Pith Number

pith:7IEE7EGJ

pith:2026:7IEE7EGJ6OA4MAF7Z6NHQHYT2L

not attested not anchored not stored refs pending

A Singularity Criterion for Countable Gaussian Mixtures Based on the Feldman-Hajek Theorem

Umberto Michelucci

arxiv:2601.03911 v3 · 2026-01-07 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7IEE7EGJ6OA4MAF7Z6NHQHYT2L}

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.

Cited by

1 paper in Pith

The Infinite-Dimensional Nature of Spectroscopy and Why Models Succeed, Fail, and Mislead

Receipt and verification

First computed	2026-06-30T02:17:14.301682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa084f90c9f381c600bfcf9a781f13d2ff57526f2cdc21c956e083fef9e9570d

Aliases

arxiv: 2601.03911 · arxiv_version: 2601.03911v3 · doi: 10.48550/arxiv.2601.03911 · pith_short_12: 7IEE7EGJ6OA4 · pith_short_16: 7IEE7EGJ6OA4MAF7 · pith_short_8: 7IEE7EGJ

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/7IEE7EGJ6OA4MAF7Z6NHQHYT2L \
  | 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: fa084f90c9f381c600bfcf9a781f13d2ff57526f2cdc21c956e083fef9e9570d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6a7b02021ffbf838c522fc62b28adf433c061129b3ee9099b7a11b0024a69cb",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-01-07T13:23:13Z",
    "title_canon_sha256": "8acec6049b8cbf5898009222a10eb443982f19c97aa33f3263312c90d740afc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.03911",
    "kind": "arxiv",
    "version": 3
  }
}