Pith Number

pith:72BJV6MG

pith:2012:72BJV6MGLSYECP2U525DUCCN2I

not attested not anchored not stored refs pending

Counting Zeros of Harmonic Rational Functions and Its Application to Gravitational Lensing

Lyndon L. Ji, Pavel M. Bleher, Roland K. W. Roeder, Youkow Homma

arxiv:1206.2273 v2 · 2012-06-11 · math.CV · gr-qc · 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{72BJV6MGLSYECP2U525DUCCN2I}

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	2026-05-18T03:38:23.451348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe829af9865cb0413f54eeba3a084dd2387fbbdaf881eb000c00c24220f1e5b1

Aliases

arxiv: 1206.2273 · arxiv_version: 1206.2273v2 · doi: 10.48550/arxiv.1206.2273 · pith_short_12: 72BJV6MGLSYE · pith_short_16: 72BJV6MGLSYECP2U · pith_short_8: 72BJV6MG

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/72BJV6MGLSYECP2U525DUCCN2I \
  | 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: fe829af9865cb0413f54eeba3a084dd2387fbbdaf881eb000c00c24220f1e5b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c9ed46d7e81219ba760a8d7f5b8816c0f86419174bae30c7f8a2e240026d7f2",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2012-06-11T16:10:29Z",
    "title_canon_sha256": "8dd88a1c97781730fedfc3e8063e4682988421349a29443ebf5562fcf566b26b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2273",
    "kind": "arxiv",
    "version": 2
  }
}