Pith Number

pith:OEOFGJ5L

pith:2014:OEOFGJ5LUFJC75JPXFWLJUE5XM

not attested not anchored not stored refs pending

Zero Focal Shift in High Numerical Aperture Focusing of a Gaussian Laser Beam through Multiple Dielectric Interfaces

Ali Mahmoudi

arxiv:1409.4021 v1 · 2014-09-14 · 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{OEOFGJ5LUFJC75JPXFWLJUE5XM}

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	2026-05-18T02:42:53.215013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

711c5327aba1522ff52fb96cb4d09dbb32240ac3db724f15a6779b6581588195

Aliases

arxiv: 1409.4021 · arxiv_version: 1409.4021v1 · doi: 10.48550/arxiv.1409.4021 · pith_short_12: OEOFGJ5LUFJC · pith_short_16: OEOFGJ5LUFJC75JP · pith_short_8: OEOFGJ5L

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/OEOFGJ5LUFJC75JPXFWLJUE5XM \
  | 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: 711c5327aba1522ff52fb96cb4d09dbb32240ac3db724f15a6779b6581588195

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2da2ce55397a28fdad04a4d93c943c27fd9db5b847d56b310a4ac2cb9ed372f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2014-09-14T06:46:46Z",
    "title_canon_sha256": "356c7c741bfb039efcd43e0bf4d3c61a2e413904e94da8bd9afd0cd22d5c8af8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.4021",
    "kind": "arxiv",
    "version": 1
  }
}