Pith Number

pith:Z7JXO4VE

pith:2014:Z7JXO4VELFKKUL4JMMHQNLI3AU

not attested not anchored not stored refs pending

Exponential bounds for the support convergence in the Single Ring Theorem

Florent Benaych-Georges

arxiv:1409.3864 v4 · 2014-09-12 · 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{Z7JXO4VELFKKUL4JMMHQNLI3AU}

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	2026-05-18T02:25:18.704726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd37772a45954aa2f89630f06ad1b05200304c331fa79db9f404b1629ed4aee

Aliases

arxiv: 1409.3864 · arxiv_version: 1409.3864v4 · doi: 10.48550/arxiv.1409.3864 · pith_short_12: Z7JXO4VELFKK · pith_short_16: Z7JXO4VELFKKUL4J · pith_short_8: Z7JXO4VE

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/Z7JXO4VELFKKUL4JMMHQNLI3AU \
  | 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: cfd37772a45954aa2f89630f06ad1b05200304c331fa79db9f404b1629ed4aee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fcc140a83af08f9d5f8b15a3127939137e4eeb18211483f83d5a99997fb0cae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-09-12T21:05:30Z",
    "title_canon_sha256": "8ddaf0f9cb1dcced884a2c52d3031ad6a434c41c0d46a9dec7f97d15a9fff36b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3864",
    "kind": "arxiv",
    "version": 4
  }
}