Pith Number

pith:IB6CMM2Y

pith:2022:IB6CMM2YLJBF4GYPGBFOCUO44B

not attested not anchored not stored refs pending

The Quadruple Image Configurations of Asymptotically Circular Gravitational Lenses

Chirag Falor, Paul L. Schechter

arxiv:2205.06269 v1 · 2022-05-12 · gr-qc · 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{IB6CMM2YLJBF4GYPGBFOCUO44B}

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	2026-07-05T04:54:58.669308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

407c2633585a425e1b0f304ae151dce07427f162f0db36285f110a5e995f55e2

Aliases

arxiv: 2205.06269 · arxiv_version: 2205.06269v1 · doi: 10.48550/arxiv.2205.06269 · pith_short_12: IB6CMM2YLJBF · pith_short_16: IB6CMM2YLJBF4GYP · pith_short_8: IB6CMM2Y

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/IB6CMM2YLJBF4GYPGBFOCUO44B \
  | 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: 407c2633585a425e1b0f304ae151dce07427f162f0db36285f110a5e995f55e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04e4486a1a0d2a206f6af921d410b8f4d34d7f16297252974f5d4d293796e68a",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-05-12T15:34:55Z",
    "title_canon_sha256": "8fae436a10da021c858e9dcd5c883c51b734dc2fc99f5f2c80a6ab00c353a057"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.06269",
    "kind": "arxiv",
    "version": 1
  }
}