Pith Number

pith:CKHURMJU

pith:2011:CKHURMJUBSCT3FWDYOBCZC3VOH

not attested not anchored not stored refs pending

Lensing by a singular isothermal sphere and a black hole

Hans Witt, Manchester), Shude Mao (NAOC

arxiv:1111.2429 v1 · 2011-11-10 · 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{CKHURMJUBSCT3FWDYOBCZC3VOH}

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	2026-05-18T01:59:42.723663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

128f48b1340c853d96c3c3822c8b7571e2b8462ef3f7c80d09c5f1a8829b33e0

Aliases

arxiv: 1111.2429 · arxiv_version: 1111.2429v1 · doi: 10.48550/arxiv.1111.2429 · pith_short_12: CKHURMJUBSCT · pith_short_16: CKHURMJUBSCT3FWD · pith_short_8: CKHURMJU

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/CKHURMJUBSCT3FWDYOBCZC3VOH \
  | 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: 128f48b1340c853d96c3c3822c8b7571e2b8462ef3f7c80d09c5f1a8829b33e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "796196ad16c534ac2b917530957af502472da2250fd3f8c62a641585dd8d2fd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-11-10T09:41:37Z",
    "title_canon_sha256": "88482296db6ceb15e511bb2fb67486b98880556b7ce3df92b555544cb18eb05f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2429",
    "kind": "arxiv",
    "version": 1
  }
}