PlanckScaleFalsifier
Recognition Science derives the Planck length, mass, and time from the golden ratio φ via the forcing chain and a base time τ₀. This structure encodes the three conditions that would falsify the derivation: absence of any φ-connection, nonexistence of a voxel scale, and the ratio τ₀/t_P differing from φ^34. A researcher testing quantum gravity predictions would cite it to articulate the refutation criteria for QG-009 and QG-010. The structure is introduced directly as a definition with no associated lemmas.
claimA structure whose fields are the propositions that the Planck scale lacks a connection to the golden ratio φ, that the voxel scale does not exist, that the ratio of the fundamental time τ₀ to the Planck time t_P is not equal to φ^{34}, and that the first and third of these propositions together imply a contradiction.
background
The module addresses QG-009 and QG-010 by deriving Planck quantities from RS principles. Planck length satisfies l_P = c τ₀ φ^{-n} for some n fixed by the phi-ladder, with similar relations for mass and time. The local setting ties these to the discrete recognition units and the eight-tick periodicity. The φ-connection denotes the explicit dependence on the self-similar fixed point φ arising from T5 J-uniqueness and T6. Voxel scale is the spatial discretization length tied to T7. The ratio τ₀ / t_P = φ^{34} is the concrete prediction obtained from the lengthHierarchy and phiLadderRung siblings. This definition renders the derivation falsifiable by listing the negations of these relations.
proof idea
As a structure definition with empty proof body, the declaration simply declares the four fields: three propositions and one implication. No upstream lemmas are invoked and the construction follows directly from the module's stated falsification criteria.
why it matters in Recognition Science
The structure provides the explicit falsifiability test for the Planck scale results in QG-009 and QG-010. It anchors the derivation to the Recognition Science landmarks T5 through T7 and the predicted φ^{34} ratio on the phi-ladder. With no current downstream theorems, it highlights the open empirical question of whether observations confirm the φ-connection and the exact exponent.
scope and limits
- Does not derive Planck length, mass, or time values.
- Does not establish the φ-connection at Planck scale.
- Does not prove the ratio equals φ^34.
- Does not define voxel scale or τ₀.
- Does not connect to forcing chain steps T0-T8.
formal statement (Lean)
195structure PlanckScaleFalsifier where
196 no_phi_connection : Prop
197 no_voxel_scale : Prop
198 ratio_not_phi34 : Prop
199 falsified : no_phi_connection ∧ ratio_not_phi34 → False
200
201end PlanckScale
202end Quantum
203end IndisputableMonolith