Pith Number

pith:BPN4JPZR

pith:1992:BPN4JPZRGKGHFOABKCGLG3V3A7

not attested not anchored not stored refs pending

The Entropy of the Gravitational Field

R. Brandenberger(Brown), T.Prokopec(Brown), V. Mukhanov(ETH, Zurich)

arxiv:gr-qc/9208009 v1 · 1992-08-20 · gr-qc · astro-ph · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BPN4JPZRGKGHFOABKCGLG3V3A7}

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.

Cited by

1 paper in Pith

A Landscape of Cosmological Decoherence

Receipt and verification

First computed	2026-07-04T15:54:50.425680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bdbc4bf31328c72b801508cb36ebb07c67939c46f6e95e4c222a17fbdb610ae

Aliases

arxiv: gr-qc/9208009 · arxiv_version: gr-qc/9208009v1 · doi: 10.48550/arxiv.gr-qc/9208009 · pith_short_12: BPN4JPZRGKGH · pith_short_16: BPN4JPZRGKGHFOAB · pith_short_8: BPN4JPZR

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/BPN4JPZRGKGHFOABKCGLG3V3A7 \
  | 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: 0bdbc4bf31328c72b801508cb36ebb07c67939c46f6e95e4c222a17fbdb610ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46ad1fe485f8a21e5d20d13414fe3c54687f6c45ef4401989e22523b839aa510",
    "cross_cats_sorted": [
      "astro-ph",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1992-08-20T13:02:29Z",
    "title_canon_sha256": "0945e62d7993cd6ac10ab8847285c7905bfa433d89a39c1f9894bb0af3174961"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9208009",
    "kind": "arxiv",
    "version": 1
  }
}