Pith Number

pith:7I3M3Z4Z

pith:2024:7I3M3Z4ZIIH444GII2JAEGJSEB

not attested not anchored not stored refs pending

A uniform formula on the number of integer matrices with given determinant and height

Muhammad Afifurrahman

arxiv:2407.08191 v5 · 2024-07-11 · 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{7I3M3Z4ZIIH444GII2JAEGJSEB}

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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	2026-07-05T10:13:01.709693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa36cde799420fce70c84692021932206140fecf4b220410683d096f54fad49f

Aliases

arxiv: 2407.08191 · arxiv_version: 2407.08191v5 · doi: 10.48550/arxiv.2407.08191 · pith_short_12: 7I3M3Z4ZIIH4 · pith_short_16: 7I3M3Z4ZIIH444GI · pith_short_8: 7I3M3Z4Z

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/7I3M3Z4ZIIH444GII2JAEGJSEB \
  | 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: fa36cde799420fce70c84692021932206140fecf4b220410683d096f54fad49f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "005c57d35fef6c81dee2ea5b859257e6d7a2ce9e8b8b867f11885114e5d1a10f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-07-11T05:18:25Z",
    "title_canon_sha256": "d9cb132ec3d4138534c8fb5f3f5896735e4ae1b07a8e80cfd7fd4b63678485e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.08191",
    "kind": "arxiv",
    "version": 5
  }
}