Pith Number

pith:2YVONSHR

pith:2010:2YVONSHRLQIQGN3MJ6JTSVMFJP

not attested not anchored not stored refs pending

On the cardinality of sumsets in torsion-free groups

K\'aroly J. B\"or\"oczky, Oriol Serra, P\'eter P. P\'alfy

arxiv:1009.6140 v1 · 2010-09-30 · math.GR · 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{2YVONSHRLQIQGN3MJ6JTSVMFJP}

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	2026-05-18T02:58:01.721679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d62ae6c8f15c1103376c4f933955854bf6d4b81d8eaec92df9afe8f1e32f3118

Aliases

arxiv: 1009.6140 · arxiv_version: 1009.6140v1 · doi: 10.48550/arxiv.1009.6140 · pith_short_12: 2YVONSHRLQIQ · pith_short_16: 2YVONSHRLQIQGN3M · pith_short_8: 2YVONSHR

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/2YVONSHRLQIQGN3MJ6JTSVMFJP \
  | 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: d62ae6c8f15c1103376c4f933955854bf6d4b81d8eaec92df9afe8f1e32f3118

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfcfcc23b815235bcd520f24876bc69f05aa6fc4aab40743cacd8fd42ef08464",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-30T14:00:52Z",
    "title_canon_sha256": "49afe69e636e64f018d46c12d0f071a9c22eef7bee94ed068383a29f02b5cb55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.6140",
    "kind": "arxiv",
    "version": 1
  }
}