Same Itô integral, fewer operations: a reproducible computational study

Reproducible computational note by Xamit Kadirbekov (GERO) on algebraic reorganization of known conditional Itô estimates. Exact identities, source code and raw measurements are supplied. Kernel speedups are local to the tested Python implementations; full cost accounting, single-query slowdowns, a polynomial-basis rounding counterexample and the unfavorable observed option-pricing result are retained. No new stochastic integral, correction to Itô/Black–Scholes, market-pricing improvement or vendor defect is claimed. Not peer reviewed; AI-assisted analysis was checked internally.

Text and original figures: CC BY 4.0. Original code: MIT. External papers are referenced only.

43-second YouTube explainer:
https://www.youtube.com/shorts/bEKztFkAtJo

Article and hosted video:
https://www.gero.uz/research/articles/ito-computation-reorganization.html

Code and full evidence:
https://github.com/kadyrbekovhamit-cyber/gero-numerical-observatory/tree/main/reports/ito-computation-reorganization

Hugging Face report:
https://huggingface.co/datasets/XamitK/gero-research-evidence-2026-09/blob/main/ito-computation-reorganization.md