Pith Number

pith:7UUNH57I

pith:2017:7UUNH57IAHOZR7NH3A4OQXFI4I

not attested not anchored not stored refs pending

Embeddings between grand, small and variable Lebesgue spaces

Alberto Fiorenza, David Cruz-Uribe, Oscar Guzman

arxiv:1706.05722 v1 · 2017-06-18 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7UUNH57IAHOZR7NH3A4OQXFI4I}

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	2026-05-18T00:42:09.099165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd28d3f7e801dd98fda7d838e85ca8e222b5aa9d55ae204582f140e56b045a4a

Aliases

arxiv: 1706.05722 · arxiv_version: 1706.05722v1 · doi: 10.48550/arxiv.1706.05722 · pith_short_12: 7UUNH57IAHOZ · pith_short_16: 7UUNH57IAHOZR7NH · pith_short_8: 7UUNH57I

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/7UUNH57IAHOZR7NH3A4OQXFI4I \
  | 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: fd28d3f7e801dd98fda7d838e85ca8e222b5aa9d55ae204582f140e56b045a4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e874e3615b8be0ae6a88aaaa743055a1dd620630cb677974a5be91338a67beea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-06-18T20:38:43Z",
    "title_canon_sha256": "08cb67d61bb7c1989da265e6ed835d8da16ca6528871f2ede02d35545ab735fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.05722",
    "kind": "arxiv",
    "version": 1
  }
}