Pith Number

pith:MHPAQQVT

pith:2004:MHPAQQVTVIU7VJTOZMMEVI4YM2

not attested not anchored not stored refs pending

Martin Capacity for Markov Chains

Itai Benjamini, Robin Pemantle, Yuval Peres

arxiv:math/0404054 v1 · 2004-04-02 · 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{MHPAQQVTVIU7VJTOZMMEVI4YM2}

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	2026-07-04T14:38:29.741610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61de0842b3aa29faa66ecb184aa3986698b977508493f50b3aa674d4889e6b87

Aliases

arxiv: math/0404054 · arxiv_version: math/0404054v1 · doi: 10.48550/arxiv.math/0404054 · pith_short_12: MHPAQQVTVIU7 · pith_short_16: MHPAQQVTVIU7VJTO · pith_short_8: MHPAQQVT

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/MHPAQQVTVIU7VJTOZMMEVI4YM2 \
  | 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: 61de0842b3aa29faa66ecb184aa3986698b977508493f50b3aa674d4889e6b87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b433feab055f91b4fb4662a30c67653a9700c6f1a02a5903062e073b78236aa",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-04-02T23:55:01Z",
    "title_canon_sha256": "36b4c75432ff7ccb2c22354dc612384efd484f081e2d68606c9b2d71edc2e2e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404054",
    "kind": "arxiv",
    "version": 1
  }
}