Pith Number

pith:4HI53HSI

pith:2006:4HI53HSILDQPYYT6NZCTNKDFTL

not attested not anchored not stored refs pending

Strong consistency of MLE for finite mixtures of location-scale distributions when the ratios of the scale parameters are exponentially small

Kentaro Tanaka

arxiv:math/0609678 v2 · 2006-09-25 · 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{4HI53HSILDQPYYT6NZCTNKDFTL}

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	2026-05-18T04:08:53.236031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1d1dd9e4858e0fc627e6e4536a8659ae9b6243bb8cd7c4e34825655d7944e37

Aliases

arxiv: math/0609678 · arxiv_version: math/0609678v2 · doi: 10.48550/arxiv.math/0609678 · pith_short_12: 4HI53HSILDQP · pith_short_16: 4HI53HSILDQPYYT6 · pith_short_8: 4HI53HSI

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/4HI53HSILDQPYYT6NZCTNKDFTL \
  | 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: e1d1dd9e4858e0fc627e6e4536a8659ae9b6243bb8cd7c4e34825655d7944e37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d9643f276c1235f442c8633aa22c93f848822c26d3a47626240adba8e14db24",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "",
    "primary_cat": "math.ST",
    "submitted_at": "2006-09-25T03:19:54Z",
    "title_canon_sha256": "80bab1ae6829cbbb00d3376288584183634813e8532241380bd821e0cf88a79f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609678",
    "kind": "arxiv",
    "version": 2
  }
}