Pith Number

pith:4B4HAPIR

pith:1996:4B4HAPIRHKVZDORGEV3QC3IFYY

not attested not anchored not stored refs pending

Extended Perturbation Theory for the Local Density Distribution Function

F. Bernardeau, F.R. Bouchet, L. Hernquist, S. Colombi

arxiv:astro-ph/9610253 v1 · 1996-10-30 · 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{4B4HAPIRHKVZDORGEV3QC3IFYY}

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	2026-05-18T01:40:18.990035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e078703d113aab91ba262577016d05c634f3709cd61cbc110bac8c8f01ba6c87

Aliases

arxiv: astro-ph/9610253 · arxiv_version: astro-ph/9610253v1 · doi: 10.48550/arxiv.astro-ph/9610253 · pith_short_12: 4B4HAPIRHKVZ · pith_short_16: 4B4HAPIRHKVZDORG · pith_short_8: 4B4HAPIR

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/4B4HAPIRHKVZDORGEV3QC3IFYY \
  | 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: e078703d113aab91ba262577016d05c634f3709cd61cbc110bac8c8f01ba6c87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4eb72b59706787a44bf82396e66dc77802699bb888ad5ad122ad68e42c8a0416",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1996-10-30T18:27:23Z",
    "title_canon_sha256": "1891343043f354294fa21a8b25d3c5869d5da2abfd3b6b756783ce61f79abdac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9610253",
    "kind": "arxiv",
    "version": 1
  }
}