Pith Number

pith:DL5BZJZ2

pith:2015:DL5BZJZ2MWNL6GVGOH4BCWDVK4

not attested not anchored not stored refs pending

On Elliptic Systems involving critical Hardy-Sobolev exponents (Part II)

Wenming Zou, Xuexiu Zhong

arxiv:1504.02939 v2 · 2015-04-12 · 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{DL5BZJZ2MWNL6GVGOH4BCWDVK4}

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	2026-05-18T01:37:13.401872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1afa1ca73a659abf1aa671f81158755727583397b32dedbcf2cfb218b5267240

Aliases

arxiv: 1504.02939 · arxiv_version: 1504.02939v2 · doi: 10.48550/arxiv.1504.02939 · pith_short_12: DL5BZJZ2MWNL · pith_short_16: DL5BZJZ2MWNL6GVG · pith_short_8: DL5BZJZ2

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/DL5BZJZ2MWNL6GVGOH4BCWDVK4 \
  | 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: 1afa1ca73a659abf1aa671f81158755727583397b32dedbcf2cfb218b5267240

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fed2d8892cbb1ebb625ec324a74cf5d611289850752aad12b59acb0a7bbb3e99",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-12T07:22:27Z",
    "title_canon_sha256": "48c8455f8a487bec7c25405150df1a0a877f15ffcc5c36a3708b7f8c5ded3903"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02939",
    "kind": "arxiv",
    "version": 2
  }
}