Pith Number

pith:B3DHQD2A

pith:2011:B3DHQD2AEPG3GKNZMTFXBERPCI

not attested not anchored not stored refs pending

Paraxial and nonparaxial polynomial beams and the analytic approach to propagation

Joerg B Goette, Mark R Dennis, Michael A Morgan, Miguel A Alonso, Robert P King

arxiv:1108.5906 v1 · 2011-08-30 · 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{B3DHQD2AEPG3GKNZMTFXBERPCI}

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	2026-05-18T03:54:39.343988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ec6780f4023cdb329b964cb70922f1220d28ed7dd75e59ad565428f04bdbf2b

Aliases

arxiv: 1108.5906 · arxiv_version: 1108.5906v1 · doi: 10.48550/arxiv.1108.5906 · pith_short_12: B3DHQD2AEPG3 · pith_short_16: B3DHQD2AEPG3GKNZ · pith_short_8: B3DHQD2A

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/B3DHQD2AEPG3GKNZMTFXBERPCI \
  | 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: 0ec6780f4023cdb329b964cb70922f1220d28ed7dd75e59ad565428f04bdbf2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fd08022624ed94c5870845ba9a4081f0f1c36b570411a7f2615e509444dfbfa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2011-08-30T10:26:18Z",
    "title_canon_sha256": "ef7558a04a1b7b99e449d2797fadb22a8b74beb5be12a584205572a63a6dc591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5906",
    "kind": "arxiv",
    "version": 1
  }
}