Pith Number

pith:N7FY5K3I

pith:2015:N7FY5K3I3FOZPCQDU2FVRQIJNS

not attested not anchored not stored refs pending

The sharp maximal function approach to $L^{p}$ estimates for operators structured on H\"{o}rmander's vector fields

Marco Bramanti, Marisa Toschi

arxiv:1511.03536 v1 · 2015-11-11 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N7FY5K3I3FOZPCQDU2FVRQIJNS}

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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	2026-05-18T01:27:08.786550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fcb8eab68d95d978a03a68b58c1096cbd50ecdca7e4b90c94ce34948aab956a

Aliases

arxiv: 1511.03536 · arxiv_version: 1511.03536v1 · doi: 10.48550/arxiv.1511.03536 · pith_short_12: N7FY5K3I3FOZ · pith_short_16: N7FY5K3I3FOZPCQD · pith_short_8: N7FY5K3I

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/N7FY5K3I3FOZPCQDU2FVRQIJNS \
  | 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: 6fcb8eab68d95d978a03a68b58c1096cbd50ecdca7e4b90c94ce34948aab956a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a553e80ff2cf6efd22c70cb02babb70e3f22dc70b82e8442dd7dfa2bbb5448d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-11T15:34:16Z",
    "title_canon_sha256": "16b0588087c0d15ab0d15c31a3d43a948c4f8f54caa6c2ef6e93fbdc9cfd607e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03536",
    "kind": "arxiv",
    "version": 1
  }
}