Pith Number

pith:4BP5OJ32

pith:2016:4BP5OJ32OR4F44VKZEB5CZQIZM

not attested not anchored not stored refs pending

Beyond lensing by the cosmological constant

Marianne Lapierre-Leonard (Bishop's University), Valerio Faraoni

arxiv:1608.03164 v2 · 2016-08-10 · 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{4BP5OJ32OR4F44VKZEB5CZQIZM}

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	2026-05-18T00:52:09.367412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e05fd7277a74785e72aac903d16608cb163acdb943bad99a6a92b26ffdc14d1f

Aliases

arxiv: 1608.03164 · arxiv_version: 1608.03164v2 · doi: 10.48550/arxiv.1608.03164 · pith_short_12: 4BP5OJ32OR4F · pith_short_16: 4BP5OJ32OR4F44VK · pith_short_8: 4BP5OJ32

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/4BP5OJ32OR4F44VKZEB5CZQIZM \
  | 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: e05fd7277a74785e72aac903d16608cb163acdb943bad99a6a92b26ffdc14d1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b05d3d1a9dae11d10aa29628c5b1159f204a93da5a42dcfd56dc61180a4e3ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-08-10T13:26:06Z",
    "title_canon_sha256": "b9ec4f2dd288116fa4d7bda1b7ec6fe166974e2edc0fa1e32b80b3a82a9af818"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.03164",
    "kind": "arxiv",
    "version": 2
  }
}