This Zenodo record accompanies my article where the resonance projection formula is presented. This upload provides reproducible empirical evidence for the operational core of the idea: a delta-epsilon-like resonance window (frequency-selective gating) integrated into an Ss3-style pipeline. The purpose is to enable independent reproduction and further testing by the community. Data and preprocessing: Dataset: JWST NIRISS / NISSOSS, Level 2b x1dints spectra, segments seg001–seg003. Extraction: EXTRACT1D (HDU=3). Aggregation: median over integrations to form a 1D spectrum. Cleaning: finite mask + sorting by wavelength. After cleaning: 2038 points per segment. Algorithm / IP (programmer-facing core): Name: RWSS (Resonant-Window Structural Stabilizer) over Ss3. Inputs: flux (x): 1D spectrum (median aggregated, masked, sorted) Ss3 parameters: alpha (EWMA), q (quantile threshold) Resonance parameters: wN (window length), wres (target frequency bin), eps (gate width) Noise test parameters: noiseₚct, seed TDA parameters: m, tau, subsample Baseline Ss3 operator: Shape: G = abs (gradient (flux) ) Memory: Mi = alpha*Mi-1 + (1-alpha) *Gi Threshold: theta = quantile (M, q) Events (optional): Ei = 1 if Mi > theta else 0 Delta-epsilon-like resonance window (gate): Compute a local dominant-frequency proxy omega (x) from abs (gradient (flux) ) using a sliding window (length wN) and FFT; select the maximal non-DC bin index. Gate: W (x) = exp (-0. 5 * ( (omega (x) - wres) / eps) ²) Apply to the gradient channel and reconstruct a gated signal by cumulative integration (cumsum) with mean alignment: dF = gradient (noisyflux) dFgated = dF * Wfluxᵣes = cumsum (dFgated), then shift to match mean (noisyflux) Compute Ss3 Memory on fluxᵣes (same alpha), and use it for validation. Hard validation: Topological Data Analysis (TDA) stability under noisePrimary validation uses a structural criterion on Ss3 Memory M: Compute Memory M for base, for noisy data, and for noisy data with resonance gating. Perform delay embedding on M and compute H1 persistence lifetimes (TDA). Measure drift using Kolmogorov–Smirnov (KS) distance between lifetime distributions. Define DeltaKS = KS (base vs resonance) minus KS (base vs noise). Negative DeltaKS indicates reduced drift (stabilization) relative to noise-only. Fixed test settings (reported here): Noise: 20% additive Gaussian noise (sigma = 0. 20 * std (flux) ) Resonance parameters: wN = 64, wres = 2, eps = 8 TDA parameters: m = 8, tau = 2, subsample = 600 Seeds: 30 random seeds per segment (seg001–seg003), total n = 90 Result (empirical evidence): Across all segments and seeds, resonance gating significantly reduces TDA (H1) drift of the Ss3 Memory representation under 20% noise. ALL (n = 90): mean DeltaKS = -0. 042800 with 95% CI +/- 0. 014810 Segment-level mean DeltaKS values are also negative (seg001–seg003). Scope statement: This record provides empirical, reproducible validation of the resonance-window mechanism on real JWST spectra. It does not claim a complete formal proof of any quantum gravity framework; the operator-level derivation remains separate work. The intent is open verification and extension by independent researchers. Included artifacts: Scripts for reproduction of the TDA seed-scan. CSV outputs with per-seed metrics and summary statistics. Цей запис Zenodo містить повний відтворюваний пакет валідації RWSS/Ss3: резонансне “вікно” (delta-epsilon-подібний частотний gate), інтегроване в Ss3-pipeline, та перевірене на JWST NIRISS/NISSOSS Level 2b *ₓ1dints. fits (seg001–seg003). Пакет включає PDF з формулами та скріншотами запуску, таблиці seed-scan і скрипти для відтворення. Ключова метрика стабілізації: ΔKS = KSᵣes − KSₙoise, де ΔKS < 0 означає, що резонансне вікно зменшує дрейф (структура стабілізується краще, ніж у режимі “noise-only”). DOI: 10. 5281/zenodo. 18926157ORCID: 0009-0000-2209-5862
Serhii Saparniiazov (Sun,) studied this question.