Pith Number

pith:DBJEK7WB

pith:2026:DBJEK7WBDHKLY6NERG5HBHNCPC

not attested not anchored not stored refs pending

Sign-balance of random Laplace eigenfunctions

Igor Wigman, Stephen Muirhead

Random Laplace eigenfunctions are sign-balanced above a precisely determined scale with almost full probability.

arxiv:2604.22567 v2 · 2026-04-24 · math.PR · math-ph · math.MP

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\usepackage{pith}
\pithnumber{DBJEK7WBDHKLY6NERG5HBHNCPC}

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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

random eigenfunctions are sign-balanced above a precisely determined scale with almost full probability. The scale is proven to be optimal up to a logarithmic power of the energy.

C2weakest assumption

The random eigenfunctions are modeled as centered Gaussian fields with covariance given by the spectral projector onto a narrow energy window; the strong notion of sign-balance is the appropriate one for capturing small-scale distribution.

C3one line summary

Random eigenfunctions of the Laplace operator are sign-balanced above a precisely determined scale (optimal up to log factors of the energy) with almost full probability.

Receipt and verification

First computed	2026-05-22T01:04:03.077246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1852457ec119d4bc79a489ba709da278b8333e3bf58d0348ab37cde9d4bc40ba

Aliases

arxiv: 2604.22567 · arxiv_version: 2604.22567v2 · doi: 10.48550/arxiv.2604.22567 · pith_short_12: DBJEK7WBDHKL · pith_short_16: DBJEK7WBDHKLY6NE · pith_short_8: DBJEK7WB

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/DBJEK7WBDHKLY6NERG5HBHNCPC \
  | 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: 1852457ec119d4bc79a489ba709da278b8333e3bf58d0348ab37cde9d4bc40ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a182ab0bb86d7758c43b429f830cdc03638d72a1e3e4cf26c30ea9097a960279",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-24T13:58:38Z",
    "title_canon_sha256": "f42eccf0295095e927d0b90c30dbeba5a837d7347e0007f8bad398ab613c6583"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.22567",
    "kind": "arxiv",
    "version": 2
  }
}