Pith Number

pith:47MR7S3B

pith:2011:47MR7S3BWWBEX5CDVWHYXDVDOX

not attested not anchored not stored refs pending

The maximal density of product-free sets in Z/nZ

Carl Pomerance, Jeffrey C. Lagarias, Par Kurlberg

arxiv:1111.2634 v2 · 2011-11-11 · 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{47MR7S3BWWBEX5CDVWHYXDVDOX}

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	2026-05-18T03:13:58.507702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7d91fcb61b5824bf443ad8f8b8ea375f7925abaa4ff9caa3b4548fd9cf37fc3

Aliases

arxiv: 1111.2634 · arxiv_version: 1111.2634v2 · doi: 10.48550/arxiv.1111.2634 · pith_short_12: 47MR7S3BWWBE · pith_short_16: 47MR7S3BWWBEX5CD · pith_short_8: 47MR7S3B

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/47MR7S3BWWBEX5CDVWHYXDVDOX \
  | 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: e7d91fcb61b5824bf443ad8f8b8ea375f7925abaa4ff9caa3b4548fd9cf37fc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "207728a3acd117a6b057ffb6b1e3936b36eb537b682bd30228e7f387ede1c284",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-11-11T00:06:46Z",
    "title_canon_sha256": "6b4adef2780422d4b0802ccc00fbaa7865440aef0acb2e9e4c569e0f22975b0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2634",
    "kind": "arxiv",
    "version": 2
  }
}