Pith Number

pith:5ZDNNVFI

pith:2008:5ZDNNVFIIXOCWVGNMKBSOUFJEN

not attested not anchored not stored refs pending

A reduction method for noncommutative $L_p$-spaces and applications

Marius Junge, Quanhua Xu, Uffe Haagerup

arxiv:0806.3635 v2 · 2008-06-23 · math.OA · 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{5ZDNNVFIIXOCWVGNMKBSOUFJEN}

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.

Cited by

2 papers in Pith

Integral representations of $f$-divergences for general von Neumann algebras

A general proof of integer R\'enyi QNEC

Receipt and verification

First computed	2026-07-04T15:48:36.588133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee46d6d4a845dc2b54cd62832750a9235dd9d5ae4c325967296940c00e56e7d6

Aliases

arxiv: 0806.3635 · arxiv_version: 0806.3635v2 · doi: 10.48550/arxiv.0806.3635 · pith_short_12: 5ZDNNVFIIXOC · pith_short_16: 5ZDNNVFIIXOCWVGN · pith_short_8: 5ZDNNVFI

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/5ZDNNVFIIXOCWVGNMKBSOUFJEN \
  | 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: ee46d6d4a845dc2b54cd62832750a9235dd9d5ae4c325967296940c00e56e7d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1b12c2e2700087be53f8ce29526d1a3d66fc2402b26f00846899235b9eebd03",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2008-06-23T08:45:04Z",
    "title_canon_sha256": "be7a9e1eab878c40ca10b11b432029bcf4c6137e68035fa9c4e2628c55e119ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.3635",
    "kind": "arxiv",
    "version": 2
  }
}