Pith Number

pith:VZSOKZFX

pith:2010:VZSOKZFXEN2N2CW44PNLAU5CW2

not attested not anchored not stored refs pending

Sharp norm inequalities for commutators of classical operators

David Cruz-Uribe, Kabe Moen

arxiv:1008.0381 v3 · 2010-08-02 · math.CA · 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{VZSOKZFXEN2N2CW44PNLAU5CW2}

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	2026-05-18T04:13:16.103067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae64e564b72374dd0adce3dab053a2b6a4f89863022fca27a43c4bffe017ebfb

Aliases

arxiv: 1008.0381 · arxiv_version: 1008.0381v3 · doi: 10.48550/arxiv.1008.0381 · pith_short_12: VZSOKZFXEN2N · pith_short_16: VZSOKZFXEN2N2CW4 · pith_short_8: VZSOKZFX

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/VZSOKZFXEN2N2CW44PNLAU5CW2 \
  | 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: ae64e564b72374dd0adce3dab053a2b6a4f89863022fca27a43c4bffe017ebfb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc78e6758fb740355942e3e2d82f8dacc65b26336afad587ac82d1af37828314",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-08-02T19:13:08Z",
    "title_canon_sha256": "786c9bb5fc41bc34616763cc292a33adea340f1c013dbb05cf1af24c8ff6da0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.0381",
    "kind": "arxiv",
    "version": 3
  }
}