Pith Number

pith:OALTJ4T5

pith:2009:OALTJ4T5ZPAJFRAFNJKOZTM7YM

not attested not anchored not stored refs pending

A Universal Magnification Theorem II. Generic Caustics up to Codimension Five

Amir B. Aazami, Arlie O. Petters

arxiv:0904.2236 v4 · 2009-04-15 · math-ph · astro-ph.CO · gr-qc · 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{OALTJ4T5ZPAJFRAFNJKOZTM7YM}

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	2026-05-18T02:14:00.371758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

701734f27dcbc092c4056a54eccd9fc3394145da9ccdf9a2dfbe832995544a61

Aliases

arxiv: 0904.2236 · arxiv_version: 0904.2236v4 · doi: 10.48550/arxiv.0904.2236 · pith_short_12: OALTJ4T5ZPAJ · pith_short_16: OALTJ4T5ZPAJFRAF · pith_short_8: OALTJ4T5

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/OALTJ4T5ZPAJFRAFNJKOZTM7YM \
  | 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: 701734f27dcbc092c4056a54eccd9fc3394145da9ccdf9a2dfbe832995544a61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a7395b35d643507a3dbda4f103cf7bef8ffd8dd659fd1641dcf1be81b8ce617",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "gr-qc",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-04-15T04:13:08Z",
    "title_canon_sha256": "acaa09eeb6de403570d7b5b89a06ccba02012c2d42674e9b82ba9acf8741b135"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.2236",
    "kind": "arxiv",
    "version": 4
  }
}