Pith Number

pith:CZ23SYPM

pith:2026:CZ23SYPMDOMUYAWR4234FWTMFC

not attested not anchored not stored refs resolved

Computational aspects of the Volterra Signature

Fabian N. Harang, Luca Pelizzari, Paul P. Hager, Samy Tindel

The Volterra signature with matrix-valued kernels admits efficient computation via quadratic approximation, FFT acceleration, and low-dimensional recursion.

arxiv:2605.18406 v1 · 2026-05-18 · math.NA · cs.NA · stat.ML

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\pithnumber{CZ23SYPMDOMUYAWR4234FWTMFC}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

The paper provides a general approximative scheme with quadratic complexity O(J^2), an FFT-based acceleration with O(J log J) for convolution kernels on uniform grids, and an exact recursion with O(J R^2) for kernels admitting a state-space representation of dimension R, while retaining standard signature complexity in path dimension and truncation level N.

C2weakest assumption

The decomposition of the Chen-type convolution relation into analytic and arithmetic parts (referenced from arXiv:2603.04525) can be performed without introducing errors that propagate into the final signature components for general matrix-valued kernels.

C3one line summary

Algorithms for Volterra signature computation achieve O(J^2), O(J log J) via FFT, and O(J R^2) via recursion, plus a predictor-corrector scheme, all implemented in a public JAX package.

References

43 extracted · 43 resolved · 1 Pith anchors

[1] Dover Publications, Inc., USA, 1974 1974

[2] Al-Mohy and Bahar Arslan 2021

[3] Springer Finance

[4] 2 COMPUTATIONAL ASPECTS OF THE VOLTERRA SIGNATURE 58 2025

[5] Cohen, Terry Lyons, Joël Mouterde, and Benjamin Walker 2026

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:59.133433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1675b961ec1b994c02d1e6b7c2da6c28b4145eaafb51a27db9aacff25615c7db

Aliases

arxiv: 2605.18406 · arxiv_version: 2605.18406v1 · doi: 10.48550/arxiv.2605.18406 · pith_short_12: CZ23SYPMDOMU · pith_short_16: CZ23SYPMDOMUYAWR · pith_short_8: CZ23SYPM

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/CZ23SYPMDOMUYAWR4234FWTMFC \
  | 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: 1675b961ec1b994c02d1e6b7c2da6c28b4145eaafb51a27db9aacff25615c7db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee11e6cffedd5d02dbc3964f070caeb13a89a168ce698c1e41b5e003e2801560",
    "cross_cats_sorted": [
      "cs.NA",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-18T13:46:47Z",
    "title_canon_sha256": "71031a1f0ba907c423148fd9883543cbef45cbd6a1eff8f14862b8b834e5b696"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18406",
    "kind": "arxiv",
    "version": 1
  }
}