Pith Number

pith:LOZG5334

pith:2011:LOZG53346MZFWMRVGAJO54FAFN

not attested not anchored not stored refs pending

Fractional Vector-Valued Littlewood-Paley-Stein Theory for Semigroups

Chao Zhang, Jos\'e L. Torrea

arxiv:1105.6022 v3 · 2011-05-30 · 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{LOZG53346MZFWMRVGAJO54FAFN}

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	2026-05-18T04:14:28.926109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bb26eef7cf3325b32353012eef0a02b5efe97a864c52df9b9bd988435b7eabe

Aliases

arxiv: 1105.6022 · arxiv_version: 1105.6022v3 · doi: 10.48550/arxiv.1105.6022 · pith_short_12: LOZG53346MZF · pith_short_16: LOZG53346MZFWMRV · pith_short_8: LOZG5334

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/LOZG53346MZFWMRVGAJO54FAFN \
  | 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: 5bb26eef7cf3325b32353012eef0a02b5efe97a864c52df9b9bd988435b7eabe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfe2704061309550c4b32cbe44a5c24a9db25f76e0c87e3291a71a4ef1e44a27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-05-30T15:51:35Z",
    "title_canon_sha256": "3da324b8f4dec7839fc0f6234a335022e775c4b2cb34bb824218847e63669c61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.6022",
    "kind": "arxiv",
    "version": 3
  }
}