Pith Number

pith:XK66BY7S

pith:2015:XK66BY7S72OPVUZJEPQFIDR6GN

not attested not anchored not stored refs pending

Transition between self-focusing and self-defocusing in nonlocally nonlinear media

Demetrios N. Christodoulides, Guo Liang, Jing Wang, Qi Guo, Senyue Lou, Wei Hu, Weiyi Hong, Yahong Hu, Yingbing Li, Zhuo Wang

arxiv:1510.05759 v1 · 2015-10-20 · 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{XK66BY7S72OPVUZJEPQFIDR6GN}

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	2026-05-17T23:43:38.618309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

babde0e3f2fe9cfad32923e0540e3e335f3ad0994effd4fd2b30e2f5c27756f9

Aliases

arxiv: 1510.05759 · arxiv_version: 1510.05759v1 · doi: 10.48550/arxiv.1510.05759 · pith_short_12: XK66BY7S72OP · pith_short_16: XK66BY7S72OPVUZJ · pith_short_8: XK66BY7S

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/XK66BY7S72OPVUZJEPQFIDR6GN \
  | 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: babde0e3f2fe9cfad32923e0540e3e335f3ad0994effd4fd2b30e2f5c27756f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac0ebfad557f6b22cd55bbdb315618d011cf53af10a7592ed753728f2a9aa2f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2015-10-20T05:46:55Z",
    "title_canon_sha256": "e30ee08e8b26b414d5520d6e5f2445a502d13d8a7d6b95ecb26805f1896844e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05759",
    "kind": "arxiv",
    "version": 1
  }
}