Pith Number

pith:UV532JBZ

pith:2026:UV532JBZ3APPBPO7WYPZJ3CBRY

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Inlier Recovery for Robust Registration via Gram-Matrix Overlap

Ruizi Wu, Wanjie Wang, YueHaw Khoo

The row-sum method recovers exact inlier matches from Gram-matrix overlaps even when inliers drop to order sqrt(n) and their fraction vanishes.

arxiv:2605.14444 v1 · 2026-05-14 · stat.ME

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Claims

C1strongest claim

the row-sum method achieves exact recovery under a broader range of dimensional scalings. In particular, when the dimension is comparable to the sample size, exact recovery is possible even when the inlier fraction vanishes, with the number of inliers as small as order √n, up to logarithmic factors.

C2weakest assumption

The inlier recovery guarantees rely on the Gram-matrix overlap producing a sufficiently structured signal that separates inliers from outliers, which implicitly assumes specific statistical models for noise and outlier distribution that are not detailed in the abstract.

C3one line summary

Gram-matrix overlap turns inlier identification into a structured recovery problem, enabling exact recovery with as few as order sqrt(n) inliers when dimension matches sample size.

References

29 extracted · 29 resolved · 1 Pith anchors

[1] Finding a large hidden clique in a random graph.Random Structures & Algorithms, 13(3–4):457–466, 1998 1998

[2] Community detection in dense random networks.The Annals of Statistics, 42(3):940–969, 2014 2014

[3] K. S. Arun, T. S. Huang, and S. D. Blostein. Least-squares fitting of two 3-d point sets.IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9(5):698–700, 1987 1987

[4] Maximizing robustness of point-set registration by leveraging non-convexity.arXiv preprint arXiv:2004.08772, 2020 2004

[5] Cesar Cadena, Luca Carlone, Henry Carrillo, Yasir Latif, Davide Scaramuzza, Jos´ e Neira, Ian Reid, and John J. Leonard. Past, present, and future of simultaneous localization and mapping: Toward the 2016

Receipt and verification

First computed	2026-05-17T23:39:06.978891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a57bbd2439d81ef0bddfb61f94ec418e2738092bcf7e41b72862698080ac62cb

Aliases

arxiv: 2605.14444 · arxiv_version: 2605.14444v1 · doi: 10.48550/arxiv.2605.14444 · pith_short_12: UV532JBZ3APP · pith_short_16: UV532JBZ3APPBPO7 · pith_short_8: UV532JBZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UV532JBZ3APPBPO7WYPZJ3CBRY \
  | 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: a57bbd2439d81ef0bddfb61f94ec418e2738092bcf7e41b72862698080ac62cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31dd38f0dd774c7b3515af9d4819a1283c7616fa54f19bde95cb3af91e3e3fc8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-14T06:39:36Z",
    "title_canon_sha256": "4af3475c19f0123bf07fc82df00131d750b0cda969b06ed8510a37e270c5159e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14444",
    "kind": "arxiv",
    "version": 1
  }
}