Pith Number

pith:JUPRQKN7

pith:2012:JUPRQKN7W6B6C5BWTOIPU6GRH3

not attested not anchored not stored refs pending

A Cauchy-Davenport theorem for semigroups

Salvatore Tringali

arxiv:1210.4203 v5 · 2012-10-15 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JUPRQKN7W6B6C5BWTOIPU6GRH3}

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	2026-05-18T02:28:21.165452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d1f1829bfb783e174369b90fa78d13eca4e76a682e9a60c5b3021d5f5cca3eb

Aliases

arxiv: 1210.4203 · arxiv_version: 1210.4203v5 · doi: 10.48550/arxiv.1210.4203 · pith_short_12: JUPRQKN7W6B6 · pith_short_16: JUPRQKN7W6B6C5BW · pith_short_8: JUPRQKN7

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/JUPRQKN7W6B6C5BWTOIPU6GRH3 \
  | 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: 4d1f1829bfb783e174369b90fa78d13eca4e76a682e9a60c5b3021d5f5cca3eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed10756c4d920d93b5955f35c235aaf1d2d4adad95711dc9e5527a6317b11d5b",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-15T21:42:36Z",
    "title_canon_sha256": "6d6991a4d7cf37d3abf29044273a166b410fb613cf993d2afa5e3bb4ae3d8250"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4203",
    "kind": "arxiv",
    "version": 5
  }
}