Scalar Generators: Entropy-Coupled Framework for Coherent Manifestation Dynamics

Scalar Generators: Entropy-Coupled Framework for Coherent Manifestation Dynamics

Kevin L. Brown, Independent Researcher
September 2025
10.5281/zenodo.17230855

Informational Physics Ontology Paper

Abstract

This paper formalizes a reproducible, instrument-driven framework for testing Scalar Generators (SGs)—structured stacks of metals, crystals, and geometric substrates—using a dimensionless Scalar Generator Index (SGI). The framework resolves prior ambiguities by (i) preserving the sign of the normalized entropy shift $\Delta H^*$, (ii) fixing the phase-coherence metric to a spectral-purity ratio $\Psi^*$ in a specified band (100 Hz–10 kHz), (iii) specifying entropy estimation (Sturges/Rice binning; Miller–Madow correction), (iv) providing uncertainty propagation and Monte Carlo resampling, (v) enforcing multiple-testing control (Bonferroni/FDR), confidence intervals, and explicit power analysis, and (vi) benchmarking detectability against thermal and Johnson–Nyquist noise. The aim is not to assert metaphysical outcomes but to enable falsifiable, independently replicable measurements of whether SG configurations produce statistically significant departures from sham controls.

Key Contributions

• Dimensionless, sign-aware SGI:
  $\mathrm{SGI}=\alpha \cdot \Delta H^* \cdot (TEI^* \times GID^* \times \Psi^*)$ with all factors bounded in $[0,1]$ except $\Delta H^*\in[-1,1]$; $\alpha$ constrained to $[0.8,1.2]$ and fixed at 1.0 absent documented drift.

• Operational entropy protocol:
  Shannon entropy with Miller–Madow correction; Sturges rule (or Rice for long traces); $H_{\max}=\log_2(N_{\text{bins}})$; $\Delta H^*=(H_{\text{active}}-H_{\text{sham}})/H_{\max}$ (sign preserved).

• Fixed-band phase coherence:
  $\Psi^*=\max |FFT(f)|^2 / \sum |FFT(f)|^2$ over 100 Hz–10 kHz with Hanning windows and overlap, removing DC bias and out-of-band artifacts.

• Statistical rigor and reproducibility:
  Two-sigma criterion, effect sizes (Cohen’s $d$), 95% CIs, Bonferroni/FDR corrections, worked power analysis, noise-floor numerics, error propagation, and sensitivity to $\alpha$.

• Correlation robustness:
  Factor-independence checks with correlation matrices; PCA option if $|r|\ge 0.7$ to avoid redundant amplification in the multiplicative model.

Testability and Protocol

Measurement procedure (replicable):

1. Record matched active vs sham sessions with identical sensors and sampling; pre-register endpoints and analysis.

2. Estimate $H$ from time series using Sturges (or Rice) and Miller–Madow; compute $\Delta H^*$ (sign preserved).

3. Compute $\Psi^*$ via spectral-purity ratio in 100 Hz–10 kHz with Hanning windows.

4. Normalize $TEI^*$ and $GID^*$ to [0,1] from their frameworks.

5. Calculate SGI and its uncertainty (analytic propagation + Monte Carlo).

6. Apply two-sigma decision rule, report $d$, 95% CIs; correct for multiple tests.

7. Benchmark against noise floors; report SNR.

Controls and safeguards: Sham devices matched in geometry/inertia but inert; full blinding (participants and analysts); phase-scrambled nulls to challenge $\Psi^*$; Levene/Welch handling for variance inequality.

Falsifiability

• Null confirmation: If $|\mu_{\text{act}}-\mu_{\text{sham}}| < 2\sigma_{\text{pooled}}$ (post-correction), SGs are indistinguishable from sham.

• Noise dominance: If effects do not exceed thermal/Johnson noise after averaging, claims fail detectability.

• Correlation inflation: If factor correlations $|r|\ge 0.7$ and PCA-adjusted SGI still fails thresholds, the model is rejected.

Scientific Significance

This framework converts speculative ideas into falsifiable, instrumented protocols any laboratory can implement. Even null results are valuable, bounding SG-induced effects relative to noise floors and constraining claims. Positive results, if independently replicated, would motivate deeper exploration of geometry–entropy–coherence coupling within physics.

Foundational Papers in THD Integration

THD: Scalar Field Framework for Quantum–Gravity Unification
https://doi.org/10.5281/zenodo.15686919

THD Equilibrium Index: Axiomatic Stability Metrics
{https://doi.org/10.5281/zenodo.16990955

Phase Harmonic Synchronization (PHS): Cross-Domain Coherence
https://doi.org/10.5281/zenodo.17216677

Entropy–Coupled Harmonic Field Dynamics
https://doi.org/10.5281/zenodo.

Supplemental Independent Review Protocol

Reviewers should evaluate:

• Mathematical coherence: Are $\Delta H^*$, $TEI^*$, $GID^*$, $\Psi^*$ operationally defined?

• Statistical validity: Are sigma tests, CIs, and corrections properly applied?

• Noise realism: Do claimed effects exceed noise limits?

• Correlation robustness: Are factor correlations reported, PCA applied if needed?

• Reproducibility: Are methods sufficient for byte-level re-runs?

Final Output – Reviewers Should Provide:

• Point-by-point rigor assessment

• Numerical scores (0–100%) for: rigor, testability, reproducibility, statistical correctness, noise realism

• Final judgment: Is SGI a valid and falsifiable index for SG experiments?

DOI: 10.5281/zenodo.17230855
Paper Version: SG
Keywords: Scalar Generators, SGI, entropy normalization, spectral purity, coherence metrics, THD integration, falsifiability, noise benchmarking, reproducibility