{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LNWZHZFL4AVLND4FOCE43I3KKO","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":"78b3f299344c0c8b2996407b30900f555a143c07a5437a1cb528b2c9d5475623","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2019-05-11T13:08:49Z","title_canon_sha256":"460fae48da18993723a65c4dd3199322c3868ebb29b78d8579c44b6690540c2f"},"schema_version":"1.0","source":{"id":"1905.04521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04521","created_at":"2026-05-17T23:46:24Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04521v1","created_at":"2026-05-17T23:46:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04521","created_at":"2026-05-17T23:46:24Z"},{"alias_kind":"pith_short_12","alias_value":"LNWZHZFL4AVL","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LNWZHZFL4AVLND4F","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LNWZHZFL","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:bf97e9aadacd5c44a9b33a78acce79b717c8a944ea33ce17d73731a76ccd63a0","target":"graph","created_at":"2026-05-17T23:46:24Z","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"},"paper":{"abstract_excerpt":"Equivalence of convex optimization, saddle-point problems, and variational inequalities is a well-established concept. The variational inequality (VI) is a static problem which is studied under dynamical settings using a framework called the projected dynamical system, whose stationary points coincide with the static solutions of the associated VI. VI has rich properties concerning the monotonicity of its vector-valued map and the uniqueness of its solution, which can be extended to convex optimization and saddle-point problems. Moreover, these properties also extend to the representative proj","authors_text":"N. M. Singh, P. A. Bansode, R. Pasumarthy, S. R. Wagh, V. Chinde","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2019-05-11T13:08:49Z","title":"On the Exponential Stability of Projected Primal-Dual Dynamics on a Riemannian Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04521","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:b1e11c4274b8ce4d5995065248f9722cc519d8f856fe71653b797d945f065569","target":"record","created_at":"2026-05-17T23:46:24Z","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":"78b3f299344c0c8b2996407b30900f555a143c07a5437a1cb528b2c9d5475623","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2019-05-11T13:08:49Z","title_canon_sha256":"460fae48da18993723a65c4dd3199322c3868ebb29b78d8579c44b6690540c2f"},"schema_version":"1.0","source":{"id":"1905.04521","kind":"arxiv","version":1}},"canonical_sha256":"5b6d93e4abe02ab68f857089cda36a5388a738e9dfa585569d4c1b0ceacac181","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b6d93e4abe02ab68f857089cda36a5388a738e9dfa585569d4c1b0ceacac181","first_computed_at":"2026-05-17T23:46:24.566946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:24.566946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"04ff8xz+OUKnU9WJ92C6rqrlVIMSszUjoKaP2TTTarD7QrRgYvWskKBvTThWOyDWSxh7+lyCJPi6rkO05lBeBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:24.567598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1e11c4274b8ce4d5995065248f9722cc519d8f856fe71653b797d945f065569","sha256:bf97e9aadacd5c44a9b33a78acce79b717c8a944ea33ce17d73731a76ccd63a0"],"state_sha256":"3118f4efd7a7bbc96ad79874748520a6a8fec901182fca728252d5fdc978a24e"}