Pith Number

pith:3UG2OOI2

pith:2013:3UG2OOI2JWLH652YO4FLUFZA6O

not attested not anchored not stored refs pending

Counting the Angels and Devils in Escher's Circle Limit IV

John Choi, Nicholas Pippenger

arxiv:1310.1357 v1 · 2013-10-04 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3UG2OOI2JWLH652YO4FLUFZA6O}

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	2026-05-18T03:11:22.543619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd0da7391a4d967f7758770aba1720f38f9fd43191af5098e7e7f310d58bb7ff

Aliases

arxiv: 1310.1357 · arxiv_version: 1310.1357v1 · doi: 10.48550/arxiv.1310.1357 · pith_short_12: 3UG2OOI2JWLH · pith_short_16: 3UG2OOI2JWLH652Y · pith_short_8: 3UG2OOI2

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/3UG2OOI2JWLH652YO4FLUFZA6O \
  | 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: dd0da7391a4d967f7758770aba1720f38f9fd43191af5098e7e7f310d58bb7ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d08caea43577443d0851a117350e713eec3e4ac4774f06d5cdf10cbbc515167e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-10-04T18:17:34Z",
    "title_canon_sha256": "1ddfcfc1665d5a41829152ee7f844bf1ff8f1cbf600af3dfce288e2f21416209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.1357",
    "kind": "arxiv",
    "version": 1
  }
}