Pith Number

pith:MDAEKLRN

pith:2012:MDAEKLRNU6JPKXQWYMLK7TYNO6

not attested not anchored not stored refs pending

On the total mass of closed universes

L\'aszl\'o B Szabados

arxiv:1212.0147 v3 · 2012-12-01 · gr-qc · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDAEKLRNU6JPKXQWYMLK7TYNO6}

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	2026-05-18T03:15:20.904269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60c0452e2da792f55e16c316afcf0d779d418b1dbde5bf970e83d6e027d6f1df

Aliases

arxiv: 1212.0147 · arxiv_version: 1212.0147v3 · doi: 10.48550/arxiv.1212.0147 · pith_short_12: MDAEKLRNU6JP · pith_short_16: MDAEKLRNU6JPKXQW · pith_short_8: MDAEKLRN

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/MDAEKLRNU6JPKXQWYMLK7TYNO6 \
  | 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: 60c0452e2da792f55e16c316afcf0d779d418b1dbde5bf970e83d6e027d6f1df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d35aa87ddd16fe12da53d2a3900222fe1ced6accd9153b357550a737bfd16d63",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-12-01T18:43:10Z",
    "title_canon_sha256": "f034a6a191cdb5ae587072deafb6fdf0377c0a2bbbbd7e1f477badda14581032"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0147",
    "kind": "arxiv",
    "version": 3
  }
}