Pith Number

pith:4TCA6DOF

pith:2021:4TCA6DOFYTKLDY3BXGIZ5BTW53

not attested not anchored not stored refs pending

Understanding Gravitational Entropy of Black Holes: A New Proposal via Curvature Invariants

Daniele Gregoris, Yen Chin Ong

arxiv:2109.11968 v2 · 2021-09-24 · 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{4TCA6DOFYTKLDY3BXGIZ5BTW53}

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	2026-07-05T04:22:17.021216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4c40f0dc5c4d4b1e361b9919e8676eeef696090e7f1b68adb07cf41a11b9c50

Aliases

arxiv: 2109.11968 · arxiv_version: 2109.11968v2 · doi: 10.48550/arxiv.2109.11968 · pith_short_12: 4TCA6DOFYTKL · pith_short_16: 4TCA6DOFYTKLDY3B · pith_short_8: 4TCA6DOF

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/4TCA6DOFYTKLDY3BXGIZ5BTW53 \
  | 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: e4c40f0dc5c4d4b1e361b9919e8676eeef696090e7f1b68adb07cf41a11b9c50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c5e8651b0fb0ccad8babc874fc1005010f62944989b6c941cd6226beb5f0528",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-09-24T13:55:24Z",
    "title_canon_sha256": "7fee68dd248a79e3604a067a2c1e9ae581d7dccdb34f59d1f1e685a68c26c788"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.11968",
    "kind": "arxiv",
    "version": 2
  }
}