Pith Number

pith:W6SS4VSJ

pith:2021:W6SS4VSJYXZCF7PXRZCNU2QL2W

not attested not anchored not stored refs pending

Gap probability for products of random matrices in the critical regime

Eugene Strahov, Sergey Berezin

arxiv:2107.06169 v2 · 2021-07-13 · 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{W6SS4VSJYXZCF7PXRZCNU2QL2W}

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	2026-07-05T03:42:02.432297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7a52e5649c5f222fdf78e44da6a0bd5b7f21342778d171e0d368fcb30c88d69

Aliases

arxiv: 2107.06169 · arxiv_version: 2107.06169v2 · doi: 10.48550/arxiv.2107.06169 · pith_short_12: W6SS4VSJYXZC · pith_short_16: W6SS4VSJYXZCF7PX · pith_short_8: W6SS4VSJ

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/W6SS4VSJYXZCF7PXRZCNU2QL2W \
  | 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: b7a52e5649c5f222fdf78e44da6a0bd5b7f21342778d171e0d368fcb30c88d69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dca20dc0e8bed2d5314e307055f59c360d62955d071a28e31ca6090e579a2189",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-07-13T15:28:39Z",
    "title_canon_sha256": "5d4d8a93cb0897ebe2d654810592a55bbe288fbba6b9ed4bc20a26eb3f4bb41c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.06169",
    "kind": "arxiv",
    "version": 2
  }
}