Pith Number

pith:3GSESU34

pith:2026:3GSESU34J2UEKWALRZGPDIDYPA

not attested not anchored not stored refs pending

From a stochastic maximal inequality to infinite-dimensional martingales, towards high-dimensional statistics

Yoichi Nishiyama

A novel oracle maximal inequality via integration by parts yields sharp bounds for martingale random field suprema.

arxiv:2603.29739 v3 · 2026-03-31 · math.PR

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\usepackage{pith}
\pithnumber{3GSESU34J2UEKWALRZGPDIDYPA}

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Record completeness

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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

A novel approach is proposed to establish a sharp upper bound on the expected supremum of a separable martingale random field, serving as an alternative to classical universal chaining-based methods. This yields a generalization of Lenglart's inequality to finite-dimensional and certain infinite-dimensional settings via a finite approximation device.

C2weakest assumption

The finite approximation device successfully extends the finite-dimensional generalization to the relevant infinite-dimensional cases while preserving the sharpness of the bound, assuming the martingale random field is separable.

C3one line summary

A new oracle maximal inequality for finite submartingales is derived via integration by parts, generalizing Lenglart's inequality to finite- and certain infinite-dimensional martingale random fields through finite approximation from below.

Receipt and verification

First computed	2026-06-10T01:11:00.338419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9a449537c4ea845580b8e4cf1a078782f9794ec5f32305ecc5134d3196562b7

Aliases

arxiv: 2603.29739 · arxiv_version: 2603.29739v3 · doi: 10.48550/arxiv.2603.29739 · pith_short_12: 3GSESU34J2UE · pith_short_16: 3GSESU34J2UEKWAL · pith_short_8: 3GSESU34

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/3GSESU34J2UEKWALRZGPDIDYPA \
  | 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: d9a449537c4ea845580b8e4cf1a078782f9794ec5f32305ecc5134d3196562b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36949734d46c86f77f7cd7cea123a7f51d61c4be606a0e8d2fb1f809866fbd7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-03-31T13:37:15Z",
    "title_canon_sha256": "1e6f2c5977292fef63e85ce4edb58e7ca8e0faca56c79ae92df5c226c4fbbd2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.29739",
    "kind": "arxiv",
    "version": 3
  }
}