Pith Number

pith:NFU5VJQB

pith:2022:NFU5VJQB3MB2UXPTGFJH46ADNV

not attested not anchored not stored refs pending

The Normalized Cross Density Functional: A Framework to Quantify Statistical Dependence for Random Processes

Bo Hu, Jose C. Principe

arxiv:2212.04631 v3 · 2022-12-09 · cs.LG · cs.AI · cs.IT · math.IT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NFU5VJQB3MB2UXPTGFJH46ADNV}

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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

Time-Series Classification with Multivariate Statistical Dependence Features

Receipt and verification

First computed	2026-07-05T07:47:24.280362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6969daa601db03aa5df331527e78036d4444094b522db71a6b929efc35b15cad

Aliases

arxiv: 2212.04631 · arxiv_version: 2212.04631v3 · doi: 10.48550/arxiv.2212.04631 · pith_short_12: NFU5VJQB3MB2 · pith_short_16: NFU5VJQB3MB2UXPT · pith_short_8: NFU5VJQB

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/NFU5VJQB3MB2UXPTGFJH46ADNV \
  | 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: 6969daa601db03aa5df331527e78036d4444094b522db71a6b929efc35b15cad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c41c263670f7e124160169190395256a0e537e73a49d2d021c5bc0bf5ea1d6a8",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2022-12-09T02:12:41Z",
    "title_canon_sha256": "f9699ce7cc70d7b9e5bd837cd01a2844b4691a091bcb536835776ac6392fcde8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.04631",
    "kind": "arxiv",
    "version": 3
  }
}