Pith Number

pith:R3MBYOWQ

pith:2016:R3MBYOWQBXMS5HTRZDQS6BG72T

not attested not anchored not stored refs pending

Revisiting Studies of the Statistical Property of a Strong Gravitational Lens System and Model-independent Constraint on the Curvature of the Universe

Guo-Jian Wang, Hai Yu, Jun-Qing Xia, Shuo Cao, Shu-Xun Tian, Zheng-Xiang Li, Zong-Hong Zhu

arxiv:1611.04731 v2 · 2016-11-15 · 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{R3MBYOWQBXMS5HTRZDQS6BG72T}

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	2026-05-18T00:52:37.881500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ed81c3ad00dd92e9e71c8e12f04dfd4e9fede2fffb3f5a4fe1747211bcbc463

Aliases

arxiv: 1611.04731 · arxiv_version: 1611.04731v2 · doi: 10.48550/arxiv.1611.04731 · pith_short_12: R3MBYOWQBXMS · pith_short_16: R3MBYOWQBXMS5HTR · pith_short_8: R3MBYOWQ

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/R3MBYOWQBXMS5HTRZDQS6BG72T \
  | 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: 8ed81c3ad00dd92e9e71c8e12f04dfd4e9fede2fffb3f5a4fe1747211bcbc463

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f84873ac76ffe11f5b355107a1951046645662835391dc5fbaed8c8e67a0578f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2016-11-15T08:11:21Z",
    "title_canon_sha256": "ef56913ce69101e9e6f1c3713b5b051cc4ea84f8f2a4edf6a505f27e73dab9b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04731",
    "kind": "arxiv",
    "version": 2
  }
}