Pith Number

pith:TV4TCWAN

pith:2009:TV4TCWAN5DT6DXY6IFEZDQGL54

not attested not anchored not stored refs pending

Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph

Charles Bordenave, Djalil Chafa\"i, Pietro Caputo

arxiv:0903.3528 v5 · 2009-03-20 · 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{TV4TCWAN5DT6DXY6IFEZDQGL54}

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	2026-05-18T03:40:38.925721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d7931580de8e7e1df1e414991c0cbef0d0ad43eaa925a13e1461605263989f8

Aliases

arxiv: 0903.3528 · arxiv_version: 0903.3528v5 · doi: 10.48550/arxiv.0903.3528 · pith_short_12: TV4TCWAN5DT6 · pith_short_16: TV4TCWAN5DT6DXY6 · pith_short_8: TV4TCWAN

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/TV4TCWAN5DT6DXY6IFEZDQGL54 \
  | 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: 9d7931580de8e7e1df1e414991c0cbef0d0ad43eaa925a13e1461605263989f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0465a87a1a84687ce1d4164c1fcb30b0316f0e24bff9111b5105a857c5260463",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-03-20T14:26:00Z",
    "title_canon_sha256": "ff8e4a49fc542e678709ec1071470cdc6fffac458edfc9e4a53452fed676362b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.3528",
    "kind": "arxiv",
    "version": 5
  }
}