Pith Number

pith:3A7UBK3Z

pith:2015:3A7UBK3ZC367UXNANB7DI5DVNO

not attested not anchored not stored refs pending

Explicit Integration of Friedmann's Equation with Nonlinear Equations of State

Gary W. Gibbons, Shouxin Chen, Yisong Yang

arxiv:1502.05042 v2 · 2015-02-17 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3A7UBK3ZC367UXNANB7DI5DVNO}

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	2026-05-18T02:03:34.257155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d83f40ab7916fdfa5da0687e3474756b9d6f0bf977ad821808369e412e70baca

Aliases

arxiv: 1502.05042 · arxiv_version: 1502.05042v2 · doi: 10.48550/arxiv.1502.05042 · pith_short_12: 3A7UBK3ZC367 · pith_short_16: 3A7UBK3ZC367UXNA · pith_short_8: 3A7UBK3Z

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/3A7UBK3ZC367UXNANB7DI5DVNO \
  | 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: d83f40ab7916fdfa5da0687e3474756b9d6f0bf977ad821808369e412e70baca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "514aff4dec5592ad1566d72ced96f8ca90f7c4605b2692b07b545c7c2d12f983",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-02-17T18:10:09Z",
    "title_canon_sha256": "69ce73e678a58a1943b35c24a5ad52cc304a4eb6d454bc8c3a076d5e3964aa0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.05042",
    "kind": "arxiv",
    "version": 2
  }
}