Pith Number

pith:T6B7LYMK

pith:2011:T6B7LYMKUQCHJDKTX4G5BI2YPP

not attested not anchored not stored refs pending

Functional aspects of the Hardy inequality. Appearance of a hidden energy

J. L. V\'azquez, N. B. Zographopoulos

arxiv:1102.5661 v1 · 2011-02-28 · math.AP · 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{T6B7LYMKUQCHJDKTX4G5BI2YPP}

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	2026-05-18T04:27:46.326877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f83f5e18aa404748d53bf0dd0a3587bca95b498e9d73131f374d3c6269fbc1b

Aliases

arxiv: 1102.5661 · arxiv_version: 1102.5661v1 · doi: 10.48550/arxiv.1102.5661 · pith_short_12: T6B7LYMKUQCH · pith_short_16: T6B7LYMKUQCHJDKT · pith_short_8: T6B7LYMK

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/T6B7LYMKUQCHJDKTX4G5BI2YPP \
  | 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: 9f83f5e18aa404748d53bf0dd0a3587bca95b498e9d73131f374d3c6269fbc1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48d9cb6dee22124c3fb60ac34795d330eedc23340654bca2970a73cf0aecfd9d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-02-28T13:51:01Z",
    "title_canon_sha256": "a8aa7896963a8f2d0fd9a199c776ad55689a0e06e2dbba0359a32044b3b1eeff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5661",
    "kind": "arxiv",
    "version": 1
  }
}