Pith Number

pith:K7X7NVOG

pith:2003:K7X7NVOGIB3ELS4AM67RGYCPHM

not attested not anchored not stored refs pending

The Penrose Inequality

Hubert L. Bray, Piotr T. Chrusciel

arxiv:gr-qc/0312047 v2 · 2003-12-08 · gr-qc · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K7X7NVOGIB3ELS4AM67RGYCPHM}

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.

Cited by

1 paper in Pith

Black Hole Entropy Bounded by the Specific Heat

Receipt and verification

First computed	2026-07-04T14:25:43.724568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57eff6d5c6407645cb8067bf13604f3b13a8372f23055604e40fec40db0ff9a2

Aliases

arxiv: gr-qc/0312047 · arxiv_version: gr-qc/0312047v2 · doi: 10.48550/arxiv.gr-qc/0312047 · pith_short_12: K7X7NVOGIB3E · pith_short_16: K7X7NVOGIB3ELS4A · pith_short_8: K7X7NVOG

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/K7X7NVOGIB3ELS4AM67RGYCPHM \
  | 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: 57eff6d5c6407645cb8067bf13604f3b13a8372f23055604e40fec40db0ff9a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4788fe6b3461439d0f5a7e04d90702d1f055ecafde245d3d967ebf05a36732c",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2003-12-08T23:08:19Z",
    "title_canon_sha256": "22ee432fb4683fcf1de0a5e595de312d29c8c7111130f720c85165b8d21ab6e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0312047",
    "kind": "arxiv",
    "version": 2
  }
}