Pith Number

pith:ANXLIIQP

pith:2026:ANXLIIQPX4FY3HLYV4OKU47S62

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Varieties and quasivarieties of lattices with complementation

H. L\"anger, I. Chajda, J. K\"uhr, V. Cenker

A semidirect-product-like construction creates infinitely many finite subdirectly irreducible modular lattices with complementation satisfying a quasi-identity.

arxiv:2605.17274 v1 · 2026-05-17 · math.RA

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Record completeness

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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

A construction resembling a semidirect product yields infinitely many finite subdirectly irreducible modular lattices with complementation satisfying the quasi-identity (x'∧y≈0 & x∧y'≈0) ⇒ x≈y.

C2weakest assumption

The semidirect-product-like construction produces structures that remain lattices, are modular, and satisfy the stated quasi-identity for the chosen complementation operation.

C3one line summary

Presents a construction for infinitely many finite subdirectly irreducible modular lattices with complementation satisfying a quasi-identity and axiomatizes small covering varieties generated by small modular De Morgan lattices.

References

14 extracted · 14 resolved · 0 Pith anchors

[1] In: Kudryavtsev, V.B., Rosenberg, I.G., Goldstein, M 2005

[2] AMS, Providence (1979) 30 V 1979

[3] Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer, London (2005) 2005

[4] Springer, New York (1981) 1981

[5] Cenker, V., Chajda, I., L¨ anger, H.: Properties of the symmetric difference in lat- tices with complementation.https://doi.org/10.48550/arXiv.2506.19980 · doi:10.48550/arxiv.2506.19980

Receipt and verification

First computed	2026-05-20T00:03:49.209636Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

036eb4220fbf0b8d9d78af1caa73f2f6a2494024b014e8b6917f427933b098b9

Aliases

arxiv: 2605.17274 · arxiv_version: 2605.17274v1 · doi: 10.48550/arxiv.2605.17274 · pith_short_12: ANXLIIQPX4FY · pith_short_16: ANXLIIQPX4FY3HLY · pith_short_8: ANXLIIQP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ANXLIIQPX4FY3HLYV4OKU47S62 \
  | 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: 036eb4220fbf0b8d9d78af1caa73f2f6a2494024b014e8b6917f427933b098b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b2969871639222f0ef215a1feca9d9c430a84f243f1e2a9d28b3513caaf8ff5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-05-17T05:52:31Z",
    "title_canon_sha256": "f340317818e891a9f9858a2d50d86ec92c2aedc5fd86d7a3f6133b3235baa085"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17274",
    "kind": "arxiv",
    "version": 1
  }
}