Pith Number

pith:WNK4CX4A

pith:2026:WNK4CX4ALDWITPNL7BO5KHXZXX

not attested not anchored not stored refs pending

There are matroid toric ideals without quadratic Gr\"obner bases

Jes\'us A. De Loera, J\"org Rambau, Luis Ferroni, Santiago Morales

arxiv:2606.11014 v1 · 2026-06-09 · math.CO · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WNK4CX4ALDWITPNL7BO5KHXZXX}

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.

Cited by

1 paper in Pith

Simplex faces and quadratic toric ideals of lattice polytopes

Receipt and verification

First computed	2026-06-10T01:11:03.753228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b355c15f8058ec89bdabf85dd51ef9bddd27c039c1c5a765a4832b5af1984829

Aliases

arxiv: 2606.11014 · arxiv_version: 2606.11014v1 · doi: 10.48550/arxiv.2606.11014 · pith_short_12: WNK4CX4ALDWI · pith_short_16: WNK4CX4ALDWITPNL · pith_short_8: WNK4CX4A

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/WNK4CX4ALDWITPNL7BO5KHXZXX \
  | 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: b355c15f8058ec89bdabf85dd51ef9bddd27c039c1c5a765a4832b5af1984829

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd1c5a665bc88060d9c39d5c40b13583505de53bb6137af560066c411ccb9f7c",
    "cross_cats_sorted": [
      "math.AC",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-09T15:53:19Z",
    "title_canon_sha256": "9a369948996e2ecc9c0cf544e804eec66d34ca0442203ad2030c00f03f82b7d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11014",
    "kind": "arxiv",
    "version": 1
  }
}