Pith Number

pith:CY2Z4FBB

pith:2017:CY2Z4FBBAOYBKYWKCT7QRPHUSE

not attested not anchored not stored refs pending

On the Neumann Problem of Hardy-Sobolev critical equations with the multiple singularities

Chun-Hsiung Hsia, Gyeongha Hwang, Masato Hashizume

arxiv:1709.07685 v1 · 2017-09-22 · 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{CY2Z4FBBAOYBKYWKCT7QRPHUSE}

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	2026-05-18T00:34:32.566901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16359e142103b01562ca14ff08bcf4911b4ff7cfd115ab83e2fc02e4ad28009a

Aliases

arxiv: 1709.07685 · arxiv_version: 1709.07685v1 · doi: 10.48550/arxiv.1709.07685 · pith_short_12: CY2Z4FBBAOYB · pith_short_16: CY2Z4FBBAOYBKYWK · pith_short_8: CY2Z4FBB

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/CY2Z4FBBAOYBKYWKCT7QRPHUSE \
  | 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: 16359e142103b01562ca14ff08bcf4911b4ff7cfd115ab83e2fc02e4ad28009a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fd47f714bfc5420b7e1d8ac05a74f254f5d551e718ec059cbf6fec2a6076e75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-09-22T10:45:16Z",
    "title_canon_sha256": "c1125713bc57da76cc8f6c59a22b052c194c688b0c22f511eecc1dd56b22c6f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.07685",
    "kind": "arxiv",
    "version": 1
  }
}