Pith Number

pith:W5CZMZCK

pith:2015:W5CZMZCK65MHHZNNMBLQYJXNQJ

not attested not anchored not stored refs pending

Physical meaning of the radial index of Laguerre-Gauss beams

Mario Krenn, William N. Plick

arxiv:1509.06875 v1 · 2015-09-23 · quant-ph · 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{W5CZMZCK65MHHZNNMBLQYJXNQJ}

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	2026-05-18T01:12:49.636947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b74596644af75873e5ad60570c26ed8241c37f366b3db466e9e3d3d7cd801c4c

Aliases

arxiv: 1509.06875 · arxiv_version: 1509.06875v1 · doi: 10.48550/arxiv.1509.06875 · pith_short_12: W5CZMZCK65MH · pith_short_16: W5CZMZCK65MHHZNN · pith_short_8: W5CZMZCK

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/W5CZMZCK65MHHZNNMBLQYJXNQJ \
  | 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: b74596644af75873e5ad60570c26ed8241c37f366b3db466e9e3d3d7cd801c4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d4bc5f0a4574ecff8b25ae2940c78e7c8cad978819235d01ea8066f1450102e",
    "cross_cats_sorted": [
      "physics.optics"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-09-23T08:14:07Z",
    "title_canon_sha256": "ca83d1bcb3d310b109778d4a6d300012d9c446a0131c93b03d338e1e157e1451"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06875",
    "kind": "arxiv",
    "version": 1
  }
}