Pith Number

pith:3BYLFQ3Z

pith:2011:3BYLFQ3ZFMU5PE32QZMVWY5EEY

not attested not anchored not stored refs pending

The first returning speed and the last exit speed of a type of Markov chain

Huizeng Zhang, Lei Wang, Minzhi Zhao

arxiv:1101.1161 v1 · 2011-01-06 · 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{3BYLFQ3ZFMU5PE32QZMVWY5EEY}

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	2026-05-18T04:32:00.418623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d870b2c3792b29d7937a86595b63a4261015bd6d378c9d329d91ab6005b403e2

Aliases

arxiv: 1101.1161 · arxiv_version: 1101.1161v1 · doi: 10.48550/arxiv.1101.1161 · pith_short_12: 3BYLFQ3ZFMU5 · pith_short_16: 3BYLFQ3ZFMU5PE32 · pith_short_8: 3BYLFQ3Z

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/3BYLFQ3ZFMU5PE32QZMVWY5EEY \
  | 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: d870b2c3792b29d7937a86595b63a4261015bd6d378c9d329d91ab6005b403e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22e7015cc4ddd180bb6a80388d6377d7722509b68e53786860ddedc14704a54d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-06T08:19:55Z",
    "title_canon_sha256": "bfaa97564c833e654a39fa19a40596e75adddbd7c498bfc7e4dff8a522007762"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1161",
    "kind": "arxiv",
    "version": 1
  }
}