Pith Number

pith:VPMWYXFB

pith:2026:VPMWYXFBMI3JVLUDULNFSFUNP7

not attested not anchored not stored refs pending

Anticoncentration of the Permanent in Ginibre Ensembles

Frederic Koehler, Pui Kuen Leung

arxiv:2607.20329 v1 · 2026-07-22 · math.PR · cs.CC · math-ph · math.MP · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPMWYXFBMI3JVLUDULNFSFUNP7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-07-23T01:25:14.686615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd96c5ca162369aae83a2da59168d7ff543a676009a4ff2b498ce289550542d

Aliases

arxiv: 2607.20329 · arxiv_version: 2607.20329v1 · doi: 10.48550/arxiv.2607.20329 · pith_short_12: VPMWYXFBMI3J · pith_short_16: VPMWYXFBMI3JVLUD · pith_short_8: VPMWYXFB

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/VPMWYXFBMI3JVLUDULNFSFUNP7 \
  | 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: abd96c5ca162369aae83a2da59168d7ff543a676009a4ff2b498ce289550542d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "066eaed639efaf6ed6dcdfed70db9542cea2175580c1e0d991d7a1f048615620",
    "cross_cats_sorted": [
      "cs.CC",
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-22T16:15:28Z",
    "title_canon_sha256": "dec1e0d7d81a56c20555bebe67c498d5a22d86ab3c7f6e5c1fc6de6eff556acb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20329",
    "kind": "arxiv",
    "version": 1
  }
}