Pith Number

pith:MWXKUGYD

pith:2026:MWXKUGYDYACFJLB5CLHVFUD2PL

not attested not anchored not stored refs resolved

Representability of the automorphism group of finitely generated vertex algebras

Arturo Pianzola, Robin Mader, Terry Gannon

The automorphism group of finitely generated vertex algebras over noetherian rings is an affine group scheme.

arxiv:2605.15605 v1 · 2026-05-15 · math.QA · math.AG · math.RA

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\usepackage{pith}
\pithnumber{MWXKUGYDYACFJLB5CLHVFUD2PL}

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Record completeness

1 Bitcoin timestamp

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

We prove that the automorphism group of finitely generated vertex algebras over noetherian rings are affine group schemes.

C2weakest assumption

The vertex algebra must be finitely generated and the base ring must be noetherian; the representability statement is stated to hold under these hypotheses and may fail without them.

C3one line summary

Automorphism groups of finitely generated vertex algebras over noetherian rings are affine group schemes.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] Bass, Big projective modules are free , Illinois J 1963

[2] R. E. Borcherds and A. J. E. Ryba, Modular Moonshine. II , Duke Math. J. 83 (1996), no. 2, 435–459 1996

[3] Bourbaki, Algebra I, Chapters 1-3 , Addison-Wesley Boston, MA, 1974 1974

[4] Carnahan, A self-dual integral form of the Moonshine module , SIGMA Symmetry Integrability Geom 2019

[5] S. Carnahan and H. Kobayashi, Automorphism group schemes of lattice vertex operator algebras, 2025, arXiv: 2502.06121 2025

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:07.722585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65aeaa1b03c00454ac3d12cf52d07a7ae4bd3ca6c3e90a404c289f9947ce0dfe

Aliases

arxiv: 2605.15605 · arxiv_version: 2605.15605v1 · doi: 10.48550/arxiv.2605.15605 · pith_short_12: MWXKUGYDYACF · pith_short_16: MWXKUGYDYACFJLB5 · pith_short_8: MWXKUGYD

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/MWXKUGYDYACFJLB5CLHVFUD2PL \
  | 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: 65aeaa1b03c00454ac3d12cf52d07a7ae4bd3ca6c3e90a404c289f9947ce0dfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37ad7692889a2fe70b9f94ebeb3b622776cfa731c56bbf1e9f49f759742f9e92",
    "cross_cats_sorted": [
      "math.AG",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-15T04:32:38Z",
    "title_canon_sha256": "b28ea015caae62fa9c1889e138c48290ad407e9fe9f8092f69fa6a14dac6b070"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15605",
    "kind": "arxiv",
    "version": 1
  }
}