Pith Number

pith:SHARBG6W

pith:2015:SHARBG6WCMCHAYKLW6VFQDOE2B

not attested not anchored not stored refs pending

Fractional nonlinear Schr\"odinger equations with singular potential in $\mathbf R^n$

Guoyuan Chen, Youquan Zheng

arxiv:1511.09124 v2 · 2015-11-30 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SHARBG6WCMCHAYKLW6VFQDOE2B}

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	2026-05-18T01:25:25.921986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91c1109bd6130470614bb7aa580dc4d0621ea080d01bfb841fe5fd653e95ac02

Aliases

arxiv: 1511.09124 · arxiv_version: 1511.09124v2 · doi: 10.48550/arxiv.1511.09124 · pith_short_12: SHARBG6WCMCH · pith_short_16: SHARBG6WCMCHAYKL · pith_short_8: SHARBG6W

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/SHARBG6WCMCHAYKLW6VFQDOE2B \
  | 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: 91c1109bd6130470614bb7aa580dc4d0621ea080d01bfb841fe5fd653e95ac02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5c0e59ca104ba26817687aa0e27f55e44e48a4de21b02d55b394717b1e224a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-30T01:05:07Z",
    "title_canon_sha256": "dbf288c2fd846c1a2232f4e1da9dd87634c78518ae53ac76f41a5b2cb2869c6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.09124",
    "kind": "arxiv",
    "version": 2
  }
}