Pith Number

pith:JVBU57OF

pith:2016:JVBU57OFOVZMYKHEG2W4TOSAJF

not attested not anchored not stored refs pending

$\mathcal{PT}$ symmetry in a fractional Schr\"odinger equation

Demetrios N. Christodoulides, Hua Zhong, Milivoj R. Beli\'c, Min Xiao, Weiping Zhong, Yanpeng Zhang, Yiqi Zhang, Yi Zhu

arxiv:1603.08345 v1 · 2016-03-28 · 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{JVBU57OFOVZMYKHEG2W4TOSAJF}

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	2026-05-18T01:14:52.331176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d434efdc57572cc28e436adc9ba40497ed31f4f815c964923a4beb0e20ea79c

Aliases

arxiv: 1603.08345 · arxiv_version: 1603.08345v1 · doi: 10.48550/arxiv.1603.08345 · pith_short_12: JVBU57OFOVZM · pith_short_16: JVBU57OFOVZMYKHE · pith_short_8: JVBU57OF

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/JVBU57OFOVZMYKHEG2W4TOSAJF \
  | 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: 4d434efdc57572cc28e436adc9ba40497ed31f4f815c964923a4beb0e20ea79c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51012736745030b1ae31cb2ade9af14686056a5dfad1e02d31ac80bfc02ac72c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2016-03-28T09:02:12Z",
    "title_canon_sha256": "52a7aad18ed9841b25acf17a95e3d85d2b5dfe614c9e889bebb3c729c2dc67c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08345",
    "kind": "arxiv",
    "version": 1
  }
}