Pith Number

pith:45DQELOE

pith:2012:45DQELOEMXFEF6B5W6ZC7XER5E

not attested not anchored not stored refs pending

Borel completeness of some aleph_0 stable theories

Michael C. Laskowski, Saharon Shelah

arxiv:1211.0558 v3 · 2012-11-02 · 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{45DQELOEMXFEF6B5W6ZC7XER5E}

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	2026-05-18T02:50:32.592539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e747022dc465ca42f83db7b22fdc91e9136f1a56d46b53ee2b44f505d97ffa3b

Aliases

arxiv: 1211.0558 · arxiv_version: 1211.0558v3 · doi: 10.48550/arxiv.1211.0558 · pith_short_12: 45DQELOEMXFE · pith_short_16: 45DQELOEMXFEF6B5 · pith_short_8: 45DQELOE

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/45DQELOEMXFEF6B5W6ZC7XER5E \
  | 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: e747022dc465ca42f83db7b22fdc91e9136f1a56d46b53ee2b44f505d97ffa3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0e38b704e281615ddaef7ba7dda6fc58dfe1ef2cc3221d42e4432977714d4e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2012-11-02T20:30:03Z",
    "title_canon_sha256": "31db20148b946dbadcab4120ac651fd17e49d12bae8b4e5d19244ae4cd30c9f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0558",
    "kind": "arxiv",
    "version": 3
  }
}