Pith Number

pith:EA3UBZ7O

pith:2011:EA3UBZ7OQXKC2EO7PPGIVJAFGK

not attested not anchored not stored refs pending

The probability of rectangular unimodular matrices over $\F_q[x]$

Guangyu Yang, Xiangqian Guo

arxiv:1107.3367 v2 · 2011-07-18 · math.PR · 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{EA3UBZ7OQXKC2EO7PPGIVJAFGK}

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	2026-05-18T03:36:25.342030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

203740e7ee85d42d11df7bcc8aa40532814d040bfac6272dfe91a6be9329b586

Aliases

arxiv: 1107.3367 · arxiv_version: 1107.3367v2 · doi: 10.48550/arxiv.1107.3367 · pith_short_12: EA3UBZ7OQXKC · pith_short_16: EA3UBZ7OQXKC2EO7 · pith_short_8: EA3UBZ7O

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/EA3UBZ7OQXKC2EO7PPGIVJAFGK \
  | 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: 203740e7ee85d42d11df7bcc8aa40532814d040bfac6272dfe91a6be9329b586

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a152775644b0777ed42991851f50068add0ca1e3812cdde61a0a05e6c9b0af8f",
    "cross_cats_sorted": [
      "math.NT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-18T06:58:12Z",
    "title_canon_sha256": "c1a27465d60fb57fcafcf7614086e1c9c551e7c52c77d2100963b3cdab8645f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3367",
    "kind": "arxiv",
    "version": 2
  }
}