Pith Number

pith:32WN2TZW

pith:2026:32WN2TZWD4H3U5H6EDENDG2225

not attested not anchored not stored refs pending

Dimension-free bounds for {R}iesz transforms on the {H}amming cube via a {B}ellman function

Alexander Volberg, Komla Domelevo, Paata Ivanisvili, Stefanie Petermichl

arxiv:2606.20289 v1 · 2026-06-18 · math.FA · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{32WN2TZWD4H3U5H6EDENDG2225}

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	2026-06-19T16:13:07.883485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

deacdd4f361f0fba74fe20c8d19b5ad7666122a4dbec30ab95f77c954706a55b

Aliases

arxiv: 2606.20289 · arxiv_version: 2606.20289v1 · doi: 10.48550/arxiv.2606.20289 · pith_short_12: 32WN2TZWD4H3 · pith_short_16: 32WN2TZWD4H3U5H6 · pith_short_8: 32WN2TZW

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/32WN2TZWD4H3U5H6EDENDG2225 \
  | 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: deacdd4f361f0fba74fe20c8d19b5ad7666122a4dbec30ab95f77c954706a55b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec95f27b408a3fc8c191021ce3d22d025e0db354232c3b2adeb60ae85afb9eab",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-18T14:30:49Z",
    "title_canon_sha256": "187080e0d1595ca21a043e2289f7a47066760d12fe4cbe1ce4af18a33647ca25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20289",
    "kind": "arxiv",
    "version": 1
  }
}