Pith Number

pith:RI5J4L4A

pith:2026:RI5J4L4AMRF7D4GTJADPWYHOPR

not attested not anchored not stored refs pending

Q-quadratic convergence of the centralized circumcentered-reflection method under a relative interior condition

Yunier Bello-Cruz

The centralized circumcentered-reflection method converges Q-quadratically when sets share an affine hull, their relative interiors intersect, and relative boundaries are twice differentiable.

arxiv:2604.11450 v2 · 2026-04-13 · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RI5J4L4AMRF7D4GTJADPWYHOPR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Cited by

1 paper in Pith

On the geometry of circumcentric directions of cones

Receipt and verification

First computed	2026-06-09T01:05:17.226547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a3a9e2f80644bf1f0d34806fb60ee7c67369c3f94ef2098f4155a335fc8a4bc

Aliases

arxiv: 2604.11450 · arxiv_version: 2604.11450v2 · doi: 10.48550/arxiv.2604.11450 · pith_short_12: RI5J4L4AMRF7 · pith_short_16: RI5J4L4AMRF7D4GT · pith_short_8: RI5J4L4A

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RI5J4L4AMRF7D4GTJADPWYHOPR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8a3a9e2f80644bf1f0d34806fb60ee7c67369c3f94ef2098f4155a335fc8a4bc

Canonical record JSON

{
  "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
  }
}