Pith Number

pith:NNV7ZPTG

pith:2021:NNV7ZPTGUIJIWLEULRH45ZGAM4

not attested not anchored not stored refs pending

Bernoulli Random Matrices

Alice Guionnet (CNRS, UMPA-ENSL)

arxiv:2112.05506 v1 · 2021-12-10 · 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{NNV7ZPTGUIJIWLEULRH45ZGAM4}

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

Sharp concentration for sums of matrices with Markovian dependence through universality

Receipt and verification

First computed	2026-07-05T03:39:49.124599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b6bfcbe66a2128b2c945c4fcee4c067001a341f446ae85cc5c73d13245f8ffa

Aliases

arxiv: 2112.05506 · arxiv_version: 2112.05506v1 · doi: 10.48550/arxiv.2112.05506 · pith_short_12: NNV7ZPTGUIJI · pith_short_16: NNV7ZPTGUIJIWLEU · pith_short_8: NNV7ZPTG

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/NNV7ZPTGUIJIWLEULRH45ZGAM4 \
  | 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: 6b6bfcbe66a2128b2c945c4fcee4c067001a341f446ae85cc5c73d13245f8ffa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac6d0ec834686576cff564dd79b06fa537e0c4bf46f64125111d5abd2297b7da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-12-10T13:17:05Z",
    "title_canon_sha256": "8f5133e7c972f0aee634148c1dbc3d0219324c4dab67f330ea85bc82c8272e2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05506",
    "kind": "arxiv",
    "version": 1
  }
}