Pith Number

pith:CFGQUS4M

pith:2013:CFGQUS4MGQ4XPRGCMCUEJMVCWL

not attested not anchored not stored refs pending

Cauchy-Binet for Pseudo-Determinants

Oliver Knill

arxiv:1306.0062 v3 · 2013-06-01 · math.RA · math.OA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CFGQUS4MGQ4XPRGCMCUEJMVCWL}

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	2026-05-18T02:49:31.813983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

114d0a4b8c343977c4c260a844b2a2b2ef499213eb4cc44c100519f90ceb54ba

Aliases

arxiv: 1306.0062 · arxiv_version: 1306.0062v3 · doi: 10.48550/arxiv.1306.0062 · pith_short_12: CFGQUS4MGQ4X · pith_short_16: CFGQUS4MGQ4XPRGC · pith_short_8: CFGQUS4M

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/CFGQUS4MGQ4XPRGCMCUEJMVCWL \
  | 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: 114d0a4b8c343977c4c260a844b2a2b2ef499213eb4cc44c100519f90ceb54ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15a85cef18cb9743ba6181c2b62b5649db1d4c1a59a2d6fa7d46194ef6f5d19a",
    "cross_cats_sorted": [
      "math.OA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-06-01T02:07:34Z",
    "title_canon_sha256": "a4c0f8e049480cf06c56d9a3be09f6c12abce40e01b35efceeb3bdd7424b23b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0062",
    "kind": "arxiv",
    "version": 3
  }
}