Pith Number

pith:CR5UPESR

pith:2025:CR5UPESRW7Z6ZPMGLJMQ2B3H3X

not attested not anchored not stored refs pending

Basic Elements of Strong Gravitational Lensing

Jeremy D. Schnittman, Paul L. Schechter

arxiv:2505.22738 v1 · 2025-05-28 · 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{CR5UPESRW7Z6ZPMGLJMQ2B3H3X}

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	2026-07-05T11:11:49.344133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

147b479251b7f3ecbd865a590d0767ddf55aa048f7b74587c8a6d8b856484c0b

Aliases

arxiv: 2505.22738 · arxiv_version: 2505.22738v1 · doi: 10.48550/arxiv.2505.22738 · pith_short_12: CR5UPESRW7Z6 · pith_short_16: CR5UPESRW7Z6ZPMG · pith_short_8: CR5UPESR

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/CR5UPESRW7Z6ZPMGLJMQ2B3H3X \
  | 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: 147b479251b7f3ecbd865a590d0767ddf55aa048f7b74587c8a6d8b856484c0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18d19832a611664e058adc5e3cb3530c500d4fea248e2ef391f8d18648bc2071",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2025-05-28T18:01:47Z",
    "title_canon_sha256": "b9521dae09f2bc244d66bd5f34acb1f0403aef6fa9df6488c34247c79f4e9487"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.22738",
    "kind": "arxiv",
    "version": 1
  }
}