Pith Number

pith:IM2HWFR6

pith:2013:IM2HWFR6FI5DWKAHLAUJ5HKKG5

not attested not anchored not stored refs pending

Fractional Hardy inequalities and visibility of the boundary

Antti V. V\"ah\"akangas, Heli Tuominen, Juha Lehrb\"ack, Lizaveta Ihnatsyeva

arxiv:1305.4616 v2 · 2013-05-20 · 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{IM2HWFR6FI5DWKAHLAUJ5HKKG5}

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	2026-05-18T01:23:59.115765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43347b163e2a3a3b280758289e9d4a374874c67283e8039b809929da7673dddf

Aliases

arxiv: 1305.4616 · arxiv_version: 1305.4616v2 · doi: 10.48550/arxiv.1305.4616 · pith_short_12: IM2HWFR6FI5D · pith_short_16: IM2HWFR6FI5DWKAH · pith_short_8: IM2HWFR6

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/IM2HWFR6FI5DWKAHLAUJ5HKKG5 \
  | 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: 43347b163e2a3a3b280758289e9d4a374874c67283e8039b809929da7673dddf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cde8d13ee8d8572ce42f696e5c9bb8056c729e1601c7c6958dae521bb356741",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-05-20T19:33:24Z",
    "title_canon_sha256": "c198da04cc8cea937bb8b70ef2d2fe6f7564e0b222d03fe7e227c17f8d22c077"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4616",
    "kind": "arxiv",
    "version": 2
  }
}