Pith Number

pith:NEFBUFTA

pith:2026:NEFBUFTA7DGPVRLVGTURLACLVQ

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Expander Evolution Algebras

Piero Giacomelli

Expander evolution algebras connect Cheeger graph expansion to algebraic connectivity and achieve the sharp Alon-Boppana eigenvalue bound over the complex numbers.

arxiv:2605.12672 v1 · 2026-05-12 · math.RA · math.CO

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

Over C we obtain the sharp Alon-Boppana lower bound for the second eigenvalue of the evolution operator, leading to the definition of Ramanujan evolution algebras as optimal expanders.

C2weakest assumption

The underlying undirected loopless graph of the algebra, in the sense of Kowalski, is an expander graph in the classical sense of Cheeger.

C3one line summary

Expander evolution algebras are nonassociative algebras whose graphs are expanders, proven connected and simple with Cheeger constant controlling subalgebra structure and spectral gaps over C.

References

15 extracted · 15 resolved · 5 Pith anchors

[1] N. Alon and V.D. Milman, λ1, isoperimetric inequalities for graphs, and superconcentrators,J. Combin. Theory Ser. B38(1985), no. 1, 73–88 1985

[2] J. Bourgain and A. Gamburd, Uniform expansion bounds for Cayley graphs of SL2(Fp),Ann. of Math. (2)167(2008), no. 2, 625–642 2008

[3] On the connection between evolution algebras, random walks and graphs 2020 · arXiv:1707.05897

[4] Some properties of evolution algebras 2013 · arXiv:1004.1987

[5] On evolution algebras 2014 · arXiv:1004.1050

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:50.163094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

690a1a1660f8ccfac57534e915804bac0b97128033eb79e1bc27774e0dc275d2

Aliases

arxiv: 2605.12672 · arxiv_version: 2605.12672v1 · doi: 10.48550/arxiv.2605.12672 · pith_short_12: NEFBUFTA7DGP · pith_short_16: NEFBUFTA7DGPVRLV · pith_short_8: NEFBUFTA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ \
  | 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: 690a1a1660f8ccfac57534e915804bac0b97128033eb79e1bc27774e0dc275d2

Canonical record JSON

{
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    "abstract_canon_sha256": "926b8f3123154322f465e06df1fc803cdd99f12c2a630651c96ecb57002598fb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-05-12T19:22:17Z",
    "title_canon_sha256": "6f32f715e742e6364280721e1fee019b2b7356b36f7ed792405a048cf5a76b40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12672",
    "kind": "arxiv",
    "version": 1
  }
}