Pith Number

pith:RNB6R5RQ

pith:2012:RNB6R5RQJ64AUVWUORZVC42ULU

not attested not anchored not stored refs pending

The analytical discussion on strong gravitaional lensing for a gravitational source with a $f(R)$ global monopole

Hongbo Cheng, Jingyun Man

arxiv:1205.4857 v3 · 2012-05-22 · gr-qc · 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{RNB6R5RQJ64AUVWUORZVC42ULU}

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	2026-05-18T01:32:35.219246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b43e8f6304fb80a56d474735173545d2e1c4ebcb42bb607600b8c4828fc9d4a

Aliases

arxiv: 1205.4857 · arxiv_version: 1205.4857v3 · doi: 10.48550/arxiv.1205.4857 · pith_short_12: RNB6R5RQJ64A · pith_short_16: RNB6R5RQJ64AUVWU · pith_short_8: RNB6R5RQ

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/RNB6R5RQJ64AUVWUORZVC42ULU \
  | 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: 8b43e8f6304fb80a56d474735173545d2e1c4ebcb42bb607600b8c4828fc9d4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe4af5054f13001793ed7f81289f17a0fa47b56a93a00de4b4aea92685e58b5d",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-05-22T09:50:08Z",
    "title_canon_sha256": "cdb56958593a40bb5a5e381b354ac3947697d3e536c9750d584f5a39b1f53c62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4857",
    "kind": "arxiv",
    "version": 3
  }
}