Pith Number

pith:4GRMQPNB

pith:2005:4GRMQPNBHVUDBY3ZGAJBDNK266

not attested not anchored not stored refs pending

Simple Analytic Models of Gravitational Collapse

J. D. Bjorken, J. S. Liu, P. Chen, R. J. Adler

arxiv:gr-qc/0502040 v1 · 2005-02-09 · gr-qc · 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{4GRMQPNBHVUDBY3ZGAJBDNK266}

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.

Cited by

1 paper in Pith

Analytic models for gravitational collapse

Receipt and verification

First computed	2026-07-04T16:55:10.157991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1a2c83da13d6830e379301211b55af7a7eeb37c5f0ea0b0c015f38e74a3cc32

Aliases

arxiv: gr-qc/0502040 · arxiv_version: gr-qc/0502040v1 · doi: 10.48550/arxiv.gr-qc/0502040 · pith_short_12: 4GRMQPNBHVUD · pith_short_16: 4GRMQPNBHVUDBY3Z · pith_short_8: 4GRMQPNB

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/4GRMQPNBHVUDBY3ZGAJBDNK266 \
  | 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: e1a2c83da13d6830e379301211b55af7a7eeb37c5f0ea0b0c015f38e74a3cc32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5686165faac4d0c78db06c87686542e1fc630afdcf6404ac019c64786564cccb",
    "cross_cats_sorted": [
      "astro-ph"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2005-02-09T21:52:56Z",
    "title_canon_sha256": "78aab3463a309f2334c6483d7e982e1c7063c326941a2df840ed680cde7efe16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0502040",
    "kind": "arxiv",
    "version": 1
  }
}