Pith Number

pith:ZRK4ZTDK

pith:2011:ZRK4ZTDKU7GIQCPGYCU5BCBYJ4

not attested not anchored not stored refs pending

On minimum sum representations for weighted voting games

Sascha Kurz

arxiv:1103.1445 v2 · 2011-03-08 · 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{ZRK4ZTDKU7GIQCPGYCU5BCBYJ4}

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	2026-05-18T00:17:02.276882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc55cccc6aa7cc8809e6c0a9d088384f283596e0d899f2914dfc693d448dd1ee

Aliases

arxiv: 1103.1445 · arxiv_version: 1103.1445v2 · doi: 10.48550/arxiv.1103.1445 · pith_short_12: ZRK4ZTDKU7GI · pith_short_16: ZRK4ZTDKU7GIQCPG · pith_short_8: ZRK4ZTDK

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/ZRK4ZTDKU7GIQCPGYCU5BCBYJ4 \
  | 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: cc55cccc6aa7cc8809e6c0a9d088384f283596e0d899f2914dfc693d448dd1ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d03e89d08549e2932ed9ea6085fe34482d3eefcc1f51b76bccd2ef8d0f5e0bad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-08T06:22:30Z",
    "title_canon_sha256": "a253779b3553d067db29af0d32abc5f8ddff24aebda22049c3580087a58c1a5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1445",
    "kind": "arxiv",
    "version": 2
  }
}