Pith Number

pith:76KYFOL4

pith:2013:76KYFOL4YBKIVGCRVKR5NBKIZG

not attested not anchored not stored refs pending

Characterizations for fractional Hardy inequality

Antti V. V\"ah\"akangas, Bart{\l}omiej Dyda

arxiv:1308.1886 v2 · 2013-08-08 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{76KYFOL4YBKIVGCRVKR5NBKIZG}

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	2026-05-18T03:07:44.221156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff9582b97cc0548a9851aaa3d68548c98b51cc88a5a284f211ae7eeebb0d011f

Aliases

arxiv: 1308.1886 · arxiv_version: 1308.1886v2 · doi: 10.48550/arxiv.1308.1886 · pith_short_12: 76KYFOL4YBKI · pith_short_16: 76KYFOL4YBKIVGCR · pith_short_8: 76KYFOL4

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/76KYFOL4YBKIVGCRVKR5NBKIZG \
  | 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: ff9582b97cc0548a9851aaa3d68548c98b51cc88a5a284f211ae7eeebb0d011f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab79e9292966c1e8e27c9c756776c7b8e6ed5a8a4d6f0c0073482ad662c9511f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-08-08T15:58:49Z",
    "title_canon_sha256": "54f075aa831ef02fd4f871cd6d2e408f92edf7fc7e64f8eb172f122fa1bba081"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.1886",
    "kind": "arxiv",
    "version": 2
  }
}