Pith Number

pith:42RNOKN5

pith:2025:42RNOKN5PARKA6GN3UPJUJ7M2E

not attested not anchored not stored refs pending

Sharp remainder of the $L^{p}$-Poincar\'e inequality for Baouendi-Grushin vector fields

Amir Zhangirbayev, Kuralay Apseit, Nurgissa Yessirkegenov

arxiv:2507.01681 v2 · 2025-07-02 · 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{42RNOKN5PARKA6GN3UPJUJ7M2E}

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.

Cited by

1 paper in Pith

Fundamental Gaps for the Dirichlet $p$-Laplacian with Convex Potentials: Sharp One-Dimensional Bounds and a Higher-Dimensional Dichotomy

Receipt and verification

First computed	2026-07-05T11:35:57.529237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6a2d729bd7822a078cddd1e9a27ecd11046539d1612aabdb607d9609dc9d3df

Aliases

arxiv: 2507.01681 · arxiv_version: 2507.01681v2 · doi: 10.48550/arxiv.2507.01681 · pith_short_12: 42RNOKN5PARK · pith_short_16: 42RNOKN5PARKA6GN · pith_short_8: 42RNOKN5

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/42RNOKN5PARKA6GN3UPJUJ7M2E \
  | 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: e6a2d729bd7822a078cddd1e9a27ecd11046539d1612aabdb607d9609dc9d3df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ef3ffda880f9d2b8c4e59640245d0864c22513ef6dd40e4c784d750a9dfba12",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-07-02T13:05:21Z",
    "title_canon_sha256": "17e53b718a926f70122f9abc4254331f05c2b9d79b888b6b9ac406e825ce24cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.01681",
    "kind": "arxiv",
    "version": 2
  }
}