Pith Number

pith:ZCSIBUOK

pith:2013:ZCSIBUOKU2K3WUREKNPRYSMMU4

not attested not anchored not stored refs pending

Cauchy-Davenport type theorems for semigroups

Salvatore Tringali

arxiv:1307.8396 v2 · 2013-07-31 · math.GR · math.CO · 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{ZCSIBUOKU2K3WUREKNPRYSMMU4}

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	2026-05-18T01:25:08.906125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8a480d1caa695bb5224535f1c498ca7072cfdc0114dc555d1f1d2795ebef35f

Aliases

arxiv: 1307.8396 · arxiv_version: 1307.8396v2 · doi: 10.48550/arxiv.1307.8396 · pith_short_12: ZCSIBUOKU2K3 · pith_short_16: ZCSIBUOKU2K3WURE · pith_short_8: ZCSIBUOK

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/ZCSIBUOKU2K3WUREKNPRYSMMU4 \
  | 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: c8a480d1caa695bb5224535f1c498ca7072cfdc0114dc555d1f1d2795ebef35f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c531013dfda6f370ea84a7720ff34b5a6eed603229c860bf32aef8acecded214",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-07-31T17:31:04Z",
    "title_canon_sha256": "1596f5e7566dfed4f547661ae37e25cdd64a938047a57829f6cd3615cddb67e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.8396",
    "kind": "arxiv",
    "version": 2
  }
}