Pith Number

pith:MG4IPHSN

pith:2015:MG4IPHSNHIQHRYUSQLIU647SOL

not attested not anchored not stored refs pending

Spontaneous generation of singularities in paraxial optical fields

Andrea Aiello

arxiv:1512.01444 v4 · 2015-12-04 · 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{MG4IPHSNHIQHRYUSQLIU647SOL}

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	2026-05-18T01:15:43.732147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61b8879e4d3a2078e29282d14f73f272cbf945f29edfc3ee6dcffa463bec0087

Aliases

arxiv: 1512.01444 · arxiv_version: 1512.01444v4 · doi: 10.48550/arxiv.1512.01444 · pith_short_12: MG4IPHSNHIQH · pith_short_16: MG4IPHSNHIQHRYUS · pith_short_8: MG4IPHSN

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/MG4IPHSNHIQHRYUSQLIU647SOL \
  | 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: 61b8879e4d3a2078e29282d14f73f272cbf945f29edfc3ee6dcffa463bec0087

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3919d31b0bfc7a26252d1eeadc6313af013c1c8fe9c19ab9460445d42e970a3f",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2015-12-04T15:01:20Z",
    "title_canon_sha256": "dd0dfa764a21f26f1f173d01230ca4727bd9de3b9363245b46b1a388c6bbeaac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01444",
    "kind": "arxiv",
    "version": 4
  }
}