Pith Number

pith:IZROZ2I5

pith:2025:IZROZ2I5UZX5F3LOD5EZ54H22T

not attested not anchored not stored refs pending

Exchangeability and randomness for infinite and finite sequences

Vladimir Vovk

arxiv:2512.22162 v3 · 2025-12-16 · math.ST · stat.ME · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IZROZ2I5UZX5F3LOD5EZ54H22T}

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	2026-08-11T01:20:19.998394Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4662ece91da66fd2ed6e1f499ef0fad4d2a99472888d335ad8f8bfefd159b5e4

Aliases

arxiv: 2512.22162 · arxiv_version: 2512.22162v3 · doi: 10.48550/arxiv.2512.22162 · pith_short_12: IZROZ2I5UZX5 · pith_short_16: IZROZ2I5UZX5F3LO · pith_short_8: IZROZ2I5

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/IZROZ2I5UZX5F3LOD5EZ54H22T \
  | 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: 4662ece91da66fd2ed6e1f499ef0fad4d2a99472888d335ad8f8bfefd159b5e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a93cffb730f48557b1d74a76055282b309b44b5df0db0ef1e6119e15df47ead4",
    "cross_cats_sorted": [
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2025-12-16T12:30:00Z",
    "title_canon_sha256": "52c8691dcee7ea1259c623ce2c4c434aad2160386931d5a132c72b67c841d04a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.22162",
    "kind": "arxiv",
    "version": 3
  }
}