Pith Number

pith:RAPN4MUN

pith:2018:RAPN4MUNAC5XY3PGJ7B7JAPBWY

not attested not anchored not stored refs pending

Independent amplitude and trajectory/beam-width control of nonparaxial beams

Michael Goutsoulas, Nikolaos K. Efremidis, Raluca-Sorina Penciu

arxiv:1807.03906 v1 · 2018-07-10 · 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{RAPN4MUNAC5XY3PGJ7B7JAPBWY}

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	2026-05-18T00:10:58.720226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

881ede328d00bb7c6de64fc3f481e1b603ac9285cfcad76fbb5fa17ed7485b50

Aliases

arxiv: 1807.03906 · arxiv_version: 1807.03906v1 · doi: 10.48550/arxiv.1807.03906 · pith_short_12: RAPN4MUNAC5X · pith_short_16: RAPN4MUNAC5XY3PG · pith_short_8: RAPN4MUN

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/RAPN4MUNAC5XY3PGJ7B7JAPBWY \
  | 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: 881ede328d00bb7c6de64fc3f481e1b603ac9285cfcad76fbb5fa17ed7485b50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f421708288ce1ce2b6ed06eb820a209edaf0052c8521c880412a88d5b65f0bcb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2018-07-10T23:57:45Z",
    "title_canon_sha256": "1160b25d128ad3074c16c1b35577e7219d71e950ef7f042c703c66a9516ba622"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.03906",
    "kind": "arxiv",
    "version": 1
  }
}