copy-paste

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 / NIS_SOSS, 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: noise_pct, seed

• TDA parameters: m, tau, subsample

Baseline Ss3 operator:

1. Shape: G = abs(gradient(flux))

2. Memory: M[i] = alpha*M[i-1] + (1-alpha)*G[i]

3. Threshold: theta = quantile(M, q)

4. Events (optional): E[i] = 1 if M[i] > 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(noisy_flux)
  dF_gated = dF * W
  flux_res = cumsum(dF_gated), then shift to match mean(noisy_flux)

• Compute Ss3 Memory on flux_res (same alpha), and use it for validation.

Hard validation: Topological Data Analysis (TDA) stability under noise
Primary 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 Delta_KS = KS(base vs resonance) minus KS(base vs noise). Negative Delta_KS 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 Delta_KS = -0.042800 with 95% CI +/- 0.014810

• Segment-level mean Delta_KS 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/NIS_SOSS 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 = KS_res − KS_noise, де ΔKS < 0 означає, що резонансне вікно зменшує дрейф (структура стабілізується краще, ніж у режимі “noise-only”).

  DOI: 10.5281/zenodo.18926157
  ORCID: 0009-0000-2209-5862