Pith Number

pith:4R4AT34A

pith:2025:4R4AT34A5QFZ5354RDKDCUXJCE

not attested not anchored not stored refs pending

Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields

Avas Banerjee, Prasun Roychowdhury, Riju Basak

arxiv:2504.19864 v2 · 2025-04-28 · math.AP · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4R4AT34A5QFZ5354RDKDCUXJCE}

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	2026-07-05T11:03:59.494648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e47809ef80ec0b9eefbc88d43152e9112703b2244f597347a614240cddacf5a3

Aliases

arxiv: 2504.19864 · arxiv_version: 2504.19864v2 · doi: 10.48550/arxiv.2504.19864 · pith_short_12: 4R4AT34A5QFZ · pith_short_16: 4R4AT34A5QFZ5354 · pith_short_8: 4R4AT34A

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/4R4AT34A5QFZ5354RDKDCUXJCE \
  | 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: e47809ef80ec0b9eefbc88d43152e9112703b2244f597347a614240cddacf5a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c739ecf9c0b7502169b7765fe7ed6879a63931de53b36b9e6d4ebbb754384e30",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-04-28T14:56:12Z",
    "title_canon_sha256": "0d716dd38893015c27ea09fd3f6fdc933e7b7019c90c52a0393780449de99826"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.19864",
    "kind": "arxiv",
    "version": 2
  }
}