Pith Number

pith:GOEQTXUA

pith:2002:GOEQTXUARS3GK7ZNE2EN6EIAJ6

not attested not anchored not stored refs pending

Polynomial growth of sumsets in abelian semigroups

Imre Z. Ruzsa, Melvyn B. Nathanson

arxiv:math/0204052 v1 · 2002-04-03 · 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{GOEQTXUARS3GK7ZNE2EN6EIAJ6}

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	2026-05-18T00:53:46.011808Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

338909de808cb6657f2d2688df11004fbba989d45f9583c9cce1f8c735728992

Aliases

arxiv: math/0204052 · arxiv_version: math/0204052v1 · doi: 10.48550/arxiv.math/0204052 · pith_short_12: GOEQTXUARS3G · pith_short_16: GOEQTXUARS3GK7ZN · pith_short_8: GOEQTXUA

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/GOEQTXUARS3GK7ZNE2EN6EIAJ6 \
  | 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: 338909de808cb6657f2d2688df11004fbba989d45f9583c9cce1f8c735728992

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc893ceee274cdf6c9a96e2a12b9cb639dccb111e34fda5727639f512e61f78b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2002-04-03T20:41:34Z",
    "title_canon_sha256": "6f9e884c2f3b622902cea9b7b5f93067baaf6a180a1c8089520e2f768e96e8bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0204052",
    "kind": "arxiv",
    "version": 1
  }
}