Pith Number

pith:QJEJZR7U

pith:2011:QJEJZR7U3OP3EFBTY2NQSAMEF4

not attested not anchored not stored refs pending

Curvature properties of $\phi$-null Osserman Lorentzian $\mathcal{S}$-manifolds

Angelo V. Caldarella, Letizia Brunetti

arxiv:1112.1050 v2 · 2011-12-05 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJEJZR7U3OP3EFBTY2NQSAMEF4}

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	2026-05-18T03:08:27.410409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82489cc7f4db9fb21433c69b0901842f24cf93bbc8b4b72275d17be6f561a191

Aliases

arxiv: 1112.1050 · arxiv_version: 1112.1050v2 · doi: 10.48550/arxiv.1112.1050 · pith_short_12: QJEJZR7U3OP3 · pith_short_16: QJEJZR7U3OP3EFBT · pith_short_8: QJEJZR7U

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/QJEJZR7U3OP3EFBTY2NQSAMEF4 \
  | 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: 82489cc7f4db9fb21433c69b0901842f24cf93bbc8b4b72275d17be6f561a191

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41900930a5c0fd0620b1a8e7c19a1687f26bfef9287626df0f503e2d42533b71",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-05T20:34:48Z",
    "title_canon_sha256": "82a0d58f87384c97297364fc31397c91d013319f29cec31ada5e68600a74a086"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1050",
    "kind": "arxiv",
    "version": 2
  }
}