{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XCAQVB22GME4OC4EL3ZRFI3DOM","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":"34bf3491dd78bd27bffca6fc290f040eb915023675dad010d745177bd34a97c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-04T06:26:06Z","title_canon_sha256":"324a43202417e11e79445baf48912f2563809c06963449928f48e00d1a994b6b"},"schema_version":"1.0","source":{"id":"1312.1039","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1039","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1039v3","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1039","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"XCAQVB22GME4","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XCAQVB22GME4OC4E","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XCAQVB22","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:d13095184a80146389647be940b587d087964ab0218be6a794f5923f7e260179","target":"graph","created_at":"2026-05-18T00:14:29Z","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"},"paper":{"abstract_excerpt":"We develop \\emph{geometric optimisation} on the manifold of Hermitian positive definite (HPD) matrices. In particular, we consider optimising two types of cost functions: (i) geodesically convex (g-convex); and (ii) log-nonexpansive (LN). G-convex functions are nonconvex in the usual euclidean sense, but convex along the manifold and thus allow global optimisation. LN functions may fail to be even g-convex, but still remain globally optimisable due to their special structure. We develop theoretical tools to recognise and generate g-convex functions as well as cone theoretic fixed-point optimis","authors_text":"Reshad Hosseini, Suvrit Sra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-04T06:26:06Z","title":"Conic geometric optimisation on the manifold of positive definite matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1039","kind":"arxiv","version":3},"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":"sha256:72e64aad0ead232a011ddde165503bd6a7810ca9e4752aa51b78456d425d44fb","target":"record","created_at":"2026-05-18T00:14:29Z","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":"34bf3491dd78bd27bffca6fc290f040eb915023675dad010d745177bd34a97c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-04T06:26:06Z","title_canon_sha256":"324a43202417e11e79445baf48912f2563809c06963449928f48e00d1a994b6b"},"schema_version":"1.0","source":{"id":"1312.1039","kind":"arxiv","version":3}},"canonical_sha256":"b8810a875a3309c70b845ef312a363731a75254e6fedce55f5091dad73b8899b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8810a875a3309c70b845ef312a363731a75254e6fedce55f5091dad73b8899b","first_computed_at":"2026-05-18T00:14:29.421421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.421421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aRULjOZ2RKd5QRdmnADTzUJHzchZG2tf/gFqHtchpRgSJPNLIyuQJcyMK6J1hZVD+2UuV9opFnTTuUod5Q1fAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.422093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1039","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72e64aad0ead232a011ddde165503bd6a7810ca9e4752aa51b78456d425d44fb","sha256:d13095184a80146389647be940b587d087964ab0218be6a794f5923f7e260179"],"state_sha256":"476b8c3c7665c0d876d0dd03b322f5c227111be57caadce733e8b7e0e4d856b2"}