Pith Number

pith:GS6UNHLE

pith:2026:GS6UNHLEL3J3BLZ2DVDHVPSQ6F

not attested not anchored not stored refs resolved

The category of centralizer lattices of groups

Mark L. Lewis, Ryan McCulloch, William Cocke

Centralizer-respecting homomorphisms form a category that maps via functor to centralizer lattices of groups.

arxiv:2605.14095 v1 · 2026-05-13 · math.GR

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\pithnumber{GS6UNHLEL3J3BLZ2DVDHVPSQ6F}

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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

There is a functor from the category of centralizer-respecting homomorphisms to the category of centralizer lattices.

C2weakest assumption

That the proposed definition of centralizer-respecting homomorphism yields a well-defined category and that the centralizer operation interacts with the homomorphism in a way that produces a valid functor.

C3one line summary

Introduces centralizer-respecting homomorphisms between groups and a functor from their category to the category of centralizer lattices.

References

9 extracted · 9 resolved · 0 Pith anchors

[1] Subgroup lattices of groups , author=. 1994 , publisher= 1994

[2] Structure of a group and the structure of its lattice of subgroups , author=. 2012 , publisher= 2012

[3] Exploring the 2016

[4] Finite groups with few subgroups not in the 2026

[5] Bulletin of the Australian Mathematical Society , author= 2026

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:12.160956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34bd469d645ed3b0af3a1d467abe50f17480f4a5c3cde6c813cecc6f08fcdd99

Aliases

arxiv: 2605.14095 · arxiv_version: 2605.14095v1 · doi: 10.48550/arxiv.2605.14095 · pith_short_12: GS6UNHLEL3J3 · pith_short_16: GS6UNHLEL3J3BLZ2 · pith_short_8: GS6UNHLE

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/GS6UNHLEL3J3BLZ2DVDHVPSQ6F \
  | 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: 34bd469d645ed3b0af3a1d467abe50f17480f4a5c3cde6c813cecc6f08fcdd99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfa081d667c8a29713d05c4e09a21024a87818a48554d130e36c13d0e26627b5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-13T20:27:15Z",
    "title_canon_sha256": "14c8b45dde0195fd4121098ae5e0757f2e0d57c06bc7b5653ccd91b57224043c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14095",
    "kind": "arxiv",
    "version": 1
  }
}