Pith Number

pith:6QFT5RYK

pith:2010:6QFT5RYKVXFJ3N7LMZTDFOCNYM

not attested not anchored not stored refs pending

Gravitational Collapse: Expanding and Collapsing Regions

G. Abbas, M. Sharif

arxiv:1008.2805 v1 · 2010-08-17 · 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{6QFT5RYKVXFJ3N7LMZTDFOCNYM}

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	2026-05-18T04:25:49.568481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f40b3ec70aadca9db7eb666632b84dc3206347f22a9871856fcb95893f3198ff

Aliases

arxiv: 1008.2805 · arxiv_version: 1008.2805v1 · doi: 10.48550/arxiv.1008.2805 · pith_short_12: 6QFT5RYKVXFJ · pith_short_16: 6QFT5RYKVXFJ3N7L · pith_short_8: 6QFT5RYK

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/6QFT5RYKVXFJ3N7LMZTDFOCNYM \
  | 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: f40b3ec70aadca9db7eb666632b84dc3206347f22a9871856fcb95893f3198ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb7e0e2f597ce98572b57efdcebe4ef0b5fe03c5c091476a4e8782d91e9f3eea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-08-17T02:30:38Z",
    "title_canon_sha256": "fa4dc4a8efa8dfd55fd2550b89d2798ba36dabe13fde1615d20e4307275c88ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2805",
    "kind": "arxiv",
    "version": 1
  }
}