Pith Number

pith:CGQGRAE7

pith:2006:CGQGRAE7PBW4CLXWMG3J4GSEKA

not attested not anchored not stored refs pending

Statistical Mechanics of the Self-Gravitating Gas: Thermodynamic Limit, Unstabilities and Phase Diagrams

H. J. de Vega, N. G. Sanchez

arxiv:astro-ph/0601600 v1 · 2006-01-26 · astro-ph · cond-mat.stat-mech · gr-qc · 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{CGQGRAE7PBW4CLXWMG3J4GSEKA}

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	2026-05-18T01:40:32.634734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11a068809f786dc12ef661b69e1a445012ec51e2c423ab504039b8981a62c816

Aliases

arxiv: astro-ph/0601600 · arxiv_version: astro-ph/0601600v1 · doi: 10.48550/arxiv.astro-ph/0601600 · pith_short_12: CGQGRAE7PBW4 · pith_short_16: CGQGRAE7PBW4CLXW · pith_short_8: CGQGRAE7

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/CGQGRAE7PBW4CLXWMG3J4GSEKA \
  | 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: 11a068809f786dc12ef661b69e1a445012ec51e2c423ab504039b8981a62c816

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d122dc1facf9367974396dd542ac399b79e467c6e233bd3da40195a87e503f20",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "gr-qc",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-01-26T14:27:17Z",
    "title_canon_sha256": "68c783a7489429365a790842ec7f69fbb159bb211f9c4e660f835d6b378dc3cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0601600",
    "kind": "arxiv",
    "version": 1
  }
}