Pith Number

pith:6LZKNXNE

pith:2012:6LZKNXNEL4ZL4652XGWN7YOYYS

not attested not anchored not stored refs pending

Monotone Boolean functions capture their primes

Jean Bourgain

arxiv:1211.6760 v1 · 2012-11-28 · 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{6LZKNXNEL4ZL4652XGWN7YOYYS}

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	2026-05-18T03:39:43.055108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2f2a6dda45f32be7bbab9acdfe1d8c48567c91189a5118b6f9d35d5b8c682e3

Aliases

arxiv: 1211.6760 · arxiv_version: 1211.6760v1 · doi: 10.48550/arxiv.1211.6760 · pith_short_12: 6LZKNXNEL4ZL · pith_short_16: 6LZKNXNEL4ZL4652 · pith_short_8: 6LZKNXNE

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/6LZKNXNEL4ZL4652XGWN7YOYYS \
  | 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: f2f2a6dda45f32be7bbab9acdfe1d8c48567c91189a5118b6f9d35d5b8c682e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5ce26e888b2efd5fc909f0dde28b469d6966b2914fae577ba3c11f55570c284",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-28T21:46:28Z",
    "title_canon_sha256": "3d26007ed7dfdc284e84e4eb1a9b68b058956623fed05e9e0860ad0ef95d985d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6760",
    "kind": "arxiv",
    "version": 1
  }
}