Pith Number

pith:2DGZYQRE

pith:2015:2DGZYQREUSB2NGX5DK3CE5CCC3

not attested not anchored not stored refs pending

On Elliptic Systems involving critical Hardy-Sobolev exponents

Wenming Zou, Xuexiu Zhong

arxiv:1504.01005 v2 · 2015-04-04 · 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{2DGZYQREUSB2NGX5DK3CE5CCC3}

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	2026-05-18T01:37:13.459257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0cd9c4224a483a69afd1ab622744216df37785f15d3311b41decd17b2fcb225

Aliases

arxiv: 1504.01005 · arxiv_version: 1504.01005v2 · doi: 10.48550/arxiv.1504.01005 · pith_short_12: 2DGZYQREUSB2 · pith_short_16: 2DGZYQREUSB2NGX5 · pith_short_8: 2DGZYQRE

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/2DGZYQREUSB2NGX5DK3CE5CCC3 \
  | 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: d0cd9c4224a483a69afd1ab622744216df37785f15d3311b41decd17b2fcb225

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "259f2870002fd1699845301e326f6ee963b886b51eaaf5f6e54a688177acd9ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-04T10:54:39Z",
    "title_canon_sha256": "369c38c82a5093d82ebbf6d069a0de59d937a36377d2cf62b037c9c978764f64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01005",
    "kind": "arxiv",
    "version": 2
  }
}