Pith Number

pith:CUGSFKY2

pith:2016:CUGSFKY2ECKOTNDEGJ2VSTM2NJ

not attested not anchored not stored refs pending

Multiple positive solutions for Kirchhoff type problems involving concave and critical nonlinearities in ${R}^3$

Jun Wang, Junxiang Xu, Xiaofei Cao

arxiv:1605.06404 v1 · 2016-05-20 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CUGSFKY2ECKOTNDEGJ2VSTM2NJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:14:18.975932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

150d22ab1a2094e9b4643275594d9a6a54863366c20fb884451e17863e82cc5e

Aliases

arxiv: 1605.06404 · arxiv_version: 1605.06404v1 · doi: 10.48550/arxiv.1605.06404 · pith_short_12: CUGSFKY2ECKO · pith_short_16: CUGSFKY2ECKOTNDE · pith_short_8: CUGSFKY2

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/CUGSFKY2ECKOTNDEGJ2VSTM2NJ \
  | 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: 150d22ab1a2094e9b4643275594d9a6a54863366c20fb884451e17863e82cc5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d2dd0286d48221060d569fa73d8ae2a1aa8dc58541e3c52dae554c9f09a5648",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-05-20T15:26:53Z",
    "title_canon_sha256": "2578fac6f8a9678a8d2f4c183fad553791e3d1085f47b96a75c2349a37fefcd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.06404",
    "kind": "arxiv",
    "version": 1
  }
}