Pith Number

pith:DDTD5CQM

pith:2011:DDTD5CQM2ITVPSDBBX2KQITNCU

not attested not anchored not stored refs pending

Spherical Collapse in f(R) Gravity

Alex Borisov, Bhuvnesh Jain, Pengjie Zhang

arxiv:1102.4839 v1 · 2011-02-23 · astro-ph.CO · 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{DDTD5CQM2ITVPSDBBX2KQITNCU}

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

Testing General Relativity with Present and Future Astrophysical Observations

Receipt and verification

First computed	2026-05-18T02:03:05.844997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18e63e8a0cd22757c8610df4a8226d15137502e60c26c5461c81366f2eb8d2d7

Aliases

arxiv: 1102.4839 · arxiv_version: 1102.4839v1 · doi: 10.48550/arxiv.1102.4839 · pith_short_12: DDTD5CQM2ITV · pith_short_16: DDTD5CQM2ITVPSDB · pith_short_8: DDTD5CQM

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/DDTD5CQM2ITVPSDBBX2KQITNCU \
  | 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: 18e63e8a0cd22757c8610df4a8226d15137502e60c26c5461c81366f2eb8d2d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50fe44ab4e765ac224e300599aaeb166d3cd6df73eaf2c014ba5a88234650ed6",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-02-23T20:46:55Z",
    "title_canon_sha256": "f6fd7ac079bb884b5e214c21c83e26493a0af79ed0d9b4f66a9a60f2632abaf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4839",
    "kind": "arxiv",
    "version": 1
  }
}