Pith Number

pith:ID72A2MU

pith:2026:ID72A2MUMPY4VURYWKSU62RP4X

not attested not anchored not stored refs pending

On the largest sum-free subset of the lattice cube

Jeck Lim, Peter Keevash

The largest sum-free subset of the lattice cube {1,2,...,n}^d has limiting density given by two hyperplane slices for every dimension d.

arxiv:2605.00816 v2 · 2026-05-01 · 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{ID72A2MUMPY4VURYWKSU62RP4X}

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.

Claims

C1strongest claim

We determine the limiting density of the largest sum-free subset of the lattice cube {1,2,…,n}^d for all d, thus resolving the natural conjecture that it is constructed by two appropriate hyperplane slices.

C2weakest assumption

That the limiting density exists and is attained precisely by the two-hyperplane construction; the abstract provides no details on the proof techniques or any potential gaps in the argument.

C3one line summary

The limiting density of the largest sum-free subset of {1,2,…,n}^d is achieved by two appropriate hyperplane slices for every dimension d.

Receipt and verification

First computed	2026-06-19T16:10:37.947116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40ffa0699463f1cad238b2a54f6a2fe5e3abec6df244410238a9e93144760191

Aliases

arxiv: 2605.00816 · arxiv_version: 2605.00816v2 · doi: 10.48550/arxiv.2605.00816 · pith_short_12: ID72A2MUMPY4 · pith_short_16: ID72A2MUMPY4VURY · pith_short_8: ID72A2MU

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/ID72A2MUMPY4VURYWKSU62RP4X \
  | 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: 40ffa0699463f1cad238b2a54f6a2fe5e3abec6df244410238a9e93144760191

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2c472b84b87b6f68f0a38c6713155e35083e26da8217737a927d525148d31ce",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-01T17:55:19Z",
    "title_canon_sha256": "24b2cdb0336d1ee2082c102eea03e8341e27444ed8ecdc5d5590d7c8851e32e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00816",
    "kind": "arxiv",
    "version": 2
  }
}