Pith Number

pith:BUZ7AQAV

pith:2016:BUZ7AQAVORJGV7RKOEWPP2R55Z

not attested not anchored not stored refs pending

Multiple positive solutions for a class of Kirchhoff type problems involving general critical growth

Liejun Shen, Xiaohua Yao

arxiv:1607.01923 v1 · 2016-07-07 · 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{BUZ7AQAVORJGV7RKOEWPP2R55Z}

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	2026-05-18T01:11:22.985498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d33f0401574526afe2a712cf7ea3dee76a4b667abb54d8b22f646f08b26c4e7

Aliases

arxiv: 1607.01923 · arxiv_version: 1607.01923v1 · doi: 10.48550/arxiv.1607.01923 · pith_short_12: BUZ7AQAVORJG · pith_short_16: BUZ7AQAVORJGV7RK · pith_short_8: BUZ7AQAV

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/BUZ7AQAVORJGV7RKOEWPP2R55Z \
  | 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: 0d33f0401574526afe2a712cf7ea3dee76a4b667abb54d8b22f646f08b26c4e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11b05abb83af572ac3fca439ff0aa9cd4a6cf7a86c074f0e93e5db599b98d01f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-07-07T08:54:39Z",
    "title_canon_sha256": "45ee144c0222886ffa4a1be174c67546de63d50ab78d9288258bdde48414bc5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.01923",
    "kind": "arxiv",
    "version": 1
  }
}