Pith Number

pith:HGTQARRY

pith:2016:HGTQARRYJX3ZCVXIXOPOJFX5FM

not attested not anchored not stored refs pending

Knotted optical vortices in exact solutions to Maxwell's equations

Albertus Johannes Jacobus Maria de Klerk, Dirk Bouwmeester, Jan Willem Dalhuisen, Roland Ivo van der Veen

arxiv:1610.05285 v2 · 2016-10-17 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HGTQARRYJX3ZCVXIXOPOJFX5FM}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:32:55.552577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39a70046384df79156e8bb9ee496fd2b2d6b8ff5ff7db8314525196a39e422b1

Aliases

arxiv: 1610.05285 · arxiv_version: 1610.05285v2 · doi: 10.48550/arxiv.1610.05285 · pith_short_12: HGTQARRYJX3Z · pith_short_16: HGTQARRYJX3ZCVXI · pith_short_8: HGTQARRY

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/HGTQARRYJX3ZCVXIXOPOJFX5FM \
  | 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: 39a70046384df79156e8bb9ee496fd2b2d6b8ff5ff7db8314525196a39e422b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f38ad4bbe725c76551a64f37e118141941d22a0f1fb96844d525bf90ff3ee41",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-10-17T19:37:26Z",
    "title_canon_sha256": "aada1c6e0dc8dc850f7dd92e0b5d7e84df2374bef01c6302a4debd3cbb353a07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05285",
    "kind": "arxiv",
    "version": 2
  }
}