Pith Number

pith:TPR7OD4C

pith:2019:TPR7OD4CUFPWJ4ALYTF5PEVKCW

not attested not anchored not stored refs pending

On a Characterization of the Weak Expectation Property (WEP)

Gilles Pisier

arxiv:1907.06224 v2 · 2019-07-14 · 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{TPR7OD4CUFPWJ4ALYTF5PEVKCW}

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	2026-05-17T23:39:53.265766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9be3f70f82a15f64f00bc4cbd792aa158ede9215a54dd88354574890a7a9476c

Aliases

arxiv: 1907.06224 · arxiv_version: 1907.06224v2 · doi: 10.48550/arxiv.1907.06224 · pith_short_12: TPR7OD4CUFPW · pith_short_16: TPR7OD4CUFPWJ4AL · pith_short_8: TPR7OD4C

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/TPR7OD4CUFPWJ4ALYTF5PEVKCW \
  | 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: 9be3f70f82a15f64f00bc4cbd792aa158ede9215a54dd88354574890a7a9476c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "821b4888d8d8b1c71bc42c95527ab8a619338d0be9844b64ae6b27e99567360d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-07-14T13:43:22Z",
    "title_canon_sha256": "287ab304193a05c448889f8355a753e04980364b1add23b1610050b057fe131f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.06224",
    "kind": "arxiv",
    "version": 2
  }
}