Pith Number

pith:GH6CMTNA

pith:2011:GH6CMTNAXQP7CXXUY5AX3TSAS4

not attested not anchored not stored refs pending

Tail bounds for all eigenvalues of a sum of random matrices

Alex Gittens, Joel A. Tropp

arxiv:1104.4513 v2 · 2011-04-22 · 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{GH6CMTNAXQP7CXXUY5AX3TSAS4}

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

Robust and Resource Efficient Identification of Two Hidden Layer Neural Networks

Receipt and verification

First computed	2026-05-18T04:17:13.345060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31fc264da0bc1ff15ef4c7417dce4097074878c091f5bbf51e05acaef8afdb67

Aliases

arxiv: 1104.4513 · arxiv_version: 1104.4513v2 · doi: 10.48550/arxiv.1104.4513 · pith_short_12: GH6CMTNAXQP7 · pith_short_16: GH6CMTNAXQP7CXXU · pith_short_8: GH6CMTNA

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/GH6CMTNAXQP7CXXUY5AX3TSAS4 \
  | 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: 31fc264da0bc1ff15ef4c7417dce4097074878c091f5bbf51e05acaef8afdb67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bcf367ae3c7f5f79d93faac651a7e972f5cd02edfc67b04f826fcf9792bbfe9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-04-22T22:02:08Z",
    "title_canon_sha256": "a8c22200e27a957585161d104bc48e5c7b9a1c538f6f70b8d3c01507bdfc8ad3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4513",
    "kind": "arxiv",
    "version": 2
  }
}