Pith Number

pith:RWP6NBYU

pith:2012:RWP6NBYU3DR24OHHMTUWDSPY6M

not attested not anchored not stored refs pending

A reflexive Banach space whose algebra of operators is not a Grothendieck space

Tomasz Kania

arxiv:1211.2867 v3 · 2012-11-13 · math.FA · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RWP6NBYU3DR24OHHMTUWDSPY6M}

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	2026-05-18T03:32:31.465533Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d9fe68714d8e3ae38e764e961c9f8f317c8999a4ca82eb9f941af67fb91fb0a

Aliases

arxiv: 1211.2867 · arxiv_version: 1211.2867v3 · doi: 10.48550/arxiv.1211.2867 · pith_short_12: RWP6NBYU3DR2 · pith_short_16: RWP6NBYU3DR24OHH · pith_short_8: RWP6NBYU

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/RWP6NBYU3DR24OHHMTUWDSPY6M \
  | 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: 8d9fe68714d8e3ae38e764e961c9f8f317c8999a4ca82eb9f941af67fb91fb0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4e222299276a6f86b80922ddad2343fec780f1faa3048dd4ff56d213ebf49eb",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-11-13T01:34:18Z",
    "title_canon_sha256": "9bfb3dfa2794d5842145c997835777f2ba35aeaafa201da039fe17c4b61f855d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2867",
    "kind": "arxiv",
    "version": 3
  }
}