Pith Number

pith:IKF6Z3GR

pith:2015:IKF6Z3GRDPT4JIWVR25QI36KYE

not attested not anchored not stored refs pending

On Wolff's $L^{\frac{5}{2}}-$Kakeya maximal inequality in $\R^3$

Changxing Miao, Jianwei Yang, Jiqiang Zheng

arxiv:1504.05624 v1 · 2015-04-22 · math.AP · 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{IKF6Z3GRDPT4JIWVR25QI36KYE}

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	2026-05-18T01:32:37.182604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

428bececd11be7c4a2d58ebb046fcac114c34a8423f33f370edaebcd43d9ba38

Aliases

arxiv: 1504.05624 · arxiv_version: 1504.05624v1 · doi: 10.48550/arxiv.1504.05624 · pith_short_12: IKF6Z3GRDPT4 · pith_short_16: IKF6Z3GRDPT4JIWV · pith_short_8: IKF6Z3GR

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/IKF6Z3GRDPT4JIWVR25QI36KYE \
  | 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: 428bececd11be7c4a2d58ebb046fcac114c34a8423f33f370edaebcd43d9ba38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cda407adf51f1c95537855a34f3d3456cd6682e6cd35e0f4c28372bb3f019899",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-22T00:24:04Z",
    "title_canon_sha256": "9c70104a0bb78073cb9e32ea2484352c642a10f0b3dba3e985aa8b55933d4ecc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05624",
    "kind": "arxiv",
    "version": 1
  }
}