Pith Number

pith:G2FLXXR3

pith:2009:G2FLXXR343XALT3CESI2RVGSHA

not attested not anchored not stored refs pending

A Universal Magnification Theorem III. Caustics Beyond Codimension Five

Amir B. Aazami, Arlie O. Petters

arxiv:0909.5235 v2 · 2009-09-29 · 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{G2FLXXR343XALT3CESI2RVGSHA}

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	2026-05-18T02:34:27.278151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

368abbde3be6ee05cf622491a8d4d2381032b919d5480ecdf70c3a5616e74e41

Aliases

arxiv: 0909.5235 · arxiv_version: 0909.5235v2 · doi: 10.48550/arxiv.0909.5235 · pith_short_12: G2FLXXR343XA · pith_short_16: G2FLXXR343XALT3C · pith_short_8: G2FLXXR3

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/G2FLXXR343XALT3CESI2RVGSHA \
  | 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: 368abbde3be6ee05cf622491a8d4d2381032b919d5480ecdf70c3a5616e74e41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "981a96a4a185b598fd330a6aa301da3286c44b077d5cfc9d653207e369c4dfeb",
    "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": "2009-09-29T05:00:53Z",
    "title_canon_sha256": "51ab08743f797e7d91a514615c2f89d0c485076f300953ee4d274aebaef6abcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.5235",
    "kind": "arxiv",
    "version": 2
  }
}