Pith Number

pith:WDPLC4XL

pith:2008:WDPLC4XLMYQJO6YYMRKLSRHKNB

not attested not anchored not stored refs pending

Yet Another Poincare's Polyhedron Theorem

Carlos H. Grossi, Sasha Anan'in

arxiv:0812.4161 v3 · 2008-12-22 · 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{WDPLC4XLMYQJO6YYMRKLSRHKNB}

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	2026-05-18T04:16:41.106607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0deb172eb6620977b186454b944ea684f539863bdc750808af16df4c91b4bd3

Aliases

arxiv: 0812.4161 · arxiv_version: 0812.4161v3 · doi: 10.48550/arxiv.0812.4161 · pith_short_12: WDPLC4XLMYQJ · pith_short_16: WDPLC4XLMYQJO6YY · pith_short_8: WDPLC4XL

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/WDPLC4XLMYQJO6YYMRKLSRHKNB \
  | 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: b0deb172eb6620977b186454b944ea684f539863bdc750808af16df4c91b4bd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31007a805234242619521baae5f960a0502e3278da970c0b2f5c43d9e5002f71",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-12-22T11:59:40Z",
    "title_canon_sha256": "15b6ba42da0f0d0f992311906f065307ea84fcbdb186a6a84359db4331c43aa1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.4161",
    "kind": "arxiv",
    "version": 3
  }
}