Pith Number

pith:KQH43OZX

pith:2018:KQH43OZXHT4U3NKISBRAKDNQHL

not attested not anchored not stored refs pending

A perturbation approach to studying sign-changing solutions of Kirchhoff equations with a general nonlinearity

Jianjun Zhang, Yijun Lou, Zhisu Liu

arxiv:1812.09240 v2 · 2018-12-19 · 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{KQH43OZXHT4U3NKISBRAKDNQHL}

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	2026-05-17T23:47:02.188535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

540fcdbb373cf94db5489062050db03ac44c840691cecf9a46c54405ad72f5c0

Aliases

arxiv: 1812.09240 · arxiv_version: 1812.09240v2 · doi: 10.48550/arxiv.1812.09240 · pith_short_12: KQH43OZXHT4U · pith_short_16: KQH43OZXHT4U3NKI · pith_short_8: KQH43OZX

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/KQH43OZXHT4U3NKISBRAKDNQHL \
  | 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: 540fcdbb373cf94db5489062050db03ac44c840691cecf9a46c54405ad72f5c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1603f48eb4a7b025f3ea2904e0101996efca4008389a8eda8c7d316c5c214a89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-12-19T14:28:52Z",
    "title_canon_sha256": "7f1c0fc6ec7a4f0be46715dca2edace14d7ef15ef19abc0e90530927a5302963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09240",
    "kind": "arxiv",
    "version": 2
  }
}