Pith Number

pith:GWX7HVXX

pith:2015:GWX7HVXXWPRAZI5U7RSO75OJRB

not attested not anchored not stored refs pending

Monotonicity, continuity and differentiability results for the $L^p$ Hardy constant

Gerassimos Barbatis, Pier Domenico Lamberti

arxiv:1509.09107 v2 · 2015-09-30 · 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{GWX7HVXXWPRAZI5U7RSO75OJRB}

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	2026-05-18T01:29:20.382110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35aff3d6f7b3e20ca3b4fc64eff5c988759c9527d28e46f7df7aedab457614bf

Aliases

arxiv: 1509.09107 · arxiv_version: 1509.09107v2 · doi: 10.48550/arxiv.1509.09107 · pith_short_12: GWX7HVXXWPRA · pith_short_16: GWX7HVXXWPRAZI5U · pith_short_8: GWX7HVXX

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/GWX7HVXXWPRAZI5U7RSO75OJRB \
  | 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: 35aff3d6f7b3e20ca3b4fc64eff5c988759c9527d28e46f7df7aedab457614bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e321568b51469d9b5ff53ca93cb2d367c1c84b655ee8c4336e7157b66edf99d5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-30T10:07:07Z",
    "title_canon_sha256": "2fa443192ef28280e8cff9e6538f1f67feb487e1e6689a26082b8cb064d872ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09107",
    "kind": "arxiv",
    "version": 2
  }
}