Pith Number

pith:5ASKFJHC

pith:2013:5ASKFJHCYJHNJWLJ7QOKN4SLNA

not attested not anchored not stored refs pending

Lower bounds on the Graver complexity of $M$-fold matrices

Elisabeth Finhold, Raymond Hemmecke

arxiv:1311.3853 v1 · 2013-11-15 · math.CO · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ASKFJHCYJHNJWLJ7QOKN4SLNA}

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	2026-05-18T03:07:02.867665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e824a2a4e2c24ed4d969fc1ca6f24b68321559929a98064a83baa85add8bcdca

Aliases

arxiv: 1311.3853 · arxiv_version: 1311.3853v1 · doi: 10.48550/arxiv.1311.3853 · pith_short_12: 5ASKFJHCYJHN · pith_short_16: 5ASKFJHCYJHNJWLJ · pith_short_8: 5ASKFJHC

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/5ASKFJHCYJHNJWLJ7QOKN4SLNA \
  | 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: e824a2a4e2c24ed4d969fc1ca6f24b68321559929a98064a83baa85add8bcdca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "582f3d578ad9b8c48757f36adad52da67e7f70bdc6c5e70db6da55fbddeb885a",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-15T13:55:33Z",
    "title_canon_sha256": "f75f2605705277dfd8ca44a1ea216232128892c07be4173808a8eb04b6de3c9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3853",
    "kind": "arxiv",
    "version": 1
  }
}