Pith Number

pith:OGNSUDQB

pith:2012:OGNSUDQB2CSCMACLHDRWW6H33T

not attested not anchored not stored refs pending

Invertibility of random matrices: unitary and orthogonal perturbations

Mark Rudelson, Roman Vershynin

arxiv:1206.5180 v2 · 2012-06-22 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OGNSUDQB2CSCMACLHDRWW6H33T}

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	2026-05-18T02:57:24.298887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

719b2a0e01d0a426004b38e36b78fbdcca93b0330a7e42b7ed958b94ba1488e8

Aliases

arxiv: 1206.5180 · arxiv_version: 1206.5180v2 · doi: 10.48550/arxiv.1206.5180 · pith_short_12: OGNSUDQB2CSC · pith_short_16: OGNSUDQB2CSCMACL · pith_short_8: OGNSUDQB

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/OGNSUDQB2CSCMACLHDRWW6H33T \
  | 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: 719b2a0e01d0a426004b38e36b78fbdcca93b0330a7e42b7ed958b94ba1488e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecbf416c1683ddfd4e828a56df3c731cc2cd591f94421f53e64410b61716f37c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-22T15:42:30Z",
    "title_canon_sha256": "568f1383ba74adffe87fcab5634468168ea7119aecfeedd517c876c0d0b499e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.5180",
    "kind": "arxiv",
    "version": 2
  }
}