Pith Number

pith:SO2IFGTQ

pith:2019:SO2IFGTQD5R2ES63DAO4CUNZT2

not attested not anchored not stored refs pending

Minimization problem associated with an improved Hardy-Sobolev type inequality

Megumi Sano

arxiv:1908.03915 v3 · 2019-08-11 · 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{SO2IFGTQD5R2ES63DAO4CUNZT2}

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	2026-07-05T00:49:08.086468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93b4829a701f63a24bdb181dc151b99e9a7d301021836112b92313ccf37a0ae2

Aliases

arxiv: 1908.03915 · arxiv_version: 1908.03915v3 · doi: 10.48550/arxiv.1908.03915 · pith_short_12: SO2IFGTQD5R2 · pith_short_16: SO2IFGTQD5R2ES63 · pith_short_8: SO2IFGTQ

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/SO2IFGTQD5R2ES63DAO4CUNZT2 \
  | 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: 93b4829a701f63a24bdb181dc151b99e9a7d301021836112b92313ccf37a0ae2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb0e79e32ea6f7e9d26d98d41646eb3fef88daf4006cd238187fff87d9618558",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-11T14:36:38Z",
    "title_canon_sha256": "6e10f82601cb72756c70feaa9c04aed595b424c6687ca16ef30e1ec4c1efc6c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03915",
    "kind": "arxiv",
    "version": 3
  }
}