Pith Number

pith:Q67SQY7S

pith:2012:Q67SQY7SB2C4RPB4RYY3SJNCRZ

not attested not anchored not stored refs pending

On sets of integers which are both sum-free and product-free

Carl Pomerance, Jeffrey C. Lagarias, Par Kurlberg

arxiv:1201.1317 v1 · 2012-01-05 · 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{Q67SQY7SB2C4RPB4RYY3SJNCRZ}

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	2026-05-18T03:13:58.486075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87bf2863f20e85c8bc3c8e31b925a28e685b27ce6b4f504921206009b1849edb

Aliases

arxiv: 1201.1317 · arxiv_version: 1201.1317v1 · doi: 10.48550/arxiv.1201.1317 · pith_short_12: Q67SQY7SB2C4 · pith_short_16: Q67SQY7SB2C4RPB4 · pith_short_8: Q67SQY7S

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/Q67SQY7SB2C4RPB4RYY3SJNCRZ \
  | 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: 87bf2863f20e85c8bc3c8e31b925a28e685b27ce6b4f504921206009b1849edb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2eb1454d5eb00ce6204c5587962292cb20c3d1e22afd06cc51c54aff30789c4d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-01-05T22:14:29Z",
    "title_canon_sha256": "7e50f8a7f44f17cfbd0f888dd5f993efa4d4c8813ab0a4c5108febe9e524d1e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.1317",
    "kind": "arxiv",
    "version": 1
  }
}