Pith Number

pith:WNC3U5N7

pith:2025:WNC3U5N72H4B2JBZB5OXREXXRU

not attested not anchored not stored refs pending

Outline of the Wang-Zahl proof of the Kakeya conjecture in $\mathbb{R}^3$

Larry Guth

arxiv:2508.05475 v1 · 2025-08-07 · 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{WNC3U5N72H4B2JBZB5OXREXXRU}

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.

Cited by

2 papers in Pith

Bourgain's condition, sticky Kakeya, and new examples

The Kakeya conjecture, after Wang and Zahl

Receipt and verification

First computed	2026-07-05T11:50:13.879115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b345ba75bfd1f81d24390f5d7892f78d1937b57797ef15fdfbdacd04f6ecb2d0

Aliases

arxiv: 2508.05475 · arxiv_version: 2508.05475v1 · doi: 10.48550/arxiv.2508.05475 · pith_short_12: WNC3U5N72H4B · pith_short_16: WNC3U5N72H4B2JBZ · pith_short_8: WNC3U5N7

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/WNC3U5N72H4B2JBZB5OXREXXRU \
  | 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: b345ba75bfd1f81d24390f5d7892f78d1937b57797ef15fdfbdacd04f6ecb2d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "116150ca4fe22ea52f13f3cb31acdcd0ffad314c77a055b78ddfca81cde2c767",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-08-07T15:15:02Z",
    "title_canon_sha256": "cd4df36e384bfaa96b0cdaface69c9076d313f684cc793a4b5ac7716cc4494f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.05475",
    "kind": "arxiv",
    "version": 1
  }
}