Pith Number

pith:T56KOWLM

pith:2011:T56KOWLM7JHL5TBZAGLEIQDTIB

not attested not anchored not stored refs pending

Around the circular law

Charles Bordenave (IMT), Djalil Chafai (LAMA)

arxiv:1109.3343 v4 · 2011-09-15 · math.PR · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T56KOWLM7JHL5TBZAGLEIQDTIB}

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	2026-05-18T04:00:15.688478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f7ca7596cfa4ebecc3901964440734065a00518c2e105dd310f0c6ea938b1cb

Aliases

arxiv: 1109.3343 · arxiv_version: 1109.3343v4 · doi: 10.48550/arxiv.1109.3343 · pith_short_12: T56KOWLM7JHL · pith_short_16: T56KOWLM7JHL5TBZ · pith_short_8: T56KOWLM

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/T56KOWLM7JHL5TBZAGLEIQDTIB \
  | 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: 9f7ca7596cfa4ebecc3901964440734065a00518c2e105dd310f0c6ea938b1cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40ddebf2c5e1085e89b92582463cdff42a9927413341f6a733bfd84169703d9c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-15T13:19:08Z",
    "title_canon_sha256": "c9d57e84bf6c694eb1a23c65a2e89c8b40941bb1c814c4574fab562aef36f5ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3343",
    "kind": "arxiv",
    "version": 4
  }
}