Pith Number

pith:DNTLMF54

pith:2026:DNTLMF54N3OHXFOLC6ZNNN4RKD

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Asymptotic e-processes

Mattes Mollenhauer, Pierre-Fran\c{c}ois Massiani, Sebastian Schulze

A doubly indexed process approximating an e-process satisfies an asymptotic Ville inequality that uniformly bounds its excursions up to a time horizon growing with approximation quality.

arxiv:2604.19353 v2 · 2026-04-21 · math.ST · stat.ME · stat.TH

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Claims

C1strongest claim

We derive an asymptotic version of Ville's inequality, which bounds excursion probabilities of (E_{m,n})_{m,n∈ℕ} over some threshold uniformly over n up to a time horizon r_m that is determined by the quality of process approximation over m.

C2weakest assumption

The approximation quality of the doubly indexed process to an e-process as m→∞ is sufficient to determine a growing time horizon r_m over which the uniform bound holds, as stated in the abstract's description of the limiting behavior.

C3one line summary

Asymptotic e-processes approximate e-processes for large m, enabling an asymptotic Ville's inequality that bounds uniform excursion probabilities up to a time horizon r_m determined by approximation quality.

Receipt and verification

First computed	2026-05-25T02:02:15.578541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b66b617bc6edc7b95cb17b2d6b79150f267cf243aa1ab41503caf2eb6ee0aeb

Aliases

arxiv: 2604.19353 · arxiv_version: 2604.19353v2 · doi: 10.48550/arxiv.2604.19353 · pith_short_12: DNTLMF54N3OH · pith_short_16: DNTLMF54N3OHXFOL · pith_short_8: DNTLMF54

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DNTLMF54N3OHXFOLC6ZNNN4RKD \
  | 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: 1b66b617bc6edc7b95cb17b2d6b79150f267cf243aa1ab41503caf2eb6ee0aeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a99900fa7e89bce8f474d939c7f9e40e245f3fb5f5fc8122463cb7b09dde4560",
    "cross_cats_sorted": [
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-04-21T11:34:24Z",
    "title_canon_sha256": "7da79c1ae9c1e0d0e2b40c64b81e044822be740dac21c4e73b8500e50af00f26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.19353",
    "kind": "arxiv",
    "version": 2
  }
}