Pith Number

pith:2CWBM3P3

pith:2015:2CWBM3P3Z4H2226NMGVPLYRCHP

not attested not anchored not stored refs pending

Kolmogorov's axioms for probabilities with values in hyperbolic numbers

Daniel Alpay, Maria Elena Luna-Elizarrar\'as, Michael Shapiro

arxiv:1508.01350 v1 · 2015-08-06 · 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{2CWBM3P3Z4H2226NMGVPLYRCHP}

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	2026-05-18T01:35:42.818073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0ac166dfbcf0fad6bcd61aaf5e2223bfbdb6621cfe0dcd5f251a80d55512732

Aliases

arxiv: 1508.01350 · arxiv_version: 1508.01350v1 · doi: 10.48550/arxiv.1508.01350 · pith_short_12: 2CWBM3P3Z4H2 · pith_short_16: 2CWBM3P3Z4H2226N · pith_short_8: 2CWBM3P3

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/2CWBM3P3Z4H2226NMGVPLYRCHP \
  | 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: d0ac166dfbcf0fad6bcd61aaf5e2223bfbdb6621cfe0dcd5f251a80d55512732

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfd12387e3ca5294909e359d3cb1d050f4b25bd9f6baab892bb4e8ea079dcccd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-06T10:30:28Z",
    "title_canon_sha256": "0bc395a983a89f30f1dd6e722aa07d23c69a12779fa00fb95f16b4e708ba0f5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01350",
    "kind": "arxiv",
    "version": 1
  }
}