Pith Number

pith:V72IP2D6

pith:2011:V72IP2D6MHZTC6NWGYOQJDJS4M

not attested not anchored not stored refs pending

Interaction of highly focused vector beams with a metal knife-edge

2), 2) ((1) Max Planck Institute for the Science of Light, (2) Institute of Optics, C. Huber (1, Erlangen, Germany, Germany), G. Leuchs (1, Information, P. Banzer (1, Photonics, P. Marchenko (1, S. Orlov (1, S. Quabis (2), University Erlangen-Nuremberg, U. Peschel (2)

arxiv:1102.2140 v3 · 2011-02-10 · 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{V72IP2D6MHZTC6NWGYOQJDJS4M}

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	2026-05-18T04:25:12.751356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aff487e87e61f33179b6361d048d32e336f3fdecf6bb6fee0cffbb64e7e2e3b1

Aliases

arxiv: 1102.2140 · arxiv_version: 1102.2140v3 · doi: 10.48550/arxiv.1102.2140 · pith_short_12: V72IP2D6MHZT · pith_short_16: V72IP2D6MHZTC6NW · pith_short_8: V72IP2D6

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/V72IP2D6MHZTC6NWGYOQJDJS4M \
  | 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: aff487e87e61f33179b6361d048d32e336f3fdecf6bb6fee0cffbb64e7e2e3b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3afe20aacc8de5733a805de24e3d51021d7e40a25e503d063ef4f687ac7f8ef9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2011-02-10T15:09:06Z",
    "title_canon_sha256": "d2cb8d5e8fb926c98135c893be7e623b81da94af7b5027664e09994111540508"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2140",
    "kind": "arxiv",
    "version": 3
  }
}