Pith Number

pith:AOGZTM5O

pith:2014:AOGZTM5O337KLNOOE67KMZ7DYG

not attested not anchored not stored refs pending

The Complexity of Divisibility

Johannes Bausch, Toby Cubitt

arxiv:1411.7380 v2 · 2014-11-26 · math.PR · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AOGZTM5O337KLNOOE67KMZ7DYG}

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	2026-05-18T01:16:53.404870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

038d99b3aedefea5b5ce27bea667e3c1b5732f95f572862d5bd574753ad29c0d

Aliases

arxiv: 1411.7380 · arxiv_version: 1411.7380v2 · doi: 10.48550/arxiv.1411.7380 · pith_short_12: AOGZTM5O337K · pith_short_16: AOGZTM5O337KLNOO · pith_short_8: AOGZTM5O

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/AOGZTM5O337KLNOOE67KMZ7DYG \
  | 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: 038d99b3aedefea5b5ce27bea667e3c1b5732f95f572862d5bd574753ad29c0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34ace49db3960dbb39d10ec2a9d8b7bdc9f4180bc8f0e02535268dd261b114bc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-11-26T21:00:05Z",
    "title_canon_sha256": "191b90779011056e5f7c8a01c8b71f23a9f556c508cbd832a931df564d13086f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.7380",
    "kind": "arxiv",
    "version": 2
  }
}