Pith Number

pith:WUZYEPI7

pith:2009:WUZYEPI7S3JTO3IY66K7FWWALW

not attested not anchored not stored refs pending

Sharp estimates for the commutator of the Hilbert transform on weighted Lebesgue spaces

Daewon Chung

arxiv:0904.3164 v4 · 2009-04-21 · math.FA · 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{WUZYEPI7S3JTO3IY66K7FWWALW}

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	2026-05-18T04:35:05.400565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b533823d1f96d3376d18f795f2dac05d95837c6e306525363153f60e51d689ec

Aliases

arxiv: 0904.3164 · arxiv_version: 0904.3164v4 · doi: 10.48550/arxiv.0904.3164 · pith_short_12: WUZYEPI7S3JT · pith_short_16: WUZYEPI7S3JTO3IY · pith_short_8: WUZYEPI7

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/WUZYEPI7S3JTO3IY66K7FWWALW \
  | 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: b533823d1f96d3376d18f795f2dac05d95837c6e306525363153f60e51d689ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae9a589d1b02d2ed0332e96049770b5ed4337a15c2ca6a8a0e67433039c74c6b",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-04-21T05:50:21Z",
    "title_canon_sha256": "49fec3dfd18e3b038a27312dd2dc061023de629ace38613191507c0eed2f4886"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.3164",
    "kind": "arxiv",
    "version": 4
  }
}