Pith Number

pith:3CPZ7R4X

pith:2013:3CPZ7R4XOK72KJRMGML5K3RUPE

not attested not anchored not stored refs pending

Erd\H{o}s-Ginzburg-Ziv theorem for finite commutative semigroups

Guoqing Wang, Sukumar Das Adhikari, Weidong Gao

arxiv:1309.5588 v2 · 2013-09-22 · math.CO · math.AC · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3CPZ7R4XOK72KJRMGML5K3RUPE}

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	2026-05-18T03:09:47.629918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d89f9fc79772bfa5262c3317d56e34791f103ec75e3b05f514cc0519fae099bc

Aliases

arxiv: 1309.5588 · arxiv_version: 1309.5588v2 · doi: 10.48550/arxiv.1309.5588 · pith_short_12: 3CPZ7R4XOK72 · pith_short_16: 3CPZ7R4XOK72KJRM · pith_short_8: 3CPZ7R4X

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/3CPZ7R4XOK72KJRMGML5K3RUPE \
  | 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: d89f9fc79772bfa5262c3317d56e34791f103ec75e3b05f514cc0519fae099bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3399f03db75f263c43504d423b638fed14be8dfff4df9675a4338662a73bdb9b",
    "cross_cats_sorted": [
      "math.AC",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-22T10:52:07Z",
    "title_canon_sha256": "d70c2acb22670f28e9e28887f317b0ee09ea13484da07b1f7cf188ef19fa2657"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5588",
    "kind": "arxiv",
    "version": 2
  }
}