Pith Number

pith:S4O3PILV

pith:2022:S4O3PILVLO5VXPLOFYWAZ5QIYO

not attested not anchored not stored refs pending

A Proof of the Kahn-Kalai Conjecture

Huy Tuan Pham, Jinyoung Park

arxiv:2203.17207 v2 · 2022-03-31 · math.CO · cs.DM · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S4O3PILVLO5VXPLOFYWAZ5QIYO}

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

A random walk among random graphs

Receipt and verification

First computed	2026-07-05T06:00:50.591788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

971db7a1755bbb5bbd6e2e2c0cf608c3821dd6fb6191267229d8e925f02e4cae

Aliases

arxiv: 2203.17207 · arxiv_version: 2203.17207v2 · doi: 10.48550/arxiv.2203.17207 · pith_short_12: S4O3PILVLO5V · pith_short_16: S4O3PILVLO5VXPLO · pith_short_8: S4O3PILV

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/S4O3PILVLO5VXPLOFYWAZ5QIYO \
  | 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: 971db7a1755bbb5bbd6e2e2c0cf608c3821dd6fb6191267229d8e925f02e4cae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c829fe2880f22d0733c28dc4adbfd6a10ff7bcdd22bdb96a035dcc0a80b88ff",
    "cross_cats_sorted": [
      "cs.DM",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-03-31T17:32:03Z",
    "title_canon_sha256": "5d78233c9f03d84eb341cec1bfb75ac1aafcf99bb316964ca4c9a061b7ba8517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.17207",
    "kind": "arxiv",
    "version": 2
  }
}