IndisputableMonolith.Support.Powers
The Support.Powers module supplies the base identity φ^0 = 1 for integer powers of the golden ratio φ. It acts as low-level infrastructure for phi-ladder calculations in mass formulas and forcing-chain derivations. Researchers handling exponentiation in the self-similar fixed point would reference this case. The module contains one direct lemma with no extended argument.
claim$φ^{0} = 1$ for the self-similar fixed point $φ$ of the Recognition Composition Law.
background
Recognition Science derives all physics from one functional equation. The imported Constants module defines the fundamental time quantum τ₀ = 1 tick. The golden ratio φ is the self-similar fixed point forced at T6, satisfying the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). This module supplies integer power support to operate on the phi-ladder appearing in the mass formula yardstick * φ^(rung - 8 + gap(Z)).
proof idea
This is a definition module containing a single convenience lemma for the zero-exponent case. The argument applies the definition of integer exponentiation directly to obtain the identity.
why it matters in Recognition Science
The module supplies base-case support for the phi-ladder used in mass formulas and the eight-tick octave (T7). It completes the zero-power requirement for the self-similar fixed point φ at T6 in the forcing chain. No downstream theorems are recorded, indicating foundational infrastructure for higher derivations including D = 3 and the alpha band.
scope and limits
- Does not derive the numerical value or continued fraction of φ.
- Does not treat real or complex exponents.
- Does not address the Berry creation threshold or Z_cf.