{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XYQM46SUTOJTKVRF7TJJ5SIKBW","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":"0a1c0dfe4d4bc1cabc6ffbbd597a3527ab9eb71a82d909de9541e2e1dd46ad3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-13T06:34:00Z","title_canon_sha256":"028a72a7454eadc3c2e1f3dd14d0312562c97d64fa511877fc4fd117f0cd85bf"},"schema_version":"1.0","source":{"id":"2412.09898","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.09898","created_at":"2026-07-05T10:24:28Z"},{"alias_kind":"arxiv_version","alias_value":"2412.09898v2","created_at":"2026-07-05T10:24:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.09898","created_at":"2026-07-05T10:24:28Z"},{"alias_kind":"pith_short_12","alias_value":"XYQM46SUTOJT","created_at":"2026-07-05T10:24:28Z"},{"alias_kind":"pith_short_16","alias_value":"XYQM46SUTOJTKVRF","created_at":"2026-07-05T10:24:28Z"},{"alias_kind":"pith_short_8","alias_value":"XYQM46SU","created_at":"2026-07-05T10:24:28Z"}],"graph_snapshots":[{"event_id":"sha256:bb7493e80bbd91992db67720cd930a646423c09543871a6a322118538dc0be33","target":"graph","created_at":"2026-07-05T10:24:28Z","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/2412.09898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, our focus lies on the study of the second-order variational analysis of orthogonally invariant matrix functions. It is well-known that an orthogonally invariant matrix function is an extended-real-value function defined on ${\\mathbb M}_{m,n}\\,(n \\leqslant m)$ of the form $f \\circ \\sigma$ for an absolutely symmetric function $f \\colon \\R^n \\rightarrow [-\\infty,+\\infty]$ and the singular values $\\sigma \\colon {\\mathbb M}_{m,n} \\rightarrow \\R^{n}$. We establish several second-order properties of orthogonally invariant matrix functions, such as parabolic epi-differentiability, parab","authors_text":"Chao Kan, Jiahuan He, Wen Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-13T06:34:00Z","title":"Twice Epi-Differentiability of Orthogonally Invariant Matrix Functions and Application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.09898","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:a64a3539e5eee02b53fb14658924375074cf490e7f4cee42c9ffd9b0be22d20f","target":"record","created_at":"2026-07-05T10:24:28Z","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":"0a1c0dfe4d4bc1cabc6ffbbd597a3527ab9eb71a82d909de9541e2e1dd46ad3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-13T06:34:00Z","title_canon_sha256":"028a72a7454eadc3c2e1f3dd14d0312562c97d64fa511877fc4fd117f0cd85bf"},"schema_version":"1.0","source":{"id":"2412.09898","kind":"arxiv","version":2}},"canonical_sha256":"be20ce7a549b93355625fcd29ec90a0d8519ff13a6b53e40691be956ace1e702","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be20ce7a549b93355625fcd29ec90a0d8519ff13a6b53e40691be956ace1e702","first_computed_at":"2026-07-05T10:24:28.808055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:28.808055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z7dRnARdgf+wWIxKPptvrqgxU7MPBrsAezKbMtdsEEUWpA1rhWLQUF385CzgPzU1V6dAfToFE+vhrJq1GEK8Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:28.808680Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.09898","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a64a3539e5eee02b53fb14658924375074cf490e7f4cee42c9ffd9b0be22d20f","sha256:bb7493e80bbd91992db67720cd930a646423c09543871a6a322118538dc0be33"],"state_sha256":"1e19c21e0a76bb877d52426970129f555eb34be1aa0aef27063b0cfe28f091e9"}