Pith Number

pith:X4CMX5XX

pith:2014:X4CMX5XXKYZJ7BQOFGOB5NF3Z3

not attested not anchored not stored refs pending

PT-symmetry in optics beyond the paraxial approximation

Boris A Malomed, Changming Huang, Fangwei Ye, Xianfeng Chen, Yaroslav V. Kartashov

arxiv:1408.2630 v1 · 2014-08-12 · 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{X4CMX5XXKYZJ7BQOFGOB5NF3Z3}

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	2026-05-18T01:37:28.697117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf04cbf6f756329f860e299c1eb4bbcefdf4962a6337e50528e397018a59e884

Aliases

arxiv: 1408.2630 · arxiv_version: 1408.2630v1 · doi: 10.48550/arxiv.1408.2630 · pith_short_12: X4CMX5XXKYZJ · pith_short_16: X4CMX5XXKYZJ7BQO · pith_short_8: X4CMX5XX

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/X4CMX5XXKYZJ7BQOFGOB5NF3Z3 \
  | 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: bf04cbf6f756329f860e299c1eb4bbcefdf4962a6337e50528e397018a59e884

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd912a075d9c1a46f86fdf2466c192f43104eed06bafe577bfc0f51fe0699d13",
    "cross_cats_sorted": [
      "nlin.PS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2014-08-12T06:39:03Z",
    "title_canon_sha256": "ecff00238dac47d081c7f22bbbcd81fbdfba1bdf82763390c0c64c956c1d02a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.2630",
    "kind": "arxiv",
    "version": 1
  }
}