Pith Number

pith:2MCE4342

pith:2013:2MCE4342UD2RM4BC5HFC3ND3RQ

not attested not anchored not stored refs pending

A short proof of Kneser's addition theorem for abelian groups

Matt DeVos

arxiv:1303.3539 v1 · 2013-03-14 · 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{2MCE4342UD2RM4BC5HFC3ND3RQ}

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	2026-05-18T03:30:54.315621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3044e6f9aa0f5167022e9ca2db47b8c01325d6c18b43879fdfcd83f5f35bbf3

Aliases

arxiv: 1303.3539 · arxiv_version: 1303.3539v1 · doi: 10.48550/arxiv.1303.3539 · pith_short_12: 2MCE4342UD2R · pith_short_16: 2MCE4342UD2RM4BC · pith_short_8: 2MCE4342

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/2MCE4342UD2RM4BC5HFC3ND3RQ \
  | 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: d3044e6f9aa0f5167022e9ca2db47b8c01325d6c18b43879fdfcd83f5f35bbf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c31d14a48f016b911af624e181c71c582cbb6ededb5fce32a62dad85a6f4fefd",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-03-14T18:19:13Z",
    "title_canon_sha256": "a3fa68f1940c8fbc12e29665bec7e9db6ad53594a543c03824be1fa0b829e32d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3539",
    "kind": "arxiv",
    "version": 1
  }
}