Pith Number

pith:XMN2GJMB

pith:2026:XMN2GJMBGEEWRB7PUNPGMQI6S7

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Presentations of Galois groups of unramified extensions of global fields and its predicted distribution

Ken Willyard

Canonical quotients of Galois groups for unramified extensions over global fields have presentations enabling a new random model for their distributions.

arxiv:2605.14158 v1 · 2026-05-13 · math.NT

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Claims

C1strongest claim

This presentation leads us to the construction of a new random group model as in the work of Liu, Wood, and Zureick-Brown that predicts the distribution of G_∅^T(K) as we vary among Γ-extensions K/Q with prescribed local conditions at places in T, giving a generalization of the non-abelian Cohen-Lenstra-Martinet Heuristics.

C2weakest assumption

That the proven presentations of the canonical quotients are of a form that directly permits the same random-model construction used by Liu, Wood, and Zureick-Brown, and that the added prime-to-|Cl_T(Q)| condition suffices to make the model work for arbitrary global fields Q.

C3one line summary

Establishes group presentations for quotients of G_∅^T(K) in Γ-extensions and derives a random model predicting the distribution of these Galois groups over arbitrary global base fields Q.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Cohomology of

[2] Inventiones mathematicae , author = 2024

[3] Algebra & Number Theory , author =

[4] Clancy, Julien and Kaplan, Nathan and Leake, Timothy and Payne, Sam and Wood, Melanie Matchett , year =. On a. doi:10.1007/s10801-015-0598-x , journal = · doi:10.1007/s10801-015-0598-x

[5] Moments and interpretations of the · doi:10.4171/cmh/514

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.512823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb1ba3258131096887efa35e66411e97c2d010be1fedac04de19a7f6fcfb5111

Aliases

arxiv: 2605.14158 · arxiv_version: 2605.14158v1 · doi: 10.48550/arxiv.2605.14158 · pith_short_12: XMN2GJMBGEEW · pith_short_16: XMN2GJMBGEEWRB7P · pith_short_8: XMN2GJMB

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XMN2GJMBGEEWRB7PUNPGMQI6S7 \
  | 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: bb1ba3258131096887efa35e66411e97c2d010be1fedac04de19a7f6fcfb5111

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a93814668d39a9c6ab53921066931b2ef9b450afd9a2e98c44e82597fa534aca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-13T22:22:32Z",
    "title_canon_sha256": "fa5fc50ac6b47bc39267ceb007247c75e7f03dba90023dac2cea320b4551fcf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14158",
    "kind": "arxiv",
    "version": 1
  }
}