Pith Number

pith:XRRDHIPZ

pith:2019:XRRDHIPZRCN3EYU7ND74JRQDRQ

not attested not anchored not stored refs pending

Existence and multiplicity of solutions for fractional Schr\"odinger-Kirchhoff equations with Trudinger-Moser nonlinearity

Binlin Zhang, Du\v{s}an Repov\v{s}, Mingqi Xiang

arxiv:1906.07943 v1 · 2019-06-19 · math.AP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XRRDHIPZRCN3EYU7ND74JRQDRQ}

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	2026-05-17T23:42:55.091552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc6233a1f9889bb2629f68ffc4c6038c09534e0874f8d142fda8be50f7692c75

Aliases

arxiv: 1906.07943 · arxiv_version: 1906.07943v1 · doi: 10.48550/arxiv.1906.07943 · pith_short_12: XRRDHIPZRCN3 · pith_short_16: XRRDHIPZRCN3EYU7 · pith_short_8: XRRDHIPZ

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/XRRDHIPZRCN3EYU7ND74JRQDRQ \
  | 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: bc6233a1f9889bb2629f68ffc4c6038c09534e0874f8d142fda8be50f7692c75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40e2ab65e8787add5a86c47dd8d9635972f9d20063c73cce8f667f989d2fb2ca",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-06-19T07:02:16Z",
    "title_canon_sha256": "86eaf490984d74f687197047424ba2dbc4724e50ac8ff4f822979c4e7d5ec9f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.07943",
    "kind": "arxiv",
    "version": 1
  }
}