Explanation of eight_tick_forces_D3

(1) In plain English, the declaration states that if the eight-tick cycle length computed from a candidate spatial dimension D equals the fixed constant 8, then D must be exactly 3.

(2) In Recognition Science this matters because the framework requires an 8-tick ledger cycle (from T7). The theorem shows that this cycle length is compatible only with D = 3, supplying a secondary arithmetic forcing that complements the primary topological argument.

(3) The formal statement is theorem eight_tick_forces_D3 (D : Dimension) : EightTickFromDimension D = eight_tick → D = 3. It takes a natural-number dimension D, assumes the definitional equality 2^D = 8, and concludes D = 3. The proof first unfolds the definitions of EightTickFromDimension and eight_tick, then invokes the auxiliary result that any power-of-two equal to 8 forces the exponent 3.

(4) Visible dependencies in the supplied source are the auxiliary theorem power_of_2_forces_D3, the definitional equality eight_tick_is_2_cubed, and the lower-bound result simplicial_loop_tick_lower_bound. The module also imports AlexanderDuality, PhiForcing and LedgerForcing; the primary topological result linking_requires_D3 appears in the same file.

(5) The declaration does not prove the uniqueness of D = 3 under the full set of RS-compatible conditions, nor does it establish the topological linking predicate or the gap-45 synchronization; those are handled by separate theorems in the same module.