Pith Number

pith:AUDJ7CCT

pith:2024:AUDJ7CCTZMHNKYABJ4TAMLB4HI

not attested not anchored not stored refs pending

On commuting pairs in arbitrary sets of 2x2 matrices

Akshat Mudgal

arxiv:2411.10404 v2 · 2024-11-15 · math.NT · 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{AUDJ7CCTZMHNKYABJ4TAMLB4HI}

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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

1 paper in Pith

Counting $2 \times 2$ integer matrices with a given determinant

Receipt and verification

First computed	2026-07-05T10:35:41.162602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05069f8853cb0ed560014f26062c3c3a10812f79f96b22af76b20af14f21ecf1

Aliases

arxiv: 2411.10404 · arxiv_version: 2411.10404v2 · doi: 10.48550/arxiv.2411.10404 · pith_short_12: AUDJ7CCTZMHN · pith_short_16: AUDJ7CCTZMHNKYAB · pith_short_8: AUDJ7CCT

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/AUDJ7CCTZMHNKYABJ4TAMLB4HI \
  | 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: 05069f8853cb0ed560014f26062c3c3a10812f79f96b22af76b20af14f21ecf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30b3c90d3e22ffb32a1552311307a8005ddb5de0e24223de0268c03d5a7ce8d2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-11-15T18:19:49Z",
    "title_canon_sha256": "3f120642c0cbeff644d283079fe6fa8e5f76ee766e3874086e2bb3d223083c16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.10404",
    "kind": "arxiv",
    "version": 2
  }
}