weak_polarizations_near_8
plain-language theorem explainer
The theorem fixes the total number of weak boson polarization states at nine, obtained as three bosons each with three polarization modes and aligned with the eight-tick octave plus one in the ledger. A physicist counting degrees of freedom for the W and Z fields in RS-native units would cite this result when enumerating electroweak modes. The proof is a direct reflexivity step that unfolds the definition of total weak polarizations as weak boson count times three and confirms the arithmetic identity.
Claim. The total number of polarization states for the weak gauge bosons equals nine: three bosons each carrying three polarization modes, satisfying $3_{bosons} × 3_{modes} = 9$ and matching the eight-tick period plus one.
background
In the weak force emergence module the weak interaction is derived from three-dimensional ledger geometry that yields an SU(2) structure with three generators. The fundamental time quantum is the tick, defined as the RS-native unit with one octave consisting of eight ticks. Total weak polarizations is introduced as the product of the number of weak bosons and three polarization states per boson. Upstream results supply the tick as the base time unit and confirm that the eight-tick period is the fundamental evolution cycle.
proof idea
The proof is a one-line wrapper that applies reflexivity after unfolding the definition total weak polarizations equals weak boson count times three, which reduces directly to the integer nine.
why it matters
This equality anchors the polarization count for the weak bosons to the eight-tick octave of the forcing chain. It supports the emergence of three massive vector bosons from the 3D geometry and closes the mode counting in the electroweak sector. No downstream theorems are recorded, but the result supplies the numerical link between the 8-tick period and the observed three-boson structure.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.