Pith Number

pith:4QNXVIU7

pith:2011:4QNXVIU7I44TAZSGQP22ERNYNA

not attested not anchored not stored refs pending

Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness

Anna Valeria Germinario, Erasmo Caponio, Miguel S\'anchez

arxiv:1112.3892 v2 · 2011-12-16 · math.DG · 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{4QNXVIU7I44TAZSGQP22ERNYNA}

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	2026-05-18T01:19:14.645612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e41b7aa29f473930664683f5a245b86820963ae73ae1eb94c91f5bb326bdc44c

Aliases

arxiv: 1112.3892 · arxiv_version: 1112.3892v2 · doi: 10.48550/arxiv.1112.3892 · pith_short_12: 4QNXVIU7I44T · pith_short_16: 4QNXVIU7I44TAZSG · pith_short_8: 4QNXVIU7

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/4QNXVIU7I44TAZSGQP22ERNYNA \
  | 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: e41b7aa29f473930664683f5a245b86820963ae73ae1eb94c91f5bb326bdc44c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ed314dc90ff72f347082ba0066b6a29ed9a0e4904870c967cfcbe17f9d0d058",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-16T17:11:53Z",
    "title_canon_sha256": "bf0c4c40d819aeb071b9d625625d001828c93ec19191ecb0050fed790fb525c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3892",
    "kind": "arxiv",
    "version": 2
  }
}