Pith Number

pith:2BKECNQD

pith:2014:2BKECNQDJFPFB43TJ2Q4KJJBQD

not attested not anchored not stored refs pending

A proof of Rosenthal's \(\ell_1\) Theorem

Ioannis Gasparis

arxiv:1403.1163 v1 · 2014-03-05 · 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{2BKECNQDJFPFB43TJ2Q4KJJBQD}

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	2026-05-18T02:57:00.512781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d054413603495e50f3734ea1c5252180db44176edccb123563cdfa43d4c212f5

Aliases

arxiv: 1403.1163 · arxiv_version: 1403.1163v1 · doi: 10.48550/arxiv.1403.1163 · pith_short_12: 2BKECNQDJFPF · pith_short_16: 2BKECNQDJFPFB43T · pith_short_8: 2BKECNQD

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/2BKECNQDJFPFB43TJ2Q4KJJBQD \
  | 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: d054413603495e50f3734ea1c5252180db44176edccb123563cdfa43d4c212f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7981be9c9ae5a3d814a1a77d5d2a96d6397a979592a5b7c560343b174930770",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-03-05T15:38:03Z",
    "title_canon_sha256": "a76e199a0ea51c7a639369cb0e8c51db48d66a6908c9bdc3a37cd6aa0a31b6fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.1163",
    "kind": "arxiv",
    "version": 1
  }
}