Pith Number

pith:3PBZCVZL

pith:2008:3PBZCVZLECZSOOZG5ATXVHUUBO

not attested not anchored not stored refs pending

Thermodynamics in Loop Quantum Cosmology

Jian-Yang Zhu, Li-Fang Li

arxiv:0812.3544 v1 · 2008-12-18 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PBZCVZLECZSOOZG5ATXVHUUBO}

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	2026-07-04T17:26:23.630713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbc391572b20b3273b26e8277a9e940bbe91a5b9f1c4c3cf9c5ce98509b44e0e

Aliases

arxiv: 0812.3544 · arxiv_version: 0812.3544v1 · doi: 10.48550/arxiv.0812.3544 · pith_short_12: 3PBZCVZLECZS · pith_short_16: 3PBZCVZLECZSOOZG · pith_short_8: 3PBZCVZL

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/3PBZCVZLECZSOOZG5ATXVHUUBO \
  | 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: dbc391572b20b3273b26e8277a9e940bbe91a5b9f1c4c3cf9c5ce98509b44e0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79e10a835c88a54351fe406008763763582856e7646a1ff99448a9d4a0cb6e92",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2008-12-18T14:38:13Z",
    "title_canon_sha256": "fdee22a372e3b83064b2901d13fe4715e3478dd22422896184188b4a1f7bda83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.3544",
    "kind": "arxiv",
    "version": 1
  }
}