WeinbergAngleFalsifier
The structure encodes the conditions under which the Recognition Science derivation of the Weinberg angle from eight-tick phase geometry would fail. A particle physicist testing electroweak unification against precision data would cite the mismatch propositions to bound allowed deviations. It is introduced as a plain structure definition containing two propositions and an implication to falsehood.
claimLet $M_1$ be the proposition that no consistent $φ$-expression reproduces the observed value of $sin^2 θ_W$ within 5 percent. Let $M_2$ be the proposition that the energy running of the mixing angle fails to follow the predicted $φ$-ladder pattern. The structure asserts that $M_1 ∨ M_2$ implies falsehood.
background
The module derives the weak mixing angle from the eight-tick discrete phase space of Recognition Science. The angle arises as the embedding angle between electromagnetic and weak sectors that is fixed by $φ$ optimization inside that geometry. Upstream, RSNativeUnits supplies the native units in which the $φ$-ladder is defined by rung powers $φ^n$, the coherence quantum equals $φ^{-5}$, and $c=1$. The Alignment module supplies the protocol that maps one agent's coordinate frame to another's.
proof idea
The declaration is a structure definition. It introduces three fields: two propositions that record the mismatch conditions and a third field that asserts their disjunction leads to falsehood. No lemmas are applied and no tactics are used.
why it matters in Recognition Science
The structure supplies the falsification interface for the electroweak mixing derivation aimed at a PRL paper on information-theoretic principles. It rests on the eight-tick octave (T7) and the $φ$-ladder fixed point (T6) from the forcing chain. With zero downstream uses recorded, it remains an open boundary condition that awaits direct numerical confrontation with the measured $sin^2 θ_W ≈ 0.2229$ at the Z scale.
scope and limits
- Does not compute a numerical prediction for $sin^2 θ_W$.
- Does not prove consistency between $φ$-ladder and observation.
- Does not incorporate renormalization-group running from QFT.
- Does not address GUT-scale unification.
formal statement (Lean)
217structure WeinbergAngleFalsifier where
218 /-- φ-predictions don't match observation to within 5% -/
219 phi_mismatch : Prop
220 /-- Running doesn't follow predicted pattern -/
221 running_mismatch : Prop
222 /-- Falsification condition -/
223 falsified : phi_mismatch ∨ running_mismatch → False
224
225/-- Current status: Promising but incomplete. -/