Pith Number

pith:BYX7N6QU

pith:2010:BYX7N6QUBY2VCM5OMN6MVH7OZT

not attested not anchored not stored refs pending

On refined Young inequalities and reverse inequalities

Shigeru Furuichi

arxiv:1001.0535 v4 · 2010-01-04 · 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{BYX7N6QUBY2VCM5OMN6MVH7OZT}

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	2026-05-18T04:23:34.351946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e2ff6fa140e355133ae637cca9feecce3fbd7506aff0e14e211da76c3400b89

Aliases

arxiv: 1001.0535 · arxiv_version: 1001.0535v4 · doi: 10.48550/arxiv.1001.0535 · pith_short_12: BYX7N6QUBY2V · pith_short_16: BYX7N6QUBY2VCM5O · pith_short_8: BYX7N6QU

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/BYX7N6QUBY2VCM5OMN6MVH7OZT \
  | 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: 0e2ff6fa140e355133ae637cca9feecce3fbd7506aff0e14e211da76c3400b89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6fffb0eb28ac678419be96bee6958faafc4d819099f2db0d9971e8c25fa7d35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-01-04T15:29:45Z",
    "title_canon_sha256": "c4b2833f1cbf22c64dbe8972ca5ec061e090efeb7ca4af9b99f3729751ef36f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0535",
    "kind": "arxiv",
    "version": 4
  }
}