Pith Number

pith:4QFFZX54

pith:2018:4QFFZX54DTBBSMWWRH67FQNGHZ

not attested not anchored not stored refs pending

Microscopic explanation for black hole phase transitions via Ruppeiner geometry: two competing factors-the temperature and repulsive interaction among BH molecules

Haitang Li, Shao-Jun Zhang, Yong Chen

arxiv:1812.11765 v4 · 2018-12-31 · hep-th · 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{4QFFZX54DTBBSMWWRH67FQNGHZ}

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	2026-07-05T00:10:13.867306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e40a5cdfbc1cc21932d689fdf2c1a63e4182195ed5b3a954c209778221ee6476

Aliases

arxiv: 1812.11765 · arxiv_version: 1812.11765v4 · doi: 10.48550/arxiv.1812.11765 · pith_short_12: 4QFFZX54DTBB · pith_short_16: 4QFFZX54DTBBSMWW · pith_short_8: 4QFFZX54

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/4QFFZX54DTBBSMWWRH67FQNGHZ \
  | 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: e40a5cdfbc1cc21932d689fdf2c1a63e4182195ed5b3a954c209778221ee6476

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa7de2aa508ad5451affe9b90863fa982f9c4cd25bbfd580a2a8017c25dd19d4",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2018-12-31T11:21:45Z",
    "title_canon_sha256": "92978713e251e8b7d37ddf468e74f75832124a7f814cdbf26c939cb84b768ec5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.11765",
    "kind": "arxiv",
    "version": 4
  }
}