Pith Number

pith:7TKHG2KH

pith:2017:7TKHG2KHAPERAD7QVNUIRYDAIC

not attested not anchored not stored refs pending

The Descartes circles theorem and division by zero calculus

Hiroshi Okumura, Saburou Saitoh

arxiv:1711.04961 v2 · 2017-11-14 · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7TKHG2KHAPERAD7QVNUIRYDAIC}

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	2026-05-18T00:28:34.732208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcd473694703c9100ff0ab6888e060408e61dfb98746fda1661ad71d82496556

Aliases

arxiv: 1711.04961 · arxiv_version: 1711.04961v2 · doi: 10.48550/arxiv.1711.04961 · pith_short_12: 7TKHG2KHAPER · pith_short_16: 7TKHG2KHAPERAD7Q · pith_short_8: 7TKHG2KH

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/7TKHG2KHAPERAD7QVNUIRYDAIC \
  | 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: fcd473694703c9100ff0ab6888e060408e61dfb98746fda1661ad71d82496556

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c40f8d602a3cea1c7d5f8565c0442e18474dedae6ade2cf584825e015b73ca36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2017-11-14T06:02:55Z",
    "title_canon_sha256": "b04e32aa4b098e394562f0a2084767e7c4fd12c4f5c2f4adcca1b8c73da1e45b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.04961",
    "kind": "arxiv",
    "version": 2
  }
}