Pith Number

pith:4OGHNG7T

pith:2017:4OGHNG7T5Y46N5TM4RIBGHYMCZ

not attested not anchored not stored refs pending

Hardy's inequality in a limiting case on general bounded domains

Futoshi Takahashi, Jaeyoung Byeon

arxiv:1707.04018 v2 · 2017-07-13 · 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{4OGHNG7T5Y46N5TM4RIBGHYMCZ}

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	2026-05-18T00:21:46.219921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e38c769bf3ee39e6f66ce450131f0c1655f9cc6eb9150020b6a9b2e0c495e778

Aliases

arxiv: 1707.04018 · arxiv_version: 1707.04018v2 · doi: 10.48550/arxiv.1707.04018 · pith_short_12: 4OGHNG7T5Y46 · pith_short_16: 4OGHNG7T5Y46N5TM · pith_short_8: 4OGHNG7T

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/4OGHNG7T5Y46N5TM4RIBGHYMCZ \
  | 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: e38c769bf3ee39e6f66ce450131f0c1655f9cc6eb9150020b6a9b2e0c495e778

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc9ad9eb563a62e3cdbeb35f08e5f045c5301aabd8066089f0f93f2bede1b4d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-07-13T08:08:52Z",
    "title_canon_sha256": "54068d7b2b5e285489da8e370e9f89b484c6f48e943d694a2e494714b449707c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.04018",
    "kind": "arxiv",
    "version": 2
  }
}