Pith Number

pith:T3DVK34X

pith:2015:T3DVK34XT2RC45I5MQGFL45C2R

not attested not anchored not stored refs pending

The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach

Joel A. Tropp

arxiv:1506.04711 v2 · 2015-06-15 · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T3DVK34XT2RC45I5MQGFL45C2R}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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

Stability of digital and analog quantum simulations under noise

Receipt and verification

First computed	2026-05-18T01:30:00.906662Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ec7556f979ea22e751d640c55f3a2d47818d6598e695decfc8421f86cbda9a6

Aliases

arxiv: 1506.04711 · arxiv_version: 1506.04711v2 · doi: 10.48550/arxiv.1506.04711 · pith_short_12: T3DVK34XT2RC · pith_short_16: T3DVK34XT2RC45I5 · pith_short_8: T3DVK34X

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/T3DVK34XT2RC45I5MQGFL45C2R \
  | 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: 9ec7556f979ea22e751d640c55f3a2d47818d6598e695decfc8421f86cbda9a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bc0a00e97d62ec9f2e2ed8a6cb1fbbff7fbedc55ec3509cbf302daf2b66d957",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-15T19:22:03Z",
    "title_canon_sha256": "c12609a3ae5e093cab0875d0879db12c24272fb6fcbec0042bb50d26a4ffbff8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04711",
    "kind": "arxiv",
    "version": 2
  }
}