Pith Number

pith:MQMCQIE6

pith:2015:MQMCQIE6IQQDT7WDSUEHXXMTK4

not attested not anchored not stored refs pending

Sharp bound on the number of maximal sum-free subsets of integers

Andrew Treglown, Hong Liu, J\'ozsef Balogh, Maryam Sharifzadeh

arxiv:1502.07605 v2 · 2015-02-26 · 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{MQMCQIE6IQQDT7WDSUEHXXMTK4}

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	2026-05-18T00:16:15.009669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

641828209e442039fec395087bdd935727dd2093c86095bc75f9646cd7d94281

Aliases

arxiv: 1502.07605 · arxiv_version: 1502.07605v2 · doi: 10.48550/arxiv.1502.07605 · pith_short_12: MQMCQIE6IQQD · pith_short_16: MQMCQIE6IQQDT7WD · pith_short_8: MQMCQIE6

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/MQMCQIE6IQQDT7WDSUEHXXMTK4 \
  | 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: 641828209e442039fec395087bdd935727dd2093c86095bc75f9646cd7d94281

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "874aed5f02e02199023ca28016229a451499163aaf403e20a052b0a17db215f9",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-26T15:51:49Z",
    "title_canon_sha256": "46011ae42bf398c1756455af49870a17173742464c31514750339dc755fd1f6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.07605",
    "kind": "arxiv",
    "version": 2
  }
}