Pith Number

pith:AWJW5H5C

pith:2008:AWJW5H5COTMADSFOBLPNV5JTII

not attested not anchored not stored refs pending

Circular Law Theorem for Random Markov Matrices

Charles Bordenave (IMT), Djalil Chafai (LAMA), Pietro Caputo

arxiv:0808.1502 v3 · 2008-08-11 · math.PR · 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{AWJW5H5COTMADSFOBLPNV5JTII}

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	2026-05-18T03:59:26.058652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05936e9fa274d801c8ae0adedaf5334225d80ac93d3807fb69c930ca27b7df58

Aliases

arxiv: 0808.1502 · arxiv_version: 0808.1502v3 · doi: 10.48550/arxiv.0808.1502 · pith_short_12: AWJW5H5COTMA · pith_short_16: AWJW5H5COTMADSFO · pith_short_8: AWJW5H5C

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/AWJW5H5COTMADSFOBLPNV5JTII \
  | 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: 05936e9fa274d801c8ae0adedaf5334225d80ac93d3807fb69c930ca27b7df58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc3fc336d28c6e42f09b2b817ba5fc0aa2adf8e1b164de1b0b53b14b6fb594a7",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-08-11T19:15:12Z",
    "title_canon_sha256": "e82160e049e96a8d1998e485d8d85bd7646089fec7dcfd60747a6fd141a7fdf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.1502",
    "kind": "arxiv",
    "version": 3
  }
}