Pith Number

pith:DJKTIHBJ

pith:2012:DJKTIHBJCO3X2KLWL7CBMOMKOZ

not attested not anchored not stored refs pending

Fractional Hardy-type inequalities in domains with plump complement

Antti V. V\"ah\"akangas, David E. Edmunds, Ritva Hurri-Syrj\"anen

arxiv:1202.3928 v1 · 2012-02-17 · 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{DJKTIHBJCO3X2KLWL7CBMOMKOZ}

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	2026-05-18T04:02:02.456378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a55341c2913b77d29765fc416398a767386048928c2fd37cd845d02fafc5d1f

Aliases

arxiv: 1202.3928 · arxiv_version: 1202.3928v1 · doi: 10.48550/arxiv.1202.3928 · pith_short_12: DJKTIHBJCO3X · pith_short_16: DJKTIHBJCO3X2KLW · pith_short_8: DJKTIHBJ

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/DJKTIHBJCO3X2KLWL7CBMOMKOZ \
  | 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: 1a55341c2913b77d29765fc416398a767386048928c2fd37cd845d02fafc5d1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bfd51de7e4880a45ce758516efd812b273b0eb82751c84ffad3f71b4a7d6243",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-02-17T15:04:52Z",
    "title_canon_sha256": "0b22e7a27282df9c6241dcffbf892a4b520a183ffc98579158e1141501d82ef4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3928",
    "kind": "arxiv",
    "version": 1
  }
}