Pith Number

pith:QDUGA242

pith:2009:QDUGA242CYFXQJ3MCEN5QW6ZFG

not attested not anchored not stored refs pending

On the number of solutions of a transcendental equation arising in the theory of gravitational lensing

Alexandre Eremenko, Walter Bergweiler

arxiv:0908.4595 v2 · 2009-08-31 · math.CV · astro-ph.CO · math-ph · 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{QDUGA242CYFXQJ3MCEN5QW6ZFG}

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	2026-05-18T00:26:47.661263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80e8606b9a160b78276c111bd85bd92999724a9938529f50e648c9284dcac350

Aliases

arxiv: 0908.4595 · arxiv_version: 0908.4595v2 · doi: 10.48550/arxiv.0908.4595 · pith_short_12: QDUGA242CYFX · pith_short_16: QDUGA242CYFXQJ3M · pith_short_8: QDUGA242

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/QDUGA242CYFXQJ3MCEN5QW6ZFG \
  | 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: 80e8606b9a160b78276c111bd85bd92999724a9938529f50e648c9284dcac350

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa6def6d440049231bb30d479fc897eeee7c1fdb2a99c37516de1ee7b7d15c6d",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2009-08-31T18:38:02Z",
    "title_canon_sha256": "3622a6576b859ba7d9f32c238c1ce76651c923e8f6143974c43be8c206113e52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.4595",
    "kind": "arxiv",
    "version": 2
  }
}