Pith Number

pith:67MLKK37

pith:2010:67MLKK37ARTCPU5UNIQKVUCK4Y

not attested not anchored not stored refs pending

On a sumset problem for integers

Hui-Qin Cao, Shan-Shan Du, Zhi-Wei Sun

arxiv:1011.5438 v2 · 2010-11-24 · 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{67MLKK37ARTCPU5UNIQKVUCK4Y}

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	2026-05-18T02:58:33.016052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7d8b52b7f046627d3b46a20aad04ae6031f7bd15eddd340dc1edc1fe0205fc5

Aliases

arxiv: 1011.5438 · arxiv_version: 1011.5438v2 · doi: 10.48550/arxiv.1011.5438 · pith_short_12: 67MLKK37ARTC · pith_short_16: 67MLKK37ARTCPU5U · pith_short_8: 67MLKK37

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/67MLKK37ARTCPU5UNIQKVUCK4Y \
  | 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: f7d8b52b7f046627d3b46a20aad04ae6031f7bd15eddd340dc1edc1fe0205fc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3af258bdb9b461b7f68df52ca94b547d1746aa0e4376108e3b87178c34f9840",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-24T17:35:17Z",
    "title_canon_sha256": "d8af079ba4086ef1358cd33563c7e3d140926098d613bc105277f19dd34c9509"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5438",
    "kind": "arxiv",
    "version": 2
  }
}