Pith Number

pith:A2YLLH3V

pith:2015:A2YLLH3VSVR42SAHCPJBME4PSO

not attested not anchored not stored refs pending

On Kirchhoff type equations with critical Sobolev exponent and Naimen's open problems

Yisheng Huang, Yuanze Wu, Zeng Liu

arxiv:1507.05308 v1 · 2015-07-19 · 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{A2YLLH3VSVR42SAHCPJBME4PSO}

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	2026-05-18T01:36:37.225119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06b0b59f759563cd480713d216138f93bfbbf80538d4aab496237869d61cc357

Aliases

arxiv: 1507.05308 · arxiv_version: 1507.05308v1 · doi: 10.48550/arxiv.1507.05308 · pith_short_12: A2YLLH3VSVR4 · pith_short_16: A2YLLH3VSVR42SAH · pith_short_8: A2YLLH3V

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/A2YLLH3VSVR42SAHCPJBME4PSO \
  | 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: 06b0b59f759563cd480713d216138f93bfbbf80538d4aab496237869d61cc357

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8225a4eec0a31c7cd8d13705d6328cd4370c0dbd3d83034f947a0c73c0229868",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-19T17:01:27Z",
    "title_canon_sha256": "63b1515d5f4789c062ff04557ffd3b5ad262a3eceed496f7aad503e8bcf2e163"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05308",
    "kind": "arxiv",
    "version": 1
  }
}