Pith Number

pith:IVC7BA7L

pith:2021:IVC7BA7LL7GQW7PTFBNSVUFHVT

not attested not anchored not stored refs pending

Nodal solutions of fourth-order Kirchhoff equations with critical growth in $\mathbb{R}^N$

Du\v{s}an D. Repov\v{s}, Hongling Pu, Shiqi Li, Sihua Liang

arxiv:2103.14114 v1 · 2021-03-25 · 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{IVC7BA7LL7GQW7PTFBNSVUFHVT}

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	2026-07-05T02:26:30.530801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4545f083eb5fcd0b7df3285b2ad0a7acf86c5d5d74b19b9ff1431d83d6654107

Aliases

arxiv: 2103.14114 · arxiv_version: 2103.14114v1 · doi: 10.48550/arxiv.2103.14114 · pith_short_12: IVC7BA7LL7GQ · pith_short_16: IVC7BA7LL7GQW7PT · pith_short_8: IVC7BA7L

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/IVC7BA7LL7GQW7PTFBNSVUFHVT \
  | 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: 4545f083eb5fcd0b7df3285b2ad0a7acf86c5d5d74b19b9ff1431d83d6654107

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71246f836c52fa222705f1c25a5e63bef07a54992ebf5ee0ea797f17ad8f18c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-03-25T20:13:08Z",
    "title_canon_sha256": "32c4a2e806a8f0fbcd199aca423570739f6ca6eda276ae8e2e63ca478cad170a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.14114",
    "kind": "arxiv",
    "version": 1
  }
}