Pith Number

pith:YO6OG5I2

pith:2008:YO6OG5I2V5JXTTPMBYZSQQQNEU

not attested not anchored not stored refs pending

Toric ideals generated by circuits

Jose Martinez-Bernal, Rafael H. Villarreal

arxiv:0812.0195 v3 · 2008-12-01 · math.AC · 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{YO6OG5I2V5JXTTPMBYZSQQQNEU}

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	2026-05-18T03:50:09.416896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3bce3751aaf5379cdec0e3328420d252ad613f1f2eaeaca353fe7cfbab2174b

Aliases

arxiv: 0812.0195 · arxiv_version: 0812.0195v3 · doi: 10.48550/arxiv.0812.0195 · pith_short_12: YO6OG5I2V5JX · pith_short_16: YO6OG5I2V5JXTTPM · pith_short_8: YO6OG5I2

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/YO6OG5I2V5JXTTPMBYZSQQQNEU \
  | 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: c3bce3751aaf5379cdec0e3328420d252ad613f1f2eaeaca353fe7cfbab2174b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a33406da3bee42452827fc7d9b2b70ef0d19c13bdd860ab380e414a19dec7e44",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2008-12-01T01:38:55Z",
    "title_canon_sha256": "21885494bcedfddf1d9c8d4caeb4de2707fdcb9a4bb498a6b361fdbb90bd4f77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.0195",
    "kind": "arxiv",
    "version": 3
  }
}