Pith Number

pith:VPAAWMER

pith:2012:VPAAWMERBOR2XDNXU5ITJS5NFJ

not attested not anchored not stored refs pending

The generalized second law of gravitational thermodynamics on the apparent horizon in f(R)-gravity

K. Karami, M.S. Khaledian, N. Abdollahi

arxiv:1201.4817 v4 · 2012-01-23 · physics.gen-ph · 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{VPAAWMERBOR2XDNXU5ITJS5NFJ}

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	2026-05-18T03:54:25.757546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abc00b30910ba3ab8db7a75134cbad2a6746a81b7c6b63a841197fe886f5b96a

Aliases

arxiv: 1201.4817 · arxiv_version: 1201.4817v4 · doi: 10.48550/arxiv.1201.4817 · pith_short_12: VPAAWMERBOR2 · pith_short_16: VPAAWMERBOR2XDNX · pith_short_8: VPAAWMER

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/VPAAWMERBOR2XDNXU5ITJS5NFJ \
  | 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: abc00b30910ba3ab8db7a75134cbad2a6746a81b7c6b63a841197fe886f5b96a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23e1851fb69b35e1f3b5d691d18d714302bc21c82b8277e906d0a38b9ad3631b",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2012-01-23T19:11:00Z",
    "title_canon_sha256": "532659ed92f39092b0eb4a18bc265b22f7da2b8a8697862239034a20b1245732"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4817",
    "kind": "arxiv",
    "version": 4
  }
}