Pith Number

pith:T4H5J2O2

pith:2022:T4H5J2O2ARRTBV4NSBGKWJI7FT

not attested not anchored not stored refs pending

A very sharp threshold for first order logic distinguishability of random graphs

Itai Benjamini, Maksim Zhukovskii

arxiv:2207.11593 v3 · 2022-07-23 · math.CO · cs.LO · math.LO · 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{T4H5J2O2ARRTBV4NSBGKWJI7FT}

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	2026-07-05T11:36:16.770081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f0fd4e9da046330d78d904cab251f2cc0eabcb76c5ffc4a9e17e3d78ed53a89

Aliases

arxiv: 2207.11593 · arxiv_version: 2207.11593v3 · doi: 10.48550/arxiv.2207.11593 · pith_short_12: T4H5J2O2ARRT · pith_short_16: T4H5J2O2ARRTBV4N · pith_short_8: T4H5J2O2

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/T4H5J2O2ARRTBV4NSBGKWJI7FT \
  | 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: 9f0fd4e9da046330d78d904cab251f2cc0eabcb76c5ffc4a9e17e3d78ed53a89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0b163b5ec6aeced0f6c7742b6e03f7294802d14a4d1e77b9e1c9a44b7a8f3c8",
    "cross_cats_sorted": [
      "cs.LO",
      "math.LO",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-07-23T20:08:18Z",
    "title_canon_sha256": "9b1ca60ef34e4f6e421d6d573341a1bdeea99a97847eb3f2eda745b09613a848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2207.11593",
    "kind": "arxiv",
    "version": 3
  }
}