Pith Number

pith:K6J3CJAY

pith:2026:K6J3CJAY367X2GXZBKT5F2MA5Q

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Triprojective almost perfect nonlinear permutations and functions

Faruk G\"olo\u{g}lu, Lukas K\"olsch

A triprojective structure induced by GL(3, 2^m) produces almost perfect nonlinear permutations on vector spaces of every odd dimension divisible by three.

arxiv:2605.17545 v1 · 2026-05-17 · math.CO · cs.IT · math.IT

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 give a large family of almost perfect nonlinear (APN) permutations of finite vector spaces of every odd dimension divisible by three.

C2weakest assumption

The triprojective structure induced by the general linear group GL(3, 2^m) on the vector space produces functions satisfying the APN differential uniformity condition for the stated dimensions.

C3one line summary

Explicit constructions of triprojective APN permutations on vector spaces of odd dimensions divisible by three, plus non-bijective APN functions on even dimensions.

References

18 extracted · 18 resolved · 1 Pith anchors

[1] Daniele Bartoli and Pantelimon Stanica,Infinite families of APN permutations in constrained trivariate classes overF 2m, arXiv preprint arXiv:2603.15146 (2026) 2026

[2] Claude Carlet,Boolean functions for cryptography and coding theory, Cambridge University Press, 2021 2021

[3] Zieve,Determination of a class of permutation quadrinomials, Proc 2023

[4] Faruk G¨ ologlu,Classification of (q, q)-biprojective APN functions, IEEE Trans. Inf. Theory69(2023), no. 3, 1988–1999 2023

[5] Faruk G¨ olo˘ glu and Lukas K¨ olsch,An exponential bound on the number of non-isotopic commutative semifields, Transactions of the American Mathematical Society376(2023), no. 03, 1683–1716 2023

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:45.075052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5793b12418dfbf7d1af90aa7d2e980ec3f44fe19275a7eb3c3a55829e6ebdd54

Aliases

arxiv: 2605.17545 · arxiv_version: 2605.17545v1 · doi: 10.48550/arxiv.2605.17545 · pith_short_12: K6J3CJAY367X · pith_short_16: K6J3CJAY367X2GXZ · pith_short_8: K6J3CJAY

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/K6J3CJAY367X2GXZBKT5F2MA5Q \
  | 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: 5793b12418dfbf7d1af90aa7d2e980ec3f44fe19275a7eb3c3a55829e6ebdd54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31b206c4e71e38613eba4310d7fa3fd4118557c96f0a29256fd1164d3fb0510c",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-17T16:58:00Z",
    "title_canon_sha256": "453ae5e1380c08edc9ad3ced7005de066b84f5a1857a3f69806a94aac47ec0c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17545",
    "kind": "arxiv",
    "version": 1
  }
}