Pith Number

pith:7HQ4WH25

pith:2010:7HQ4WH25GL3ZBVCQDGK4444A6O

not attested not anchored not stored refs pending

Natural Density of Rectangular Unimodular Integer Matrices

G. Maze, J. Rosenthal, U. Wagner

arxiv:1005.3967 v2 · 2010-05-21 · math.NT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7HQ4WH25GL3ZBVCQDGK4444A6O}

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	2026-05-18T04:35:04.923864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9e1cb1f5d32f790d4501995ce7380f3a8962fa24747622701c9f313be6a2a38

Aliases

arxiv: 1005.3967 · arxiv_version: 1005.3967v2 · doi: 10.48550/arxiv.1005.3967 · pith_short_12: 7HQ4WH25GL3Z · pith_short_16: 7HQ4WH25GL3ZBVCQ · pith_short_8: 7HQ4WH25

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/7HQ4WH25GL3ZBVCQDGK4444A6O \
  | 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: f9e1cb1f5d32f790d4501995ce7380f3a8962fa24747622701c9f313be6a2a38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15d184cfc5c8d0d930afff74fe9f331327a88600fdf67381e9812bc1ee570fe5",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-05-21T14:06:50Z",
    "title_canon_sha256": "9fde6158eec59797e7a0b8cb45544da5794ad6b9c5dc8e7beced83becbfbb102"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3967",
    "kind": "arxiv",
    "version": 2
  }
}