omega_BIT_pos
plain-language theorem explainer
The theorem establishes that the BIT carrier frequency is strictly positive in RS-native units. Quantum computing theorists modeling decoherence via the Bosonic Identity Theorem would cite this to anchor T2 ratio derivations. The proof is a one-line term reduction that unfolds the definition and closes the inequality with positivity of phi via linarith.
Claim. $0 < 5φ$ where $φ$ is the golden-ratio fixed point of the Recognition Composition Law and the BIT carrier is defined as $ω_{BIT} := 5φ$.
background
The module treats decoherence channels that arise when a qubit substrate couples to the Bosonic Identity Theorem carrier at frequency $ω_{BIT} = 5φ$. The carrier is identified with the dark-energy / superconductivity / consciousness-substrate frequency; its positivity is required before any ratio of $T_2$ times can be formed. Upstream, the Constants structure from LawOfExistence bundles the CPM constants and supplies $φ > 0$, while carrier definitions in the engineering modules simply set carrier := 5 * phi.
proof idea
Term-mode proof: unfold omega_BIT, obtain h_phi := Constants.phi_pos, then close the goal by linarith.
why it matters
The result supplies the elementary positivity fact needed for the structural claim that $T_2$ ratios between qubit classes are integer powers of $φ$. It sits inside the algebraic layer of the Bosonic Identity Theorem (T5–T7 forcing chain) and precedes the band and ratio theorems listed as siblings. The module treats specific Z-rung assignments as open hypotheses while the $φ$-power structure itself is theorem-grade.
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