Pith Number

pith:BJOCV2I5

pith:2026:BJOCV2I5M6GREFXXM42P7K7H3I

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The Jamneshan-Tao conjecture for finite abelian groups of bounded rank

Bal\'azs Szegedy, Diego Gonz\'alez-S\'anchez, Pablo Candela

The Jamneshan-Tao conjecture holds for all finite abelian groups generated by at most R elements.

arxiv:2601.08810 v2 · 2026-01-13 · math.GR · math.CO

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Claims

C1strongest claim

We confirm the Jamneshan-Tao conjecture for finite abelian groups of rank at most a fixed integer R by proving an inverse theorem for 1-bounded functions of non-trivial Gowers norm on such groups, concluding that such a function must correlate non-trivially with a nilsequence of bounded complexity.

C2weakest assumption

The inverse theorem holds when the finite abelian group is generated by at most R elements; the argument relies on this bounded-rank restriction to control nilsequence complexity.

C3one line summary

The Jamneshan-Tao conjecture holds for finite abelian groups of rank at most R via an inverse theorem linking non-trivial Gowers norms to bounded-complexity nilsequences.

References

29 extracted · 29 resolved · 2 Pith anchors

[1] V . Bergelson, T. Tao and T. Ziegler,An inverse theorem for the uniformity seminorms associated with the action ofF ∞ p , Geom. Funct. Anal.19(2010), no. 6, 1539–1596. 1 2010

[2] Antol ´ın Camarena, B 2010

[3] Candela,Notes on nilspaces: algebraic aspects, Discrete Anal., 2017, Paper No 2017

[4] Candela,Notes on compact nilspaces, Discrete Anal., 2017, Paper No 2017

[5] P. Candela, D. Gonz ´alez-S´anchez, B. SzegedyOn nilspace systems and their morphisms, Ergodic Theory Dynam. Systems40(2020), no. 11, 3015–3029. 6 2020

Receipt and verification

First computed	2026-05-17T23:39:00.259190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a5c2ae91d678d1216f76734ffabe7da309719457229745cd0705e055eb95f33

Aliases

arxiv: 2601.08810 · arxiv_version: 2601.08810v2 · doi: 10.48550/arxiv.2601.08810 · pith_short_12: BJOCV2I5M6GR · pith_short_16: BJOCV2I5M6GREFXX · pith_short_8: BJOCV2I5

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BJOCV2I5M6GREFXXM42P7K7H3I \
  | 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: 0a5c2ae91d678d1216f76734ffabe7da309719457229745cd0705e055eb95f33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85d9b48dd31ca852afbf680661de8567fcb7f4b9dee77b207f04ee89d95e29e9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-01-13T18:48:08Z",
    "title_canon_sha256": "14b33834ed0583a1d89530b33a8620c7c10829e431389ad701d3556868b275bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.08810",
    "kind": "arxiv",
    "version": 2
  }
}