Pith Number

pith:5VOVCUR4

pith:2008:5VOVCUR4LB4DIJ3TRS5VJNAYKB

not attested not anchored not stored refs pending

The smallest singular value of a random rectangular matrix

Mark Rudelson, Roman Vershynin

arxiv:0802.3956 v4 · 2008-02-27 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5VOVCUR4LB4DIJ3TRS5VJNAYKB}

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.

Cited by

1 paper in Pith

Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory

Receipt and verification

First computed	2026-05-18T00:54:14.248227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed5d51523c58783427738cbb54b4185045208ca60a8faecc2a1cf7f7d4eeea31

Aliases

arxiv: 0802.3956 · arxiv_version: 0802.3956v4 · doi: 10.48550/arxiv.0802.3956 · pith_short_12: 5VOVCUR4LB4D · pith_short_16: 5VOVCUR4LB4DIJ3T · pith_short_8: 5VOVCUR4

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/5VOVCUR4LB4DIJ3TRS5VJNAYKB \
  | 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: ed5d51523c58783427738cbb54b4185045208ca60a8faecc2a1cf7f7d4eeea31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f40f1efa9a8b9dfa13f5738feae62079cf2088c2d19799a670b396553753551",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-02-27T06:36:03Z",
    "title_canon_sha256": "d4ac922dde16dded39d759515a8b6360e38ac116adcaac0ccdcd55f59f7b129c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.3956",
    "kind": "arxiv",
    "version": 4
  }
}