Pith Number

pith:MAKDRR4D

pith:2012:MAKDRR4DIPHZIANACJ3DUXUWB3

not attested not anchored not stored refs pending

Spherical collapse model with shear and angular momentum in dark energy cosmologies

2), A. Del Popolo (1, Brazil (3) Institute of Cosmology, F. Pace (3), Gravitation, Italy (2) Departamento de Astronomia, J. A. S. Lima (2) ((1) Astronomy Department, Portsmouth, S\~ao Paulo, SP, U.K.), Universidade de S\~ao Paulo, University of Catania, University of Portsmouth

arxiv:1212.5092 v1 · 2012-12-19 · 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{MAKDRR4DIPHZIANACJ3DUXUWB3}

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	2026-05-18T03:00:26.648342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

601438c78343cf9401a012763a5e960efd30f3af2851fbf33dc9ae1188bf327d

Aliases

arxiv: 1212.5092 · arxiv_version: 1212.5092v1 · doi: 10.48550/arxiv.1212.5092 · pith_short_12: MAKDRR4DIPHZ · pith_short_16: MAKDRR4DIPHZIANA · pith_short_8: MAKDRR4D

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/MAKDRR4DIPHZIANACJ3DUXUWB3 \
  | 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: 601438c78343cf9401a012763a5e960efd30f3af2851fbf33dc9ae1188bf327d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aecbc9423b2212f3f2f2f33c4e7d9cf5261c6ee4569c2dd80900dc1a07194eb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-12-19T20:48:06Z",
    "title_canon_sha256": "9eb44a0921d8a3a4057083e89935b4112ebc232eabf0d85abafd532ff3fca86d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5092",
    "kind": "arxiv",
    "version": 1
  }
}