Pith Number

pith:KJJATGUX

pith:2023:KJJATGUX54KEPUTMWXV5APRCFB

not attested not anchored not stored refs pending

Sharp Thresholds Imply Circuit Lower Bounds: from random 2-SAT to Planted Clique

David Gamarnik, Elchanan Mossel, Ilias Zadik

arxiv:2311.04204 v3 · 2023-11-07 · cs.CC · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KJJATGUX54KEPUTMWXV5APRCFB}

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.

Cited by

1 paper in Pith

Sensitivity Lower Bounds via Locally Testable Codes

Receipt and verification

First computed	2026-07-05T08:44:34.628418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5252099a97ef1447d26cb5ebd03e22284475ec9e975723ede830c25487f0c7ab

Aliases

arxiv: 2311.04204 · arxiv_version: 2311.04204v3 · doi: 10.48550/arxiv.2311.04204 · pith_short_12: KJJATGUX54KE · pith_short_16: KJJATGUX54KEPUTM · pith_short_8: KJJATGUX

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/KJJATGUX54KEPUTMWXV5APRCFB \
  | 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: 5252099a97ef1447d26cb5ebd03e22284475ec9e975723ede830c25487f0c7ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff4642feedfda313c1f923e368429149c63b22c29951a2aa41d1469ba505aa6b",
    "cross_cats_sorted": [
      "math.PR",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2023-11-07T18:43:27Z",
    "title_canon_sha256": "53d4e0ab6b80d5f884eaf83de4e47c2c38a3c0f545754e5fc06340e7cf56c54b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.04204",
    "kind": "arxiv",
    "version": 3
  }
}