Pith Number

pith:JVCMAGR3

pith:2011:JVCMAGR3R7L2DNSWDCQP6MEF56

not attested not anchored not stored refs pending

Layzer-Irvine equation: new perspectives and the role of interacting dark energy

A. Barreira, P. P. Avelino

arxiv:1112.0417 v1 · 2011-12-02 · astro-ph.CO · gr-qc · hep-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{JVCMAGR3R7L2DNSWDCQP6MEF56}

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	2026-05-18T03:43:18.532668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d44c01a3b8fd7a1b65618a0ff3085efb1113127ed2c9667e8d415e28f1133ac

Aliases

arxiv: 1112.0417 · arxiv_version: 1112.0417v1 · doi: 10.48550/arxiv.1112.0417 · pith_short_12: JVCMAGR3R7L2 · pith_short_16: JVCMAGR3R7L2DNSW · pith_short_8: JVCMAGR3

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/JVCMAGR3R7L2DNSWDCQP6MEF56 \
  | 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: 4d44c01a3b8fd7a1b65618a0ff3085efb1113127ed2c9667e8d415e28f1133ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4098d3daa03b023bf0ab1fa72e623b177cc351e6567a76497dc2a9cf66624d48",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-12-02T10:22:01Z",
    "title_canon_sha256": "ac808fcd648e476a523f6be29a9715b4322950af33b2c8ee5fa1bcbfeda1127b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0417",
    "kind": "arxiv",
    "version": 1
  }
}