Pith Number

pith:TUUTLDSS

pith:2010:TUUTLDSSFSGKJDK5LLS7Z7UDYX

not attested not anchored not stored refs pending

Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing

Amir B. Aazami, Arlie O. Petters, Jeffrey M. Rabin

arxiv:1004.0516 v2 · 2010-04-04 · math-ph · astro-ph.CO · math.DG · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TUUTLDSSFSGKJDK5LLS7Z7UDYX}

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	2026-05-18T04:24:54.651109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d29358e522c8ca48d5d5ae5fcfe83c5c012a2cd47c47c1584fe3be2ec046444

Aliases

arxiv: 1004.0516 · arxiv_version: 1004.0516v2 · doi: 10.48550/arxiv.1004.0516 · pith_short_12: TUUTLDSSFSGK · pith_short_16: TUUTLDSSFSGKJDK5 · pith_short_8: TUUTLDSS

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/TUUTLDSSFSGKJDK5LLS7Z7UDYX \
  | 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: 9d29358e522c8ca48d5d5ae5fcfe83c5c012a2cd47c47c1584fe3be2ec046444

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e85f7d88a46c873d516bb07e0d6f1afeeb19c87b1f4fb81b6158552d2d85f02",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-04-04T16:24:45Z",
    "title_canon_sha256": "1f568c7b8dec527cace479eebfa95cbb46a79c1a16f6fe014242e86513c3cf55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0516",
    "kind": "arxiv",
    "version": 2
  }
}