Pith Number

pith:OO7MZXLA

pith:2015:OO7MZXLACVFMAEFTTZT7NRQG2S

not attested not anchored not stored refs pending

The use of the stationary phase method as a mathematical tool to determine the path of optical beams

Silv\^ania A. Carvalho, Stefano De Leo

arxiv:1502.06765 v1 · 2015-02-24 · physics.optics · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OO7MZXLACVFMAEFTTZT7NRQG2S}

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	2026-05-18T01:40:54.773258Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73beccdd60154ac010b39e67f6c606d49a2465cdd467f1675a223ebd2fc52156

Aliases

arxiv: 1502.06765 · arxiv_version: 1502.06765v1 · doi: 10.48550/arxiv.1502.06765 · pith_short_12: OO7MZXLACVFM · pith_short_16: OO7MZXLACVFMAEFT · pith_short_8: OO7MZXLA

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/OO7MZXLACVFMAEFTTZT7NRQG2S \
  | 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: 73beccdd60154ac010b39e67f6c606d49a2465cdd467f1675a223ebd2fc52156

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c2f6154f40ae2cb164d1d97390e20f46265ffd06e6525a36a5b9062b7095b96",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2015-02-24T11:21:45Z",
    "title_canon_sha256": "820a5fa6527335d1fc4496b2527d43a18cb9cdf203bc0fb877ca1fcc682ba38d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.06765",
    "kind": "arxiv",
    "version": 1
  }
}