Pith Number

pith:PH4EXJQW

pith:2008:PH4EXJQW6QUKLNO7A6PP3JGYCJ

not attested not anchored not stored refs pending

The least singular value of a random square matrix is O(n^{-1/2})

Mark Rudelson, Roman Vershynin

arxiv:0805.3407 v1 · 2008-05-22 · 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{PH4EXJQW6QUKLNO7A6PP3JGYCJ}

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	2026-05-18T00:54:14.242622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79f84ba616f428a5b5df079efda4d8126678462653e9bd5db0b0a6ea3584cc08

Aliases

arxiv: 0805.3407 · arxiv_version: 0805.3407v1 · doi: 10.48550/arxiv.0805.3407 · pith_short_12: PH4EXJQW6QUK · pith_short_16: PH4EXJQW6QUKLNO7 · pith_short_8: PH4EXJQW

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/PH4EXJQW6QUKLNO7A6PP3JGYCJ \
  | 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: 79f84ba616f428a5b5df079efda4d8126678462653e9bd5db0b0a6ea3584cc08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9066868c9f94c632f56d4671042d35834d54aba34f7d39e5260d2145c9ddc6f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-05-22T18:44:22Z",
    "title_canon_sha256": "1b6992bd25ca24d745d44fa337ba079e188e2f320adda1c4c84b417fa1ab0f11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0805.3407",
    "kind": "arxiv",
    "version": 1
  }
}