Pith Number

pith:4MEDVYFY

pith:2005:4MEDVYFYEUIJEAEXKB6CSCZ3PL

not attested not anchored not stored refs pending

Vector-valued Littlewood-Paley-Stein theory for semigroups

Jos\'e L. Torrea, Quanhua Xu, Teresa Mart\'inez

arxiv:math/0505303 v1 · 2005-05-14 · 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{4MEDVYFYEUIJEAEXKB6CSCZ3PL}

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	2026-05-18T01:08:51.075778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3083ae0b82510920097507c290b3b7af7c7f0d32dd652a673dec7254bfc0911

Aliases

arxiv: math/0505303 · arxiv_version: math/0505303v1 · doi: 10.48550/arxiv.math/0505303 · pith_short_12: 4MEDVYFYEUIJ · pith_short_16: 4MEDVYFYEUIJEAEX · pith_short_8: 4MEDVYFY

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/4MEDVYFYEUIJEAEXKB6CSCZ3PL \
  | 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: e3083ae0b82510920097507c290b3b7af7c7f0d32dd652a673dec7254bfc0911

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "348fcda6b60d9315aad8875301a32436555335f9b04eaa2d92e9ec4aee976873",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2005-05-14T13:36:01Z",
    "title_canon_sha256": "00b88e2baf47497d63c8ecc29836563e2376a6e9a6e72c04909186846f8f1dd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505303",
    "kind": "arxiv",
    "version": 1
  }
}