CFM Formal Mechanism

This paper assembles the formal foundations of the energy-extraction mechanism proposed for the Chiral Fractal Modulator (CFM), a device comprising a counter-wound pair of golden-ratio logarithmic spiral conductors within a Casimir-regime cavity, analysed within the Master Equation Framework (MEF) on the internal manifold K₈ = [(CP² × S²) ×w (T²/Z₂)]Spinᶜ. We fix notation, separate results imported from the MEF corpus and the established literature from the physical postulates specific to the device, and prove four lemmas. (i) The Kaluza–Klein gauge kinetic function on K₈ is a function of the Quantum Coherence Dilaton ΦQC, while gauge coupling ratios are independent of ΦQC. (ii) The effective potential V(ΦQC) = V(λ e^-8ζΦQC + β e^-10ζΦQC) with λ < 0 < β possesses a unique, stable, global minimum ΦQC; the excess density ρᵣₑₛ := V - V(ΦQC) is non-negative, vanishes only at the minimum, and is bounded above for upward displacement by V(ΦQC). (iii) Rotation of the counter-wound logarithmic-spiral pair about its longitudinal axis admits no non-trivial invariance — continuous, discrete, or combined with scaling — and the laboratory-frame gap under rigid rotation at angular velocity Ω is d(θ, t) = 2a₀ (b(θ - Ω t)). (iv) The Spinᶜ holonomy about the ω-cycle factorises into a topologically fixed quarter-period lift eiπ/2 and a state-dependent geometric phase that is trivial precisely in the vacuum. Conjectures on rectification and on the thermodynamic signature are stated with explicit truth conditions. The paper closes with a pre-registered experimental discrimination protocol (§18): a differential calorimetric measurement of a chiral article against a matched, driven, non-axisymmetric achiral control, with a quantified milliwatt-scale prediction band, an enantiomer sign test, and an outcome map assigning to each measurement result its exact consequence for the framework — executable by an independent laboratory under a stated disclosure boundary. A named conjecture on source proximity (§19) adds a blinded distance protocol with derived-in-form spatial signatures and an explicit pre-registered falsification condition. The paper is standalone: every framework-specific result it uses is derived in full in Appendices B–G; only the published literature is cited. Statements suitable for machine verification are collected in Appendix A. Every numbered statement carries a classification: framework result derived in this paper (F), physical postulate (P), theorem of the main text (T), or conjecture (C).