Pith Number

pith:G5MWNYNV

pith:2013:G5MWNYNV4WGKM7A3OOHY5FSXZI

not attested not anchored not stored refs pending

On Sharp Thresholds of Monotone Properties: Bourgain's Proof Revisited

Deepak Bal

arxiv:1302.1162 v2 · 2013-02-05 · math.PR · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G5MWNYNV4WGKM7A3OOHY5FSXZI}

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	2026-05-18T03:34:24.875421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

375966e1b5e58ca67c1b738f8e9657ca0d1a67fbd8e1178b91eeab18ac55ec42

Aliases

arxiv: 1302.1162 · arxiv_version: 1302.1162v2 · doi: 10.48550/arxiv.1302.1162 · pith_short_12: G5MWNYNV4WGK · pith_short_16: G5MWNYNV4WGKM7A3 · pith_short_8: G5MWNYNV

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/G5MWNYNV4WGKM7A3OOHY5FSXZI \
  | 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: 375966e1b5e58ca67c1b738f8e9657ca0d1a67fbd8e1178b91eeab18ac55ec42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d815b09d13b6995d49edc40d30720a76d80545a92c7d5490d3ec83d0e61844a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-02-05T19:35:19Z",
    "title_canon_sha256": "f2472ed63d80c567ddc6e85eed594415427fad3f8141db91446eb0e6148188ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.1162",
    "kind": "arxiv",
    "version": 2
  }
}