Pith Number

pith:2QUFHHZ2

pith:2011:2QUFHHZ2ODG75R6CXOVYXLGUQX

not attested not anchored not stored refs pending

Invertibility of random submatrices via tail decoupling and a Matrix Chernoff Inequality

S\'ebastien Darses, St\'ephane Chr\'etien

arxiv:1103.3063 v3 · 2011-03-15 · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2QUFHHZ2ODG75R6CXOVYXLGUQX}

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	2026-05-18T03:59:47.818416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d428539f3a70cdfec7c2bbab8bacd485d850fb03c89613c41632451ba66d2c1f

Aliases

arxiv: 1103.3063 · arxiv_version: 1103.3063v3 · doi: 10.48550/arxiv.1103.3063 · pith_short_12: 2QUFHHZ2ODG7 · pith_short_16: 2QUFHHZ2ODG75R6C · pith_short_8: 2QUFHHZ2

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/2QUFHHZ2ODG75R6CXOVYXLGUQX \
  | 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: d428539f3a70cdfec7c2bbab8bacd485d850fb03c89613c41632451ba66d2c1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c1579bf067dab4d08145c4648d62cbb5cf185ad6025af44dc24fafd491a28e0",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-15T23:20:37Z",
    "title_canon_sha256": "ba961883ce24c5f16119b13c16a0365f170a108812f58f8f66ac2cab485a36e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3063",
    "kind": "arxiv",
    "version": 3
  }
}