:41.906243Z"},"content_sha256":"edf50a7d0effec04796f0d337784ea098ef43be9f90669a843d5d61654698a51","schema_version":"1.0","event_id":"sha256:edf50a7d0effec04796f0d337784ea098ef43be9f90669a843d5d61654698a51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NM5OBTDYOQIIUTQ3FJ7CYMPZ3O/bundle.json","state_url":"https://pith.science/pith/NM5OBTDYOQIIUTQ3FJ7CYMPZ3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NM5OBTDYOQIIUTQ3FJ7CYMPZ3O/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-14T15:33:41Z","links":{"resolver":"https://pith.science/pith/NM5OBTDYOQIIUTQ3FJ7CYMPZ3O","bundle":"https://pith.science/pith/NM5OBTDYOQIIUTQ3FJ7CYMPZ3O/bundle.json","state":"https://pith.science/pith/NM5OBTDYOQIIUTQ3FJ7CYMPZ3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NM5OBTDYOQIIUTQ3FJ7CYMPZ3O/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38cHTXej9Y5wZdKsI79Hiv+d4+4MDTBRG5zmLvJKF8WhGy1XEfki/ZON1zZTHN60iq2Ij48UrVWSnOc3xqUXDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T15:33:41.909879Z","bundle_sha256":"2524e66e56ea58f29dc0beb9c8c1d49834c9e3994a5a606b974acd91cb802bfc"}}