Pith Number

pith:4XSLMY23

pith:2016:4XSLMY23S6OOSXFBYMFBLF77QA

not attested not anchored not stored refs pending

Caffarelli-Kohn-Nirenberg type inequalities of fractional order with applications

Boumediene Abdellaoui, Rachid Bentifour

arxiv:1611.04724 v2 · 2016-11-15 · 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{4XSLMY23S6OOSXFBYMFBLF77QA}

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	2026-05-17T23:58:50.442331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5e4b6635b979ce95ca1c30a1597ff80355b9ead93580e352a9e6b785964c13b

Aliases

arxiv: 1611.04724 · arxiv_version: 1611.04724v2 · doi: 10.48550/arxiv.1611.04724 · pith_short_12: 4XSLMY23S6OO · pith_short_16: 4XSLMY23S6OOSXFB · pith_short_8: 4XSLMY23

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/4XSLMY23S6OOSXFBYMFBLF77QA \
  | 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: e5e4b6635b979ce95ca1c30a1597ff80355b9ead93580e352a9e6b785964c13b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb801ab3a78aee5f0347443da1b138edcc0e1abf808b665c80d950a645c87e35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-11-15T07:36:36Z",
    "title_canon_sha256": "3ded740fbc4cfba6f19d74e36e16354cff8b7fe50cc3fb9d5d9add8c5b90d495"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04724",
    "kind": "arxiv",
    "version": 2
  }
}