Pith Number

pith:QK6N4Z2G

pith:2015:QK6N4Z2GUMKNGGMFNRECEQSJ25

not attested not anchored not stored refs pending

Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus

Lei Gong, Pablo Vaveliuk, Rong-De Lu, Yue Chen, Yu-Xuan Ren, Zhao-Xiang Fang

arxiv:1511.00391 v1 · 2015-11-02 · 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{QK6N4Z2GUMKNGGMFNRECEQSJ25}

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	2026-05-18T01:22:33.508207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82bcde6746a314d319856c48224249d747d1dae68f2a9f172a1b7f01732c4d54

Aliases

arxiv: 1511.00391 · arxiv_version: 1511.00391v1 · doi: 10.48550/arxiv.1511.00391 · pith_short_12: QK6N4Z2GUMKN · pith_short_16: QK6N4Z2GUMKNGGMF · pith_short_8: QK6N4Z2G

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/QK6N4Z2GUMKNGGMFNRECEQSJ25 \
  | 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: 82bcde6746a314d319856c48224249d747d1dae68f2a9f172a1b7f01732c4d54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8886f8bd86bc5c3a1c0e91dcda8f8163af9b9d7d369ee084287729435c43fdb4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2015-11-02T06:00:01Z",
    "title_canon_sha256": "1182f161af8512e7c848ed2f0ddda04646cf146c536490b10bce28cf0e14f865"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00391",
    "kind": "arxiv",
    "version": 1
  }
}