Pith Number

pith:VV2OX7EZ

pith:2011:VV2OX7EZD6HWR66GEQGGGL7WZ2

not attested not anchored not stored refs pending

The entropy of large black holes in loop quantum gravity: A combinatorics/analysis approach

Aurelien Barrau, Xiangyu Cao

arxiv:1111.1975 v1 · 2011-11-08 · gr-qc · hep-th · 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{VV2OX7EZD6HWR66GEQGGGL7WZ2}

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	2026-05-18T04:09:03.680179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad74ebfc991f8f68fbc6240c632ff6ceaed28af171b1a73d1a951613f88e0ea7

Aliases

arxiv: 1111.1975 · arxiv_version: 1111.1975v1 · doi: 10.48550/arxiv.1111.1975 · pith_short_12: VV2OX7EZD6HW · pith_short_16: VV2OX7EZD6HWR66G · pith_short_8: VV2OX7EZ

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/VV2OX7EZD6HWR66GEQGGGL7WZ2 \
  | 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: ad74ebfc991f8f68fbc6240c632ff6ceaed28af171b1a73d1a951613f88e0ea7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae3d07e08b65b3e0712e2335da8c702c4902a75e372908f33d526ec1305bed10",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-11-08T17:06:55Z",
    "title_canon_sha256": "6adbb361892a6dbe22956bf9013003bc9f5773825564194eadded128620f3a48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1975",
    "kind": "arxiv",
    "version": 1
  }
}