Pith Number

pith:H45XRMYD

pith:2021:H45XRMYDG3OQMT2LLT26TVGRZD

not attested not anchored not stored refs pending

Line-of-sight effects in strong gravitational lensing

Jean-Philippe Uzan, Julien Larena, Pierre Fleury

arxiv:2104.08883 v5 · 2021-04-18 · 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{H45XRMYDG3OQMT2LLT26TVGRZD}

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	2026-07-05T05:20:58.198563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f3b78b30336dd064f4b5cf5e9d4d1c8ed2bf0a28ce7793eb6dead02a2caa034

Aliases

arxiv: 2104.08883 · arxiv_version: 2104.08883v5 · doi: 10.48550/arxiv.2104.08883 · pith_short_12: H45XRMYDG3OQ · pith_short_16: H45XRMYDG3OQMT2L · pith_short_8: H45XRMYD

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/H45XRMYDG3OQMT2LLT26TVGRZD \
  | 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: 3f3b78b30336dd064f4b5cf5e9d4d1c8ed2bf0a28ce7793eb6dead02a2caa034

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78fcccce7705650a5705617ab666d9c085030d1cf7b5f2993bd7e8b061ae19cf",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2021-04-18T15:38:01Z",
    "title_canon_sha256": "58d6bdd9c8649d74ad6712bba72927c74cd38230fe72776a78c916743d14ab49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.08883",
    "kind": "arxiv",
    "version": 5
  }
}