Pith Number

pith:AP7L2COL

pith:2021:AP7L2COL3F2NVDD2DGPZIITXNN

not attested not anchored not stored refs pending

Spherically Symmetric Gravitational Collapse Of Inhomogeneous Dust Cloud In The Background Of Dark Energy

Anjali Pandey, Rajesh Kumar, Sudhir Kumar Srivastava

arxiv:2106.15138 v1 · 2021-06-29 · gr-qc

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AP7L2COL3F2NVDD2DGPZIITXNN}

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	2026-07-05T02:53:05.714103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03febd09cbd974da8c7a199f9422776b492f8663ea3122843ccf9d559a885abd

Aliases

arxiv: 2106.15138 · arxiv_version: 2106.15138v1 · doi: 10.48550/arxiv.2106.15138 · pith_short_12: AP7L2COL3F2N · pith_short_16: AP7L2COL3F2NVDD2 · pith_short_8: AP7L2COL

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/AP7L2COL3F2NVDD2DGPZIITXNN \
  | 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: 03febd09cbd974da8c7a199f9422776b492f8663ea3122843ccf9d559a885abd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed72e10e97b554c1cda6a39d5890090190011d4c4676855a11dbc23d600084b1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-06-29T07:49:49Z",
    "title_canon_sha256": "87020ceaf6910c1f2938a2cd42d29b0c42d9630fa238e3d23309c17de320d845"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.15138",
    "kind": "arxiv",
    "version": 1
  }
}