Pith Number

pith:BY4WGQTG

pith:2015:BY4WGQTGNGWYE5IXSZU32JWIQN

not attested not anchored not stored refs pending

Testing the Sphericity of a covariance matrix when the dimension is much larger than the sample size

Jianfeng Yao, Zeng Li

arxiv:1508.02498 v3 · 2015-08-11 · stat.ME

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BY4WGQTGNGWYE5IXSZU32JWIQN}

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	2026-05-18T01:19:40.714878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e3963426669ad8275179669bd26c88346256f2c2431d36f03cc497cf7ad6449

Aliases

arxiv: 1508.02498 · arxiv_version: 1508.02498v3 · doi: 10.48550/arxiv.1508.02498 · pith_short_12: BY4WGQTGNGWY · pith_short_16: BY4WGQTGNGWYE5IX · pith_short_8: BY4WGQTG

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/BY4WGQTGNGWYE5IXSZU32JWIQN \
  | 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: 0e3963426669ad8275179669bd26c88346256f2c2431d36f03cc497cf7ad6449

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1d94ecb002a2d1c219ffeab4439368068f5e4ce5a991f54a4e392dc4e04871d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2015-08-11T07:20:25Z",
    "title_canon_sha256": "0ea482e675f6649334ad59b3d75ee55f25e67e32a53082f248483a5288240d6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02498",
    "kind": "arxiv",
    "version": 3
  }
}