Pith Number

pith:PE26CSKW

pith:2000:PE26CSKW7MBTGJ5Z4JQSF72NWC

not attested not anchored not stored refs pending

Decomposition of polytopes and polynomials

A.G.B. Lauder, S. Gao

arxiv:math/0012099 v1 · 2000-12-12 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PE26CSKW7MBTGJ5Z4JQSF72NWC}

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	2026-07-04T14:34:58.701259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7935e14956fb033327b9e26122ff4db0be02277576ffd6ee652261e627219d27

Aliases

arxiv: math/0012099 · arxiv_version: math/0012099v1 · doi: 10.48550/arxiv.math/0012099 · pith_short_12: PE26CSKW7MBT · pith_short_16: PE26CSKW7MBTGJ5Z · pith_short_8: PE26CSKW

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/PE26CSKW7MBTGJ5Z4JQSF72NWC \
  | 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: 7935e14956fb033327b9e26122ff4db0be02277576ffd6ee652261e627219d27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01d4cd8ef90a2ac12dab860aa152b7fb07e929ea0ce79feb90050b25f2d49292",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2000-12-12T21:29:25Z",
    "title_canon_sha256": "78587b5b9e9516d9bb2c8ebded6e25d36dde8529f70264b9f171289822f6a4f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012099",
    "kind": "arxiv",
    "version": 1
  }
}