Pith Number

pith:DM42JGRA

pith:1998:DM42JGRALPMUNVQWBG6YGZGZBL

not attested not anchored not stored refs pending

Fractal Structures and Scaling Laws in the Universe: Statistical Mechanics of the Self-Gravitating Gas

F. Combes, H. J. de Vega, N. S'anchez

arxiv:astro-ph/9807048 v1 · 1998-07-05 · astro-ph · cond-mat · gr-qc · hep-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{DM42JGRALPMUNVQWBG6YGZGZBL}

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	2026-05-18T01:40:13.955250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b39a49a205bd946d61609bd8364d90ada2ab468f2b27ff40fd0a30d80afba33

Aliases

arxiv: astro-ph/9807048 · arxiv_version: astro-ph/9807048v1 · doi: 10.48550/arxiv.astro-ph/9807048 · pith_short_12: DM42JGRALPMU · pith_short_16: DM42JGRALPMUNVQW · pith_short_8: DM42JGRA

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/DM42JGRALPMUNVQWBG6YGZGZBL \
  | 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: 1b39a49a205bd946d61609bd8364d90ada2ab468f2b27ff40fd0a30d80afba33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37e21e786e3877302874249267dcac8f14624e54f3c2a7515a9008f649293c5a",
    "cross_cats_sorted": [
      "cond-mat",
      "gr-qc",
      "hep-ph",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1998-07-05T14:23:57Z",
    "title_canon_sha256": "c43b32deaecf1267ee3c7afac9eb3ff53dd8d28538b4d766f4ba08b014ef5133"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9807048",
    "kind": "arxiv",
    "version": 1
  }
}