Pith Number

pith:XXGZGNNY

pith:2005:XXGZGNNYDL7JCA3YQPVQ4LJRC7

not attested not anchored not stored refs pending

Paraproducts in One and Several Parameters

Jason Metcalfe, Michael T Lacey

arxiv:math/0502334 v2 · 2005-02-16 · 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{XXGZGNNYDL7JCA3YQPVQ4LJRC7}

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	2026-05-18T03:56:10.996864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdcd9335b81afe91037883eb0e2d3117e7b8b81067ab87084ebbf1dc3cd41686

Aliases

arxiv: math/0502334 · arxiv_version: math/0502334v2 · doi: 10.48550/arxiv.math/0502334 · pith_short_12: XXGZGNNYDL7J · pith_short_16: XXGZGNNYDL7JCA3Y · pith_short_8: XXGZGNNY

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/XXGZGNNYDL7JCA3YQPVQ4LJRC7 \
  | 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: bdcd9335b81afe91037883eb0e2d3117e7b8b81067ab87084ebbf1dc3cd41686

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fbd725d9deca522bdcc13541c1404af5949c7335bd586f875b245744eda9c2e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2005-02-16T05:55:37Z",
    "title_canon_sha256": "b3210745ae443d6084b029dc0c40c96c925466dca5ffc1e50d07cb4727f57566"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0502334",
    "kind": "arxiv",
    "version": 2
  }
}