Pith Number

pith:XERSNHXX

pith:2016:XERSNHXXFAYB7ARCVYOM5XAOTI

not attested not anchored not stored refs pending

On the spectral radius of a random matrix: an upper bound without fourth moment

Charles Bordenave, Djalil Chafai, Konstantin Tikhomirov, Pietro Caputo

arxiv:1607.05484 v2 · 2016-07-19 · math.CO · 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{XERSNHXXFAYB7ARCVYOM5XAOTI}

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	2026-05-18T00:14:41.470138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b923269ef728301f8222ae1ccedc0e9a1b347a8ea3701d5b3cbc679907205128

Aliases

arxiv: 1607.05484 · arxiv_version: 1607.05484v2 · doi: 10.48550/arxiv.1607.05484 · pith_short_12: XERSNHXXFAYB · pith_short_16: XERSNHXXFAYB7ARC · pith_short_8: XERSNHXX

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/XERSNHXXFAYB7ARCVYOM5XAOTI \
  | 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: b923269ef728301f8222ae1ccedc0e9a1b347a8ea3701d5b3cbc679907205128

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99f28fc7fb083f6ab5a6b8823fce8cb678788cd08f591c8f3d351c3eef87c984",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-19T09:24:41Z",
    "title_canon_sha256": "a23e7220938c7565cd10d70566cdfc280611bf79e2e13b1407925c7f334e3b82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.05484",
    "kind": "arxiv",
    "version": 2
  }
}