Pith Number

pith:VGCXFWEO

pith:2012:VGCXFWEOU7IJCHG34GOAZL7KYR

not attested not anchored not stored refs pending

Rank deficiency in sparse random GF[2] matrices

Andrew R. Wade, Mathew D. Penrose, R. W. R. Darling, Sandy L. Zabell

arxiv:1211.5455 v1 · 2012-11-23 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VGCXFWEOU7IJCHG34GOAZL7KYR}

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	2026-05-18T02:41:42.764269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a98572d88ea7d0911cdbe19c0cafeac460b5ca63491866d06145653646223b1d

Aliases

arxiv: 1211.5455 · arxiv_version: 1211.5455v1 · doi: 10.48550/arxiv.1211.5455 · pith_short_12: VGCXFWEOU7IJ · pith_short_16: VGCXFWEOU7IJCHG3 · pith_short_8: VGCXFWEO

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/VGCXFWEOU7IJCHG34GOAZL7KYR \
  | 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: a98572d88ea7d0911cdbe19c0cafeac460b5ca63491866d06145653646223b1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28150b189a0e0d7ce5558dcf61702e65d244210c1e1e99eefe9063281e5d8285",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-23T10:05:06Z",
    "title_canon_sha256": "6c5a7207abf0928f092beb6dd2d9ef60627271d89b90869db58dc9c5e3b37574"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5455",
    "kind": "arxiv",
    "version": 1
  }
}