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We sharpen this to a quantitative rate: when the boundaries are $\\mathcal{C}^2$ near the limit point $\\bar z$, \\cCRM\\ converges Q-quadratically, with an asymptotic constant \\(\n  2\\max(\\kappa_X,\\kappa_Y)/\\omega \\) governed by the boundary curvatures $\\kappa_X,\\kappa_Y$ at $\\bar z$ and the local error-b","authors_text":"Yunier Bello-Cruz","cross_cats":[],"headline":"The centralized circumcentered-reflection method converges Q-quadratically when sets share an affine hull, their relative interiors intersect, and relative boundaries are twice differentiable.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-04-13T13:30:41Z","title":"Q-quadratic convergence of the centralized circumcentered-reflection method under a relative interior condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.11450","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T15:49:16.571741Z","id":"5df8d899-0d8c-4f60-a8d6-e5c611c9f631","model_set":{"reader":"grok-4.3"},"one_line_summary":"cCRM achieves Q-quadratic convergence to solutions of find z in X cap Y when aff(X)=aff(Y), ri(X) cap ri(Y) nonempty, and relative boundaries are C^2, with explicit rate constant from curvatures and local error bound.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The centralized circumcentered-reflection method converges Q-quadratically when sets share an affine hull, their relative interiors intersect, and relative boundaries are twice differentiable.","strongest_claim":"We prove that cCRM converges superlinearly when aff(X)=aff(Y), ri(X)∩ri(Y)≠∅, and the relative boundaries are C^1 of appropriate relative dimension; and Q-quadratically when the relative boundaries are C^2, with explicit asymptotic constant expressed in terms of the boundary curvatures at the limit point and the local error-bound constant.","weakest_assumption":"The assumption that aff(X)=aff(Y) and ri(X)∩ri(Y)≠∅ together with the relative boundaries being C^1 (or C^2) hypersurfaces of appropriate dimension; the paper explicitly leaves the case aff(X)≠aff(Y) as open."}},"verdict_id":"5df8d899-0d8c-4f60-a8d6-e5c611c9f631"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e09d0913b13c9dde6fc78eaa991bffe471ad32a8bc51b12fbc95c3d70fe96b11","target":"record","created_at":"2026-06-09T01:05:17Z","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":"9a57497d20f2ead863f57a257ebc89838f6b45bad4acb72779ea212bbd8b9d90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-04-13T13:30:41Z","title_canon_sha256":"a0e41e9d8aad55f81b515add800601d3344a5d766154378504c7d3efd8f9b2c0"},"schema_version":"1.0","source":{"id":"2604.11450","kind":"arxiv","version":2}},"canonical_sha256":"8a3a9e2f80644bf1f0d34806fb60ee7c67369c3f94ef2098f4155a335fc8a4bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a3a9e2f80644bf1f0d34806fb60ee7c67369c3f94ef2098f4155a335fc8a4bc","first_computed_at":"2026-06-09T01:05:17.226547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:17.226547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a3F5sBw5RSqLQ8QSLn+Me3qYqx0QMapE0C2iMASeQ0I6ts1ktho5ui4JgQNy+qCTLYyNOf4JfJ3Wva/88k2wBQ==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:17.226973Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.11450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e09d0913b13c9dde6fc78eaa991bffe471ad32a8bc51b12fbc95c3d70fe96b11","sha256:3630a3cfdd937489d7cfe8aa9afc6bcb5a3e99fbca986e569a9f186b0fe892fe"],"state_sha256":"e2cc3a2e404da764d76ef9a9385eb7a4952d71cdaef533ca4e4b50d514bf89d5"}