Pith Number

pith:67NI3HW6

pith:2007:67NI3HW67HRBFXD7DI4TUSRSGX

not attested not anchored not stored refs pending

On the limiting distributions of multivariate depth-based rank sum statistics and related tests

Xuming He, Yijun Zuo

arxiv:0708.0167 v1 · 2007-08-01 · math.ST · stat.TH

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67NI3HW67HRBFXD7DI4TUSRSGX}

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	2026-05-18T04:09:15.208081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7da8d9edef9e212dc7f1a393a4a3235d4162fce1fd5257ab56134aad8648fa2

Aliases

arxiv: 0708.0167 · arxiv_version: 0708.0167v1 · doi: 10.48550/arxiv.0708.0167 · pith_short_12: 67NI3HW67HRB · pith_short_16: 67NI3HW67HRBFXD7 · pith_short_8: 67NI3HW6

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/67NI3HW67HRBFXD7DI4TUSRSGX \
  | 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: f7da8d9edef9e212dc7f1a393a4a3235d4162fce1fd5257ab56134aad8648fa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28ff09cc45076feef9108fb9257e06bb3140e60b4cc6f51e1b1981a5dc08ddf0",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "",
    "primary_cat": "math.ST",
    "submitted_at": "2007-08-01T14:47:41Z",
    "title_canon_sha256": "f4a134b761bec030c69f6b30488b6a3d1f13b6a73d2d2458ced9a0e1470b8fac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.0167",
    "kind": "arxiv",
    "version": 1
  }
}