Pith Number

pith:VYDK4Q2R

pith:1999:VYDK4Q2RWP42WGURH7VRS6IFFP

not attested not anchored not stored refs pending

Thermodynamic equilibrium in the expanding universe

Alexander B. Balakin (Kazan), Winfried Zimdahl (Konstanz)

arxiv:gr-qc/9905015 v1 · 1999-05-06 · gr-qc · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VYDK4Q2RWP42WGURH7VRS6IFFP}

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	2026-05-18T01:39:18.051543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae06ae4351b3f9ab1a913feb1979052be02330243334beaa4632892573f969a2

Aliases

arxiv: gr-qc/9905015 · arxiv_version: gr-qc/9905015v1 · doi: 10.48550/arxiv.gr-qc/9905015 · pith_short_12: VYDK4Q2RWP42 · pith_short_16: VYDK4Q2RWP42WGUR · pith_short_8: VYDK4Q2R

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/VYDK4Q2RWP42WGURH7VRS6IFFP \
  | 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: ae06ae4351b3f9ab1a913feb1979052be02330243334beaa4632892573f969a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "314674c7936df0457b5cb829308dfed2895ae02dd6d18e81a4122a86093827d2",
    "cross_cats_sorted": [
      "astro-ph"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1999-05-06T06:50:27Z",
    "title_canon_sha256": "d39e5768a447aab0664a95f83041f891617ba9fcff5753749fc4d167fce7bfe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9905015",
    "kind": "arxiv",
    "version": 1
  }
}