Pith Number

pith:64VFXJSU

pith:2018:64VFXJSUIA3PCBJ3NB4IWXUN5Z

not attested not anchored not stored refs pending

A simple and analytical method for controlling the trajectory and multifurcation of optical beams

Michel Zamboni-Rached

arxiv:1808.01082 v2 · 2018-08-03 · 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{64VFXJSUIA3PCBJ3NB4IWXUN5Z}

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	2026-05-18T00:08:20.346393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f72a5ba6544036f1053b68788b5e8dee5a6aa029f53efbf353a1a8d4a6d7fe1f

Aliases

arxiv: 1808.01082 · arxiv_version: 1808.01082v2 · doi: 10.48550/arxiv.1808.01082 · pith_short_12: 64VFXJSUIA3P · pith_short_16: 64VFXJSUIA3PCBJ3 · pith_short_8: 64VFXJSU

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/64VFXJSUIA3PCBJ3NB4IWXUN5Z \
  | 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: f72a5ba6544036f1053b68788b5e8dee5a6aa029f53efbf353a1a8d4a6d7fe1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f8e3226f26a07d326a724e1edb514aed7a50ed5843eaa22e23264977265cf51",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2018-08-03T04:15:23Z",
    "title_canon_sha256": "4e8e6e71f99439033acddb21e22fdb438c01f20332b558e4e297514d5845ed24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.01082",
    "kind": "arxiv",
    "version": 2
  }
}