Pith Number

pith:6V4BFQ36

pith:2011:6V4BFQ36ACB7ELUY6FEGL7I5WA

not attested not anchored not stored refs pending

Vortex twins and anti-twins supported by multi-ring gain landscapes

Lluis Torner, Olga V. Borovkova, Valery E. Lobanov, Victor A. Vysloukh, Yaroslav V. Kartashov

arxiv:1109.0139 v1 · 2011-09-01 · physics.optics · nlin.PS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6V4BFQ36ACB7ELUY6FEGL7I5WA}

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	2026-05-18T02:00:43.441935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f57812c37e0083f22e98f14865fd1db003879abb169b30fc0f79ee084ac3ded5

Aliases

arxiv: 1109.0139 · arxiv_version: 1109.0139v1 · doi: 10.48550/arxiv.1109.0139 · pith_short_12: 6V4BFQ36ACB7 · pith_short_16: 6V4BFQ36ACB7ELUY · pith_short_8: 6V4BFQ36

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/6V4BFQ36ACB7ELUY6FEGL7I5WA \
  | 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: f57812c37e0083f22e98f14865fd1db003879abb169b30fc0f79ee084ac3ded5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cacc9f212bb27a302d0cb4ff6432168d3ad257c82d32132e9974a13f11520db",
    "cross_cats_sorted": [
      "nlin.PS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2011-09-01T10:03:15Z",
    "title_canon_sha256": "765ccb495a80498aa56016c6d8ea5b3b8404ba73ea85b011785321e91a831230"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0139",
    "kind": "arxiv",
    "version": 1
  }
}