Pith Number

pith:CUMYSUPR

pith:2009:CUMYSUPRG4AUPHIS2O3QSL2UXD

not attested not anchored not stored refs pending

A simple proof that random matrices are democratic

Jason N. Laska, Mark A. Davenport, Petros T. Boufounos, Richard G. Baraniuk

arxiv:0911.0736 v1 · 2009-11-04 · math.NA · cs.IT · cs.NA · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CUMYSUPRG4AUPHIS2O3QSL2UXD}

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	2026-06-03T23:06:30.389394Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15198951f13701479d12d3b7092f54b8f1617689d75ca77abfe5da283cd4cc02

Aliases

arxiv: 0911.0736 · arxiv_version: 0911.0736v1 · doi: 10.48550/arxiv.0911.0736 · pith_short_12: CUMYSUPRG4AU · pith_short_16: CUMYSUPRG4AUPHIS · pith_short_8: CUMYSUPR

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/CUMYSUPRG4AUPHIS2O3QSL2UXD \
  | 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: 15198951f13701479d12d3b7092f54b8f1617689d75ca77abfe5da283cd4cc02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d251436608523dc32259c0ffeee79911cac0489391c5a5f10e6e32993b1f01f0",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.NA",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2009-11-04T06:09:36Z",
    "title_canon_sha256": "877974922a830e0a6b4325254a52717edda65db3366f28c207c8a5f89ed56c79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.0736",
    "kind": "arxiv",
    "version": 1
  }
}