Pith Number

pith:4W4AZ3DD

pith:2026:4W4AZ3DDIMFY5EW5RQ3Y2LDSYV

not attested not anchored not stored refs pending

Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis

Avas Banerjee, Debdip Ganguly, Vivek Sahu

arxiv:2605.15748 v1 · 2026-05-15 · 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{4W4AZ3DDIMFY5EW5RQ3Y2LDSYV}

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	2026-05-20T00:01:16.081711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5b80cec63430b8e92dd8c378d2c72c542950a70649a632de169597de991d478

Aliases

arxiv: 2605.15748 · arxiv_version: 2605.15748v1 · doi: 10.48550/arxiv.2605.15748 · pith_short_12: 4W4AZ3DDIMFY · pith_short_16: 4W4AZ3DDIMFY5EW5 · pith_short_8: 4W4AZ3DD

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/4W4AZ3DDIMFY5EW5RQ3Y2LDSYV \
  | 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: e5b80cec63430b8e92dd8c378d2c72c542950a70649a632de169597de991d478

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be305ff96f90477f2b61958ab280eb948dd1412b9f4ec46410d5da596accea94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-15T09:06:31Z",
    "title_canon_sha256": "93ab1a548f6486079227ca48b873723a1858bf4556acc13dbed4efb3536fdf78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15748",
    "kind": "arxiv",
    "version": 1
  }
}