Pith Number

pith:CZK6VNFP

pith:2010:CZK6VNFPX5LYRCVSZNYWUZAQO2

not attested not anchored not stored refs pending

Variational estimates for paraproducts

Camil Muscalu, Christoph Thiele, Yen Do

arxiv:1009.5187 v1 · 2010-09-27 · 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{CZK6VNFPX5LYRCVSZNYWUZAQO2}

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	2026-05-18T04:40:19.056519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1655eab4afbf57888ab2cb716a641076b2450bfa35876fbbeadf5a5fa11cb0c9

Aliases

arxiv: 1009.5187 · arxiv_version: 1009.5187v1 · doi: 10.48550/arxiv.1009.5187 · pith_short_12: CZK6VNFPX5LY · pith_short_16: CZK6VNFPX5LYRCVS · pith_short_8: CZK6VNFP

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/CZK6VNFPX5LYRCVSZNYWUZAQO2 \
  | 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: 1655eab4afbf57888ab2cb716a641076b2450bfa35876fbbeadf5a5fa11cb0c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec58b42345cc7637e368ba2a8e62bf1b416a2bf2fa2e24a929a2d3b647d8485b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-09-27T08:42:09Z",
    "title_canon_sha256": "7c34ce5fd46c65c8eb5bfd1ea91ae43591e07bb46da1e38d0a6fcc6e69798122"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5187",
    "kind": "arxiv",
    "version": 1
  }
}