Pith Number

pith:4X52OTTV

pith:2012:4X52OTTV6VTFVVX4LVEG23RBK2

not attested not anchored not stored refs pending

The Jacobi map for gravitational lensing: the role of the exponential map

L. Raul Abramo, Paulo H. F. Reimberg

arxiv:1211.5114 v2 · 2012-11-21 · 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{4X52OTTV6VTFVVX4LVEG23RBK2}

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	2026-05-18T03:31:53.972720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5fba74e75f5665ad6fc5d486d6e215686b1f0483b8f46ec10bad5be8cf20099

Aliases

arxiv: 1211.5114 · arxiv_version: 1211.5114v2 · doi: 10.48550/arxiv.1211.5114 · pith_short_12: 4X52OTTV6VTF · pith_short_16: 4X52OTTV6VTFVVX4 · pith_short_8: 4X52OTTV

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/4X52OTTV6VTFVVX4LVEG23RBK2 \
  | 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: e5fba74e75f5665ad6fc5d486d6e215686b1f0483b8f46ec10bad5be8cf20099

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "887bf4e03bde6bf8604c7f90aed83ef393fc24b17e5bd784f67bba63164dae87",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-11-21T19:01:28Z",
    "title_canon_sha256": "1a74235660b7df93f4d4263242f519f6543c54f903eec4bbcea8acfe3c8a2644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5114",
    "kind": "arxiv",
    "version": 2
  }
}