Pith Number

pith:6KVPLPHO

pith:2008:6KVPLPHORD7VSQEKZA6XFPUL34

not attested not anchored not stored refs pending

Composition of Haar Paraproducts: The Random Case

Brett Wick, Dmitriy Bilyk, Michael Lacey, Xiaochun Li

arxiv:0803.0788 v2 · 2008-03-06 · 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{6KVPLPHORD7VSQEKZA6XFPUL34}

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	2026-05-18T03:55:22.333283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2aaf5bcee88ff59408ac83d72be8bdf1e6a5301a09847445a30a7dac22fa540

Aliases

arxiv: 0803.0788 · arxiv_version: 0803.0788v2 · doi: 10.48550/arxiv.0803.0788 · pith_short_12: 6KVPLPHORD7V · pith_short_16: 6KVPLPHORD7VSQEK · pith_short_8: 6KVPLPHO

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/6KVPLPHORD7VSQEKZA6XFPUL34 \
  | 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: f2aaf5bcee88ff59408ac83d72be8bdf1e6a5301a09847445a30a7dac22fa540

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bf69539e48149b8c0dd0ceaa393a75f3eabeaa196dcd13cb9ad3159459997de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2008-03-06T04:33:13Z",
    "title_canon_sha256": "fbf52711dca03ddaac8656819d2fc3cdd9e277b6f2a18e37229cd88bfb23d2f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0803.0788",
    "kind": "arxiv",
    "version": 2
  }
}