Pith Number

pith:KBK4OQME

pith:2018:KBK4OQMERW5EM7NGZIFQI2U2NL

not attested not anchored not stored refs pending

The distance sum rule from strong lensing systems and quasars - test of cosmic curvature and beyond

Jing-Zhao Qi, Marek Biesiada, Shuo Cao, Sixuan Zhang, Yan Wu, Zong-Hong Zhu

arxiv:1803.01990 v2 · 2018-03-06 · 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{KBK4OQMERW5EM7NGZIFQI2U2NL}

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	2026-05-17T23:54:48.548944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5055c741848dba467da6ca0b046a9a6ae9c12b43319e68d37f83971b433f97f1

Aliases

arxiv: 1803.01990 · arxiv_version: 1803.01990v2 · doi: 10.48550/arxiv.1803.01990 · pith_short_12: KBK4OQMERW5E · pith_short_16: KBK4OQMERW5EM7NG · pith_short_8: KBK4OQME

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/KBK4OQMERW5EM7NGZIFQI2U2NL \
  | 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: 5055c741848dba467da6ca0b046a9a6ae9c12b43319e68d37f83971b433f97f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "228f5541b087a0d440204f3bc0cfae8ec237b1e94e35623cf0bf0a3f3883377e",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2018-03-06T02:31:10Z",
    "title_canon_sha256": "9a23660dfd117a673814ca44d62c6be1a889a62419635eba5dfe277e7de942dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.01990",
    "kind": "arxiv",
    "version": 2
  }
}