Pith Number

pith:LPRKRLX2

pith:2021:LPRKRLX2FY6CWT7KO2IUQS34Z2

not attested not anchored not stored refs pending

Optimal Hardy inequalities associated with multipolar Schr\"odinger operators

Can Ye, Li Tang, Shoufeng Shen, Yongyang Jin

arxiv:2107.05785 v1 · 2021-07-13 · math.AP · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPRKRLX2FY6CWT7KO2IUQS34Z2}

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	2026-07-05T02:57:28.265825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5be2a8aefa2e3c2b4fea7691484b7cceb683ff6a287710e23bd6bfb33ea9554c

Aliases

arxiv: 2107.05785 · arxiv_version: 2107.05785v1 · doi: 10.48550/arxiv.2107.05785 · pith_short_12: LPRKRLX2FY6C · pith_short_16: LPRKRLX2FY6CWT7K · pith_short_8: LPRKRLX2

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/LPRKRLX2FY6CWT7KO2IUQS34Z2 \
  | 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: 5be2a8aefa2e3c2b4fea7691484b7cceb683ff6a287710e23bd6bfb33ea9554c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bd8401f7bed9a3c7b6d29dda7b0be51e11d26076825ad5aa716849a69e4b849",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-07-13T00:00:05Z",
    "title_canon_sha256": "448ce162f9a1e50be4690037639c064a981d9e31636cbec5e06b9e21d671d297"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.05785",
    "kind": "arxiv",
    "version": 1
  }
}