Pith Number

pith:ZPHUC6QJ

pith:2011:ZPHUC6QJYATNAHCL5TW3WTZFLV

not attested not anchored not stored refs pending

Analytic partial wave expansion and integral representation of Bessel beam

Amer Hodzic (Department of Physics, Kingston RI USA), University of Rhode Island

arxiv:1104.0719 v1 · 2011-04-05 · math-ph · math.MP · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZPHUC6QJYATNAHCL5TW3WTZFLV}

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	2026-05-18T04:25:02.708383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbcf417a09c026d01c4becedbb4f255d5cef240ac9b703b3b33ceb037ac29668

Aliases

arxiv: 1104.0719 · arxiv_version: 1104.0719v1 · doi: 10.48550/arxiv.1104.0719 · pith_short_12: ZPHUC6QJYATN · pith_short_16: ZPHUC6QJYATNAHCL · pith_short_8: ZPHUC6QJ

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/ZPHUC6QJYATNAHCL5TW3WTZFLV \
  | 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: cbcf417a09c026d01c4becedbb4f255d5cef240ac9b703b3b33ceb037ac29668

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb3d85e4cb3d3e7e813fba2778bd876e60eaf06d276056af316662e406df2b95",
    "cross_cats_sorted": [
      "math.MP",
      "physics.optics"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-04-05T00:58:53Z",
    "title_canon_sha256": "0806261e3ce06ec25a593cd49287e4365a18d3a34fb922260facddd67e0cb02e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0719",
    "kind": "arxiv",
    "version": 1
  }
}