Pith Number

pith:Z5QTT56M

pith:2011:Z5QTT56MYFZGCSABYNNBBDD7TE

not attested not anchored not stored refs pending

Wilson's 6-j laws and stitched Markov processes

Wlodek Bryc, Wojciech Matysiak

arxiv:1109.2539 v1 · 2011-09-12 · 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{Z5QTT56MYFZGCSABYNNBBDD7TE}

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	2026-05-18T01:11:05.484896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf6139f7ccc172614801c35a108c7f99168fef8e2690e66e3854de06b5a892ba

Aliases

arxiv: 1109.2539 · arxiv_version: 1109.2539v1 · doi: 10.48550/arxiv.1109.2539 · pith_short_12: Z5QTT56MYFZG · pith_short_16: Z5QTT56MYFZGCSAB · pith_short_8: Z5QTT56M

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/Z5QTT56MYFZGCSABYNNBBDD7TE \
  | 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: cf6139f7ccc172614801c35a108c7f99168fef8e2690e66e3854de06b5a892ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5abb1afa8e5d846743fdeabcc42a97fb6036d91f443ba504256aef1c43d014e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-12T17:11:34Z",
    "title_canon_sha256": "95ea227dedb95deb28dce7465b205235a08572e2083d1ee8b7787f21619d8ba7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2539",
    "kind": "arxiv",
    "version": 1
  }
}