Pith Number

pith:JHJWO2E2

pith:2016:JHJWO2E262OLJMJ6CBTDREWDUE

not attested not anchored not stored refs pending

Spectrum of large random Markov chains: heavy-tailed weights on the oriented complete graph

Charles Bordenave (IMT), Daniele Piras, Djalil Chafa\"i (CEREMADE), Pietro Caputo

arxiv:1610.01836 v2 · 2016-10-06 · math.SP · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JHJWO2E262OLJMJ6CBTDREWDUE}

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	2026-05-18T00:41:18.195552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49d367689af69cb4b13e10663892c3a103ecef9c1bcabfa246b61fa24abed3d3

Aliases

arxiv: 1610.01836 · arxiv_version: 1610.01836v2 · doi: 10.48550/arxiv.1610.01836 · pith_short_12: JHJWO2E262OL · pith_short_16: JHJWO2E262OLJMJ6 · pith_short_8: JHJWO2E2

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/JHJWO2E262OLJMJ6CBTDREWDUE \
  | 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: 49d367689af69cb4b13e10663892c3a103ecef9c1bcabfa246b61fa24abed3d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c656eb8d609c59166651be29deb4e3db14fa95fcf3f2b32db81ce4528ff7aee",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-10-06T12:12:53Z",
    "title_canon_sha256": "5906160758c72b4846fd5564ff3ef41ab9c03f3827418bd8b17bce6ea7809c14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01836",
    "kind": "arxiv",
    "version": 2
  }
}