Pith Number

pith:GK55I2DZ

pith:1994:GK55I2DZEHALXRFWLBBHJOAVES

not attested not anchored not stored refs pending

Densities of ultraproducts of Boolean algebras

Sabine Koppelberg, Saharon Shelah

arxiv:math/9404226 v1 · 1994-04-15 · math.LO · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GK55I2DZEHALXRFWLBBHJOAVES}

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	2026-05-18T01:05:51.431292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32bbd4687921c0bbc4b6584274b81524824ad24430284d49db4e221d055a0c32

Aliases

arxiv: math/9404226 · arxiv_version: math/9404226v1 · doi: 10.48550/arxiv.math/9404226 · pith_short_12: GK55I2DZEHAL · pith_short_16: GK55I2DZEHALXRFW · pith_short_8: GK55I2DZ

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/GK55I2DZEHALXRFWLBBHJOAVES \
  | 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: 32bbd4687921c0bbc4b6584274b81524824ad24430284d49db4e221d055a0c32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a148b30b75b846777afc6ccad0c1eff52128e93a7a955574cda65e5c0ddbc545",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "",
    "primary_cat": "math.LO",
    "submitted_at": "1994-04-15T00:00:00Z",
    "title_canon_sha256": "799c4d6b11e302a31147ef9fb0b8cd916b951cdfa1a0d36d9f2854f473b33069"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9404226",
    "kind": "arxiv",
    "version": 1
  }
}