Pith Number

pith:BA5EWSA2

pith:1993:BA5EWSA2Y5IROW6CHH33W52JEA

not attested not anchored not stored refs pending

Noncommutative vector valued $L_p$-spaces and completely $p$-summing maps

Gilles Pisier

arxiv:math/9306206 v1 · 1993-06-07 · 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{BA5EWSA2Y5IROW6CHH33W52JEA}

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

1 paper in Pith

Additivity and chain rules for quantum entropies via multi-index Schatten norms

Receipt and verification

First computed	2026-05-18T01:05:52.170132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

083a4b481ac751175bc239f7bb7749203c5dc7a72d4c651447d4d9e7ef770ead

Aliases

arxiv: math/9306206 · arxiv_version: math/9306206v1 · doi: 10.48550/arxiv.math/9306206 · pith_short_12: BA5EWSA2Y5IR · pith_short_16: BA5EWSA2Y5IROW6C · pith_short_8: BA5EWSA2

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/BA5EWSA2Y5IROW6CHH33W52JEA \
  | 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: 083a4b481ac751175bc239f7bb7749203c5dc7a72d4c651447d4d9e7ef770ead

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbada32132df3e1589444644c76255ad39075c5fdd95aaaa0e0c7f25eec91c9c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "1993-06-07T18:54:06Z",
    "title_canon_sha256": "e1fa5cb6860b52312917abe5c0e0ca028f4ce8b870cc345397957d62e853998f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9306206",
    "kind": "arxiv",
    "version": 1
  }
}