Pith Number

pith:TQBEJGZQ

pith:2016:TQBEJGZQRENMC4NI3CPVI3NXAN

not attested not anchored not stored refs pending

Analytical solution for multisingular vortex Gaussian beams: The mathematical theory of scattering modes

A. Ferrando, M.A. Garcia-March

arxiv:1602.00630 v3 · 2016-02-01 · physics.optics · cond-mat.quant-gas · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQBEJGZQRENMC4NI3CPVI3NXAN}

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	2026-05-18T01:13:55.878133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c02449b30891ac171a8d89f546db7037d58930b42730a40a006487d58954694

Aliases

arxiv: 1602.00630 · arxiv_version: 1602.00630v3 · doi: 10.48550/arxiv.1602.00630 · pith_short_12: TQBEJGZQRENM · pith_short_16: TQBEJGZQRENMC4NI · pith_short_8: TQBEJGZQ

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/TQBEJGZQRENMC4NI3CPVI3NXAN \
  | 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: 9c02449b30891ac171a8d89f546db7037d58930b42730a40a006487d58954694

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5d5d480378e13d0b2cb739836833f3ba9cef2bbee3a5c19b016f63c2877e3c4",
    "cross_cats_sorted": [
      "cond-mat.quant-gas",
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2016-02-01T18:31:36Z",
    "title_canon_sha256": "5407f98718700910216337d68195c447b5d96d87623f086171aa676765dbe880"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.00630",
    "kind": "arxiv",
    "version": 3
  }
}