Pith Number

pith:OLCKM4LK

pith:2006:OLCKM4LKRWXNKSXNHPR5CHR5OK

not attested not anchored not stored refs pending

Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes

Alexander I. Bobenko, Ivan Izmestiev

arxiv:math/0609447 v1 · 2006-09-15 · math.DG · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OLCKM4LKRWXNKSXNHPR5CHR5OK}

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	2026-05-18T00:36:44.134057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72c4a6716a8daed54aed3be3d11e3d72b15905963d381dc989ec9e38f9be9521

Aliases

arxiv: math/0609447 · arxiv_version: math/0609447v1 · doi: 10.48550/arxiv.math/0609447 · pith_short_12: OLCKM4LKRWXN · pith_short_16: OLCKM4LKRWXNKSXN · pith_short_8: OLCKM4LK

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/OLCKM4LKRWXNKSXNHPR5CHR5OK \
  | 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: 72c4a6716a8daed54aed3be3d11e3d72b15905963d381dc989ec9e38f9be9521

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e4aa4579b9721515347044ff6b4283ab81594edb7110b37d6135b5e3150b52c",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2006-09-15T15:45:49Z",
    "title_canon_sha256": "4f97677e16edee2d7898448aacc391cf16e606131002e402bf559ed7ea81be73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609447",
    "kind": "arxiv",
    "version": 1
  }
}