Pith Number

pith:UF46HZTL

pith:2018:UF46HZTLJLBUM253KMQEYTSHQM

not attested not anchored not stored refs pending

Descartes Circle Theorem, Steiner Porism, and Spherical Designs

Richard Evan Schwartz, Serge Tabachnikov

arxiv:1811.08030 v1 · 2018-11-20 · math.MG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UF46HZTLJLBUM253KMQEYTSHQM}

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	2026-05-18T00:00:17.067935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a179e3e66b4ac3466bbb53204c4e47831beccdd1c78fe82e1a47fe7ebcdc83f4

Aliases

arxiv: 1811.08030 · arxiv_version: 1811.08030v1 · doi: 10.48550/arxiv.1811.08030 · pith_short_12: UF46HZTLJLBU · pith_short_16: UF46HZTLJLBUM253 · pith_short_8: UF46HZTL

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/UF46HZTLJLBUM253KMQEYTSHQM \
  | 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: a179e3e66b4ac3466bbb53204c4e47831beccdd1c78fe82e1a47fe7ebcdc83f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3c47345339be82d9306d791ddb87753d7033c42255ad382f6c86f909589eac8",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2018-11-20T00:24:32Z",
    "title_canon_sha256": "e4e8e207a6ade4384ce13be41fd80d9cddcae3f536ef345513ed08ef76cfd372"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.08030",
    "kind": "arxiv",
    "version": 1
  }
}