Pith Number

pith:SN2PTZWL

pith:2026:SN2PTZWLVKFICPKQZKVM67M5LU

not attested not anchored not stored refs pending

Horizontal Kakeya maximal operators in finite Heisenberg groups: Exact exponents and applications

Andrea Pinamonti, Boqing Xue, Dung The Tran, Thang Pham

arxiv:2603.02111 v2 · 2026-03-02 · math.CO · math.CA · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SN2PTZWLVKFICPKQZKVM67M5LU}

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	2026-07-02T01:17:28.445167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9374f9e6cbaa8a813d50caaacf7d9d5d34e52fe1439888c1a2bfd901d26a1846

Aliases

arxiv: 2603.02111 · arxiv_version: 2603.02111v2 · doi: 10.48550/arxiv.2603.02111 · pith_short_12: SN2PTZWLVKFI · pith_short_16: SN2PTZWLVKFICPKQ · pith_short_8: SN2PTZWL

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/SN2PTZWLVKFICPKQZKVM67M5LU \
  | 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: 9374f9e6cbaa8a813d50caaacf7d9d5d34e52fe1439888c1a2bfd901d26a1846

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f76381fd2ee299aa4584cf8328c2ea434773fcca4d42c860879d0624e0e38dca",
    "cross_cats_sorted": [
      "math.CA",
      "math.GR",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-03-02T17:28:02Z",
    "title_canon_sha256": "5687ff50f776feeda89434fe7f8cf04b48dcd8c81d9122a74224512f0445d44f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.02111",
    "kind": "arxiv",
    "version": 2
  }
}