Pith Number

pith:MWLT4XTX

pith:2024:MWLT4XTXN256MZLA2PNAADKLKX

not attested not anchored not stored refs pending

Probabilistic Construction of Kakeya-Type Sets in $\mathbb{R}^2$ associated to separated sets of directions

Alexander Stokolos, Blanca Radillo-Murguia, Paul Hagelstein

arxiv:2405.17674 v2 · 2024-05-27 · math.CA · 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{MWLT4XTXN256MZLA2PNAADKLKX}

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	2026-07-05T11:35:09.973930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65973e5e776ebbe66560d3da000d4b55d73a7422fcb3e44027eee06ad64e702f

Aliases

arxiv: 2405.17674 · arxiv_version: 2405.17674v2 · doi: 10.48550/arxiv.2405.17674 · pith_short_12: MWLT4XTXN256 · pith_short_16: MWLT4XTXN256MZLA · pith_short_8: MWLT4XTX

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/MWLT4XTXN256MZLA2PNAADKLKX \
  | 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: 65973e5e776ebbe66560d3da000d4b55d73a7422fcb3e44027eee06ad64e702f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42d008138653a3cb9aa5b3c9864d821f3fc66adbbc6967b9d30321ca7b309be2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2024-05-27T21:53:51Z",
    "title_canon_sha256": "e0471ca50329c1d27b5d486162bfdf939378a3d3e17e657bd9d35b14fce175fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.17674",
    "kind": "arxiv",
    "version": 2
  }
}