Pith Number

pith:7CG3QHW2

pith:2015:7CG3QHW2V2KQSLNPUAAZOJMNN5

not attested not anchored not stored refs pending

Fractional Hardy-Sobolev elliptic problems

Jianfu Yang, Xiaohui Yu

arxiv:1503.00216 v1 · 2015-03-01 · 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{7CG3QHW2V2KQSLNPUAAZOJMNN5}

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	2026-05-18T02:25:54.883465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f88db81edaae95092dafa00197258d6f46eb92ea63936c3db0d3dec0ad061129

Aliases

arxiv: 1503.00216 · arxiv_version: 1503.00216v1 · doi: 10.48550/arxiv.1503.00216 · pith_short_12: 7CG3QHW2V2KQ · pith_short_16: 7CG3QHW2V2KQSLNP · pith_short_8: 7CG3QHW2

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/7CG3QHW2V2KQSLNPUAAZOJMNN5 \
  | 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: f88db81edaae95092dafa00197258d6f46eb92ea63936c3db0d3dec0ad061129

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce124854237d678ca204866ec401718b5012a79effe2975ea625bc39896aced7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-01T05:07:07Z",
    "title_canon_sha256": "b20f991232831f4b5b7e7ca3109839a6e46c6d52d69133feeb9e352b923c8ba2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.00216",
    "kind": "arxiv",
    "version": 1
  }
}