Pith Number

pith:HKRQUDHF

pith:2024:HKRQUDHF73HZPXDNEO2W35NMFI

not attested not anchored not stored refs pending

Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities

Hong Wang, Shukun Wu

arxiv:2411.08871 v3 · 2024-11-13 · math.CA · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HKRQUDHF73HZPXDNEO2W35NMFI}

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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.

Cited by

3 papers in Pith

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

Bourgain's condition, sticky Kakeya, and new examples

The Kakeya conjecture, after Wang and Zahl

Receipt and verification

First computed	2026-07-05T09:51:38.513378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3aa30a0ce5fecf97dc6d23b56df5ac2a2831419727c5408323db60bc14520f89

Aliases

arxiv: 2411.08871 · arxiv_version: 2411.08871v3 · doi: 10.48550/arxiv.2411.08871 · pith_short_12: HKRQUDHF73HZ · pith_short_16: HKRQUDHF73HZPXDN · pith_short_8: HKRQUDHF

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/HKRQUDHF73HZPXDNEO2W35NMFI \
  | 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: 3aa30a0ce5fecf97dc6d23b56df5ac2a2831419727c5408323db60bc14520f89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95e09e3e9836cc75180ee5189b29510641a8e13d91316e16546ff64a642b4ad0",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2024-11-13T18:50:52Z",
    "title_canon_sha256": "1accd515c5844dc4f2bf33c9aea58e3f68e7deaf9bd4546f8079bdb9172f0913"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.08871",
    "kind": "arxiv",
    "version": 3
  }
}