Pith Number

pith:5CUTVKDF

pith:2006:5CUTVKDFKFMCNMHARI57ER75HF

not attested not anchored not stored refs pending

Non-backtracking random walks mix faster

Eyal Lubetzky, Itai Benjamini, Noga Alon, Sasha Sodin

arxiv:math/0610550 v1 · 2006-10-18 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5CUTVKDFKFMCNMHARI57ER75HF}

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	2026-05-18T04:19:22.509667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8a93aa865515826b0e08a3bf247fd395696fbc2133f1d6e7b9c5ab6ad9d3a57

Aliases

arxiv: math/0610550 · arxiv_version: math/0610550v1 · doi: 10.48550/arxiv.math/0610550 · pith_short_12: 5CUTVKDFKFMC · pith_short_16: 5CUTVKDFKFMCNMHA · pith_short_8: 5CUTVKDF

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/5CUTVKDFKFMCNMHARI57ER75HF \
  | 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: e8a93aa865515826b0e08a3bf247fd395696fbc2133f1d6e7b9c5ab6ad9d3a57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc8e799d254e007431efb6b078b5bf2c222d1b10a3a90e56c30d87d296b0fb38",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-10-18T12:56:12Z",
    "title_canon_sha256": "371b337325f3cd748265dfe251fa2604d7731507b7598f34843676375560fb32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610550",
    "kind": "arxiv",
    "version": 1
  }
}