Pith Number

pith:ZKSH53VZ

pith:2013:ZKSH53VZBDOB4DGVUBNYNXVZK7

not attested not anchored not stored refs pending

Coefficients of Sylvester's Denumerant

Brandon Dutra, Jes\'us De Loera, Matthias K\"oppe, Mich\`ele Vergne, Nicole Berline, Velleda Baldoni

arxiv:1312.7147 v2 · 2013-12-26 · math.NT · 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{ZKSH53VZBDOB4DGVUBNYNXVZK7}

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	2026-05-18T01:11:55.478529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caa47eeeb908dc1e0cd5a05b86deb957d6ee883e40cad00a9646d687243474b8

Aliases

arxiv: 1312.7147 · arxiv_version: 1312.7147v2 · doi: 10.48550/arxiv.1312.7147 · pith_short_12: ZKSH53VZBDOB · pith_short_16: ZKSH53VZBDOB4DGV · pith_short_8: ZKSH53VZ

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/ZKSH53VZBDOB4DGVUBNYNXVZK7 \
  | 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: caa47eeeb908dc1e0cd5a05b86deb957d6ee883e40cad00a9646d687243474b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0ee9909928990d176030cc8bc5f0f9dec38ca5571b77d366a7a12a5762c41b5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-26T20:37:51Z",
    "title_canon_sha256": "afe1515700cb13d5517d30e1acd52a7a7e3205559e0a6360fe9538da3c6be0b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7147",
    "kind": "arxiv",
    "version": 2
  }
}