Pith Number

pith:Z5KGGD2R

pith:2000:Z5KGGD2R42LBGWSE6JDLXJAS2Y

not attested not anchored not stored refs pending

Axicon Gaussian Laser Beams

Kirk T. McDonald

arxiv:physics/0003056 v2 · 2000-03-23 · 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{Z5KGGD2R42LBGWSE6JDLXJAS2Y}

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	2026-07-04T14:43:13.918517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf54630f51e696135a44f246bba412d61fcdbdb3f4737e3ccf84f6a7fd63190d

Aliases

arxiv: physics/0003056 · arxiv_version: physics/0003056v2 · doi: 10.48550/arxiv.physics/0003056 · pith_short_12: Z5KGGD2R42LB · pith_short_16: Z5KGGD2R42LBGWSE · pith_short_8: Z5KGGD2R

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/Z5KGGD2R42LBGWSE6JDLXJAS2Y \
  | 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: cf54630f51e696135a44f246bba412d61fcdbdb3f4737e3ccf84f6a7fd63190d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "721159c4b612c38501ba71accb95c62778d6485eec33525a676ce9d4ab8e4a81",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "physics.optics",
    "submitted_at": "2000-03-23T19:50:16Z",
    "title_canon_sha256": "664de0288eb1018e72d38b3236a762e118685fe2a56a933ed4153661b468cfd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "physics/0003056",
    "kind": "arxiv",
    "version": 2
  }
}