Pith Number

pith:LUSR5NZW

pith:2026:LUSR5NZW6YFIC2PQIRX76M2FAT

not attested not anchored not stored refs pending

Explicit Matrices over $\mathbb Z_2$ with CNOT and Row Complexity $4n-\mathrm{o}(n)$ and Local Logic Gates

Andrew Yu, Sherry Gong

arxiv:2607.28598 v1 · 2026-07-30 · quant-ph · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LUSR5NZW6YFIC2PQIRX76M2FAT}

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	2026-07-31T01:39:03.873407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

5d251eb736f60a8169f0446fff334504f69238b69f080b325ef6934880b13920

Aliases

arxiv: 2607.28598 · arxiv_version: 2607.28598v1 · doi: 10.48550/arxiv.2607.28598 · pith_short_12: LUSR5NZW6YFI · pith_short_16: LUSR5NZW6YFIC2PQ · pith_short_8: LUSR5NZW

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/LUSR5NZW6YFIC2PQIRX76M2FAT \
  | 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: 5d251eb736f60a8169f0446fff334504f69238b69f080b325ef6934880b13920

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6552726da22d5bcfd39867f9e97faf2040c8c7b8e8065d607aae0ccc789d244",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-30T17:48:15Z",
    "title_canon_sha256": "f377a4cf4e784792110301da0821b8918f1091e34890052bacb32d76d02ff7d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.28598",
    "kind": "arxiv",
    "version": 1
  }
}