Pith Number

pith:CKTU5ZXB

pith:2006:CKTU5ZXBN2OEXA4UZNSVXVPCXS

not attested not anchored not stored refs pending

A primal Barvinok algorithm based on irrational decompositions

Matthias K\"oppe

arxiv:math/0603308 v4 · 2006-03-13 · 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{CKTU5ZXBN2OEXA4UZNSVXVPCXS}

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	2026-05-18T00:53:35.476058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12a74ee6e16e9c4b8394cb655bd5e2bc818d93983f0309992efe6a110ee2ce41

Aliases

arxiv: math/0603308 · arxiv_version: math/0603308v4 · doi: 10.48550/arxiv.math/0603308 · pith_short_12: CKTU5ZXBN2OE · pith_short_16: CKTU5ZXBN2OEXA4U · pith_short_8: CKTU5ZXB

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/CKTU5ZXBN2OEXA4UZNSVXVPCXS \
  | 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: 12a74ee6e16e9c4b8394cb655bd5e2bc818d93983f0309992efe6a110ee2ce41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a667cc22b3851fb248e588258b88ceb25eddcabcb8cd4528691e418c44a20e2c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-03-13T19:58:05Z",
    "title_canon_sha256": "9eb82a2839dd38239916d4b01b4127ce755eb8b942b8466f63fe3a2ceba4fa29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0603308",
    "kind": "arxiv",
    "version": 4
  }
}