Pith Number

pith:NBKZJEBX

pith:2017:NBKZJEBXFFHE4IWCDQYZSABCXB

not attested not anchored not stored refs pending

Lorenz curve of a light beam: evaluating beam quality from a mayorization perspective

Isabel Gonzalo, M. Ahmir Malik, Miguel A. Porras

arxiv:1704.04740 v2 · 2017-04-16 · 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{NBKZJEBXFFHE4IWCDQYZSABCXB}

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	2026-05-18T00:39:17.858607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6855949037294e4e22c21c31990022b8673444ce271b09b1f968d414bb227922

Aliases

arxiv: 1704.04740 · arxiv_version: 1704.04740v2 · doi: 10.48550/arxiv.1704.04740 · pith_short_12: NBKZJEBXFFHE · pith_short_16: NBKZJEBXFFHE4IWC · pith_short_8: NBKZJEBX

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/NBKZJEBXFFHE4IWCDQYZSABCXB \
  | 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: 6855949037294e4e22c21c31990022b8673444ce271b09b1f968d414bb227922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b9eff41fd8c7ecd74a2d31f2194779536486ff1204f9646804b1c1ed83874d6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2017-04-16T09:39:58Z",
    "title_canon_sha256": "ea00a495357df6d0a02f6c98c5c8206cd051d10b13966f1a7300398e5332ccb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.04740",
    "kind": "arxiv",
    "version": 2
  }
}