Pith Number

pith:4ADULB5R

pith:2012:4ADULB5RWQ3VQEUOHBKEOQ5WHJ

not attested not anchored not stored refs pending

An Ehrenfeucht-Fra\"{i}ss\'{e} Game for $L_{\omega_1\omega}$

Jouko V\"a\"an\"anen, Tong Wang

arxiv:1212.0108 v1 · 2012-12-01 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ADULB5RWQ3VQEUOHBKEOQ5WHJ}

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	2026-05-18T03:39:27.246776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0074587b1b43758128e38544743b63a49bc8e3d00d668643c9e9358b51bc80d

Aliases

arxiv: 1212.0108 · arxiv_version: 1212.0108v1 · doi: 10.48550/arxiv.1212.0108 · pith_short_12: 4ADULB5RWQ3V · pith_short_16: 4ADULB5RWQ3VQEUO · pith_short_8: 4ADULB5R

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/4ADULB5RWQ3VQEUOHBKEOQ5WHJ \
  | 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: e0074587b1b43758128e38544743b63a49bc8e3d00d668643c9e9358b51bc80d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "612e9aaa976ceb0a46246b637cfc2d39e28bfd8a17065cc8240127298adc1ba1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2012-12-01T13:07:20Z",
    "title_canon_sha256": "6191086f83b6eafd45c905ba811c1fb210e333e21d44cc4c5d955be60a295489"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0108",
    "kind": "arxiv",
    "version": 1
  }
}