Pith Number

pith:CQKTPGLX

pith:2026:CQKTPGLX7J46EAR4WWBEMW5WMQ

not attested not anchored not stored refs pending

Two-ends Furstenberg inequality for transversal families and applications to Fourier decay

Guangzeng Yi, Shukun Wu, William O'Regan

arxiv:2607.08461 v1 · 2026-07-09 · math.CA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CQKTPGLX7J46EAR4WWBEMW5WMQ}

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	2026-07-10T01:19:51.238941Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1415379977fa79e2023cb582465bb66436d408985cd0b74e341d664db4e18500

Aliases

arxiv: 2607.08461 · arxiv_version: 2607.08461v1 · doi: 10.48550/arxiv.2607.08461 · pith_short_12: CQKTPGLX7J46 · pith_short_16: CQKTPGLX7J46EAR4 · pith_short_8: CQKTPGLX

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/CQKTPGLX7J46EAR4WWBEMW5WMQ \
  | 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: 1415379977fa79e2023cb582465bb66436d408985cd0b74e341d664db4e18500

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f40564805fede0a7bf00a9017ce09f981e6bcddbc6aa2da8d45f93b952e0e189",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-07-09T13:20:12Z",
    "title_canon_sha256": "0bc7244f68ed835bc34c65472fbce30ab362272cd6d6b809c6ac58183a6e5a31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08461",
    "kind": "arxiv",
    "version": 1
  }
}