Pith Number

pith:YBZ76DID

pith:2013:YBZ76DIDGQWZGA2URPKUKI5W2S

not attested not anchored not stored refs pending

Ultraproducts as a tool for first-order inexpressibility in the finite and infinite

Philip Dittmann

arxiv:1310.3137 v1 · 2013-10-11 · 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{YBZ76DIDGQWZGA2URPKUKI5W2S}

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	2026-05-18T03:10:44.956562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c073ff0d03342d9303548bd54523b6d4a63b19c38cde534bbddb1512c6159aba

Aliases

arxiv: 1310.3137 · arxiv_version: 1310.3137v1 · doi: 10.48550/arxiv.1310.3137 · pith_short_12: YBZ76DIDGQWZ · pith_short_16: YBZ76DIDGQWZGA2U · pith_short_8: YBZ76DID

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/YBZ76DIDGQWZGA2URPKUKI5W2S \
  | 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: c073ff0d03342d9303548bd54523b6d4a63b19c38cde534bbddb1512c6159aba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40c51fcec83e2f90153b4e68578451b12e870f9ba4118d78710fe638c013e996",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-10-11T14:15:14Z",
    "title_canon_sha256": "b94422f38f17538ce131bc42a7519a676880fac889adac627a78da3ffb5e98ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.3137",
    "kind": "arxiv",
    "version": 1
  }
}