Pith Number

pith:XKUP5UBK

pith:2015:XKUP5UBKSHEFJMQNUH5ZT6GM5A

not attested not anchored not stored refs pending

Existence and local uniqueness of bubbling solutions for poly-harmonic equations with critical growth

Shuangjie Peng, Shusen Yan, Yuxia Guo

arxiv:1503.06412 v1 · 2015-03-22 · 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{XKUP5UBKSHEFJMQNUH5ZT6GM5A}

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	2026-05-18T02:20:38.510255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

baa8fed02a91c854b20da1fb99f8cce8386889b423ac31a242538a2f6637b19b

Aliases

arxiv: 1503.06412 · arxiv_version: 1503.06412v1 · doi: 10.48550/arxiv.1503.06412 · pith_short_12: XKUP5UBKSHEF · pith_short_16: XKUP5UBKSHEFJMQN · pith_short_8: XKUP5UBK

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/XKUP5UBKSHEFJMQNUH5ZT6GM5A \
  | 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: baa8fed02a91c854b20da1fb99f8cce8386889b423ac31a242538a2f6637b19b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56795f9fe2db4949d5e9808afbecfa6b39f2fad1d22c4278ea61fd2d6e8ff8b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-22T11:38:15Z",
    "title_canon_sha256": "a2429135d546e9404d3b2a565bfbfd72aff8b53ab8f01238bc63222ade21fd6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06412",
    "kind": "arxiv",
    "version": 1
  }
}