Pith Number

pith:UAZ2MGN5

pith:2009:UAZ2MGN5VE6SAZZIWFBNZDPYCQ

not attested not anchored not stored refs pending

The Plane Wave Expansion, Infinite Integrals and Identities involving Spherical Bessel Functions

Rami Mehrem

arxiv:0909.0494 v4 · 2009-09-02 · math-ph · math.MP · nucl-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UAZ2MGN5VE6SAZZIWFBNZDPYCQ}

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.

Cited by

1 paper in Pith

CMB Lensing Trispectrum as a Probe of Parity Violation in LSS

Receipt and verification

First computed	2026-05-18T04:14:45.208776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a033a619bda93d206728b142dc8df8142543fd5bd8a23dc073aed5a4cd367603

Aliases

arxiv: 0909.0494 · arxiv_version: 0909.0494v4 · doi: 10.48550/arxiv.0909.0494 · pith_short_12: UAZ2MGN5VE6S · pith_short_16: UAZ2MGN5VE6SAZZI · pith_short_8: UAZ2MGN5

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/UAZ2MGN5VE6SAZZIWFBNZDPYCQ \
  | 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: a033a619bda93d206728b142dc8df8142543fd5bd8a23dc073aed5a4cd367603

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18f06b1dae4252b3397c465b76e10b5fbb7467c7b6344ad0fa0af0570eac7c59",
    "cross_cats_sorted": [
      "math.MP",
      "nucl-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-09-02T18:52:41Z",
    "title_canon_sha256": "b66c0222f2537c96ccd927be48c2ca2309fcab064a808c2ecc625329a367eedb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0494",
    "kind": "arxiv",
    "version": 4
  }
}