Pith Number

pith:N3WGOG5W

pith:2013:N3WGOG5WOQEL76WT3URQWWZYDC

not attested not anchored not stored refs pending

Bounding the smallest singular value of a random matrix without concentration

Shahar Mendelson, Vladimir Koltchinskii

arxiv:1312.3580 v1 · 2013-12-12 · 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{N3WGOG5WOQEL76WT3URQWWZYDC}

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	2026-05-18T03:04:50.492274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6eec671bb67408bffad3dd230b5b38188bdeda671a2eee2ceec6171b800c22f5

Aliases

arxiv: 1312.3580 · arxiv_version: 1312.3580v1 · doi: 10.48550/arxiv.1312.3580 · pith_short_12: N3WGOG5WOQEL · pith_short_16: N3WGOG5WOQEL76WT · pith_short_8: N3WGOG5W

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/N3WGOG5WOQEL76WT3URQWWZYDC \
  | 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: 6eec671bb67408bffad3dd230b5b38188bdeda671a2eee2ceec6171b800c22f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9968ccb5018567990bf0d1bb9edaca76b3da8294ca1442f98270d2dedd446cf2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-12T18:37:03Z",
    "title_canon_sha256": "90ddc1eca470c571d91dcd6a132b054d28c4c45dd4648c04d9648aa4155a60c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3580",
    "kind": "arxiv",
    "version": 1
  }
}