Pith Number

pith:WZRR6NKV

pith:2011:WZRR6NKVGOLZKTRTA2IN7IC7RF

not attested not anchored not stored refs pending

Sharp weak type estimates for weights in the class $A_{p_1, p_2}$

Alexander Reznikov

arxiv:1105.4848 v1 · 2011-05-24 · 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{WZRR6NKVGOLZKTRTA2IN7IC7RF}

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	2026-05-18T04:21:21.735546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6631f35553397954e330690dfa05f8952e6cd43e2b743fe76de20f07b89553d

Aliases

arxiv: 1105.4848 · arxiv_version: 1105.4848v1 · doi: 10.48550/arxiv.1105.4848 · pith_short_12: WZRR6NKVGOLZ · pith_short_16: WZRR6NKVGOLZKTRT · pith_short_8: WZRR6NKV

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/WZRR6NKVGOLZKTRTA2IN7IC7RF \
  | 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: b6631f35553397954e330690dfa05f8952e6cd43e2b743fe76de20f07b89553d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71566541ebf91e57963fc72c695ac736368b3b062cb1fee29b58e6f28b4a0646",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-05-24T18:17:35Z",
    "title_canon_sha256": "33ce5b14066fe52d97e33cb2c67accf6bd8beccfbc2258385e1f9411d7333685"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4848",
    "kind": "arxiv",
    "version": 1
  }
}