Pith Number

pith:YCUIOWHN

pith:1998:YCUIOWHNZGQBDVT37O7BTV6DX3

not attested not anchored not stored refs pending

Shapes of polyhedra and triangulations of the sphere

William P. Thurston

arxiv:math/9801088 v2 · 1998-01-19 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YCUIOWHNZGQBDVT37O7BTV6DX3}

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.

Cited by

2 papers in Pith

Triangulations of the Sphere

The Four Color Theorem meets Shapes of Polyhedra

Receipt and verification

First computed	2026-07-04T14:40:25.505102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0a88758edc9a011d67bfbbe19d7c3bed33ed1ea8eb72ba55c22d8a56b043f4f

Aliases

arxiv: math/9801088 · arxiv_version: math/9801088v2 · doi: 10.48550/arxiv.math/9801088 · pith_short_12: YCUIOWHNZGQB · pith_short_16: YCUIOWHNZGQBDVT3 · pith_short_8: YCUIOWHN

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/YCUIOWHNZGQBDVT37O7BTV6DX3 \
  | 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: c0a88758edc9a011d67bfbbe19d7c3bed33ed1ea8eb72ba55c22d8a56b043f4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "891a35bc6a6c38542bc1914f0a03c6d07dd646cfe00d1c8b90f0d93d1fbd4681",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-01-19T22:47:58Z",
    "title_canon_sha256": "44544263fcf9f42c0c2f604e29abe2b8e46e164a80645740f0daa1db2768bdfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9801088",
    "kind": "arxiv",
    "version": 2
  }
}