Pith Number

pith:2SALJS6I

pith:2026:2SALJS6I6RZFU44PSFICT7KCHC

not attested not anchored not stored refs pending

Cauchy-Gaussian Overbound for Heavy-tailed GNSS Measurement Errors

Li-Ta Hsu, Penggao Yan, Weisong Wen, Zhengdao Li

A Cauchy core plus Gaussian tails tightly overbounds heavy-tailed GNSS errors while preserving the property through convolution.

arxiv:2601.07299 v2 · 2026-01-12 · stat.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2SALJS6I6RZFU44PSFICT7KCHC}

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.

Claims

C1strongest claim

our method can sharply bound heavy-tailed errors at both core and tail regions. In the position domain, the proposed method reduces the average vertical protection level by 15% for s.u. heavy-tailed errors compared to the single-CDF Gaussian overbound, and by 21% to 47% for n.s.u. heavy-tailed errors compared to the Navigation Discrete ENvelope and two-step Gaussian overbounds.

C2weakest assumption

The heavy-tailed GNSS measurement errors are unimodal (symmetric or not) and can be overbounded by a Cauchy core plus Gaussian tails with parameters chosen via the proposed procedure without violating the overbound in real data.

C3one line summary

A Cauchy-Gaussian overbound is developed to sharply bound heavy-tailed GNSS errors in core and tails, with a procedure for symmetric and asymmetric unimodal cases, a proof that the bound is preserved under convolution, and experimental reductions in vertical protection levels of 15-47% versus prior

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-28T01:04:35.221776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d480b4cbc8f4725a738f915029fd4238a91f2900285331769ce6bd583fec21a1

Aliases

arxiv: 2601.07299 · arxiv_version: 2601.07299v2 · doi: 10.48550/arxiv.2601.07299 · pith_short_12: 2SALJS6I6RZF · pith_short_16: 2SALJS6I6RZFU44P · pith_short_8: 2SALJS6I

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/2SALJS6I6RZFU44PSFICT7KCHC \
  | 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: d480b4cbc8f4725a738f915029fd4238a91f2900285331769ce6bd583fec21a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2faef143507cc1e18332275b1fa0aac2cbb1aeba9201ecdc8b8d0a6f06c7055d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.AP",
    "submitted_at": "2026-01-12T08:21:14Z",
    "title_canon_sha256": "aa1508aea4beb43bbe3afecd48c9b2810ff45826bc2017045816af0c38b9f9b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.07299",
    "kind": "arxiv",
    "version": 2
  }
}