Pith Number

pith:XN5MHUNE

pith:2021:XN5MHUNE7ALSMBIICCQSI2SPTF

not attested not anchored not stored refs pending

Exponential growth of random determinants beyond invariance

Benjamin McKenna, G\'erard Ben Arous, Paul Bourgade

arxiv:2105.05000 v2 · 2021-05-11 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XN5MHUNE7ALSMBIICCQSI2SPTF}

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.

Cited by

1 paper in Pith

The Legendre structure of the TAP complexity for the Ising spin glass

Receipt and verification

First computed	2026-07-05T05:43:45.538110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb7ac3d1a4f81726050810a1246a4f9970cb6a68b3acf080521434f5421656b6

Aliases

arxiv: 2105.05000 · arxiv_version: 2105.05000v2 · doi: 10.48550/arxiv.2105.05000 · pith_short_12: XN5MHUNE7ALS · pith_short_16: XN5MHUNE7ALSMBII · pith_short_8: XN5MHUNE

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/XN5MHUNE7ALSMBIICCQSI2SPTF \
  | 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: bb7ac3d1a4f81726050810a1246a4f9970cb6a68b3acf080521434f5421656b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f2b1fc99ba30b1c72f9c6f16e36f9d0b269d637cc75de471c2c2ad75d11c746",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-05-11T13:03:18Z",
    "title_canon_sha256": "1e94e4b2e09fe068c2e1dd936adfa6bb3c5dd14404f82520769a18770b07cd33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.05000",
    "kind": "arxiv",
    "version": 2
  }
}