Pith Number

pith:C44O4AMJ

pith:2012:C44O4AMJG3LKUE2JURGL5IYRGJ

not attested not anchored not stored refs pending

Bounds for the quantifier depth in finite-variable logics: Alternation hierarchy

Andreas Krebs, Christoph Berkholz, Oleg Verbitsky

arxiv:1212.2747 v4 · 2012-12-12 · cs.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{C44O4AMJG3LKUE2JURGL5IYRGJ}

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	2026-05-18T03:16:28.957129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1738ee018936d6aa1349a44cbea311324fdb8de80e153d4bf0befae1bc8456de

Aliases

arxiv: 1212.2747 · arxiv_version: 1212.2747v4 · doi: 10.48550/arxiv.1212.2747 · pith_short_12: C44O4AMJG3LK · pith_short_16: C44O4AMJG3LKUE2J · pith_short_8: C44O4AMJ

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/C44O4AMJG3LKUE2JURGL5IYRGJ \
  | 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: 1738ee018936d6aa1349a44cbea311324fdb8de80e153d4bf0befae1bc8456de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85ddaec363340c22e48b9d22ee2f87db3ae796e7047d76bf6b18df7f3d6dc3e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2012-12-12T09:43:17Z",
    "title_canon_sha256": "13d4e109fe765f1b12f7b604199d995cda0077bff07a3692999af51bfab6a27c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2747",
    "kind": "arxiv",
    "version": 4
  }
}