Pith Number

pith:P5BP7J3D

pith:2012:P5BP7J3D36UQSP5TWZLHU52RXY

not attested not anchored not stored refs pending

Optimal relations between Lp-norms for the Hardy operator and its dual

Viktor Kolyada

arxiv:1206.1731 v1 · 2012-06-08 · 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{P5BP7J3D36UQSP5TWZLHU52RXY}

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	2026-05-18T03:54:03.426022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f42ffa763dfa9093fb3b6567a7751be106e9e0134cd89c51dfaa72a0e5251e0

Aliases

arxiv: 1206.1731 · arxiv_version: 1206.1731v1 · doi: 10.48550/arxiv.1206.1731 · pith_short_12: P5BP7J3D36UQ · pith_short_16: P5BP7J3D36UQSP5T · pith_short_8: P5BP7J3D

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/P5BP7J3D36UQSP5TWZLHU52RXY \
  | 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: 7f42ffa763dfa9093fb3b6567a7751be106e9e0134cd89c51dfaa72a0e5251e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65b462ae0956a9c8c5223ae4c6c7d00cb2b9205b6cbf70ef64aa699a82d37b1e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-06-08T11:22:41Z",
    "title_canon_sha256": "df26840dac5f461709d615ef05f0bb5b3a7d4a59120e45c1da3076968ceb662d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1731",
    "kind": "arxiv",
    "version": 1
  }
}