Pith Number

pith:V5S4NNU4

pith:2019:V5S4NNU4DPOFDVVGLKO37UOHVM

not attested not anchored not stored refs pending

Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups

Eugeny Ostrovsky, Leonid Sirota, Maria Rosaria Formica

arxiv:1904.09226 v1 · 2019-04-19 · 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{V5S4NNU4DPOFDVVGLKO37UOHVM}

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	2026-05-17T23:48:07.954629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af65c6b69c1bdc51d6a65a9dbfd1c7ab344d6113b2830e245d32182910f26cac

Aliases

arxiv: 1904.09226 · arxiv_version: 1904.09226v1 · doi: 10.48550/arxiv.1904.09226 · pith_short_12: V5S4NNU4DPOF · pith_short_16: V5S4NNU4DPOFDVVG · pith_short_8: V5S4NNU4

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/V5S4NNU4DPOFDVVGLKO37UOHVM \
  | 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: af65c6b69c1bdc51d6a65a9dbfd1c7ab344d6113b2830e245d32182910f26cac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c3b04708c993f34831b40704974a04240961d212e1b739623ace1ebce85f048",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-04-19T15:17:37Z",
    "title_canon_sha256": "d701dd71e006a1617bb0e16f26ed96859921ac5fa3cfe10c519cea78fc6cb6d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.09226",
    "kind": "arxiv",
    "version": 1
  }
}