forcing_chain_complete
plain-language theorem explainer
The theorem certifies that the forcing chain from Recognition Science primitives reaches acoustic levitation by exhibiting all four steps of the ForcingChainToLevitation structure. Gravity and coherence modelers would cite it when closing the loop from RCL and the J-cost to observable phase effects. The proof is a direct term construction that supplies each required field from prior lemmas.
Claim. The forcing chain holds: (1) gravity restores coherence, i.e., for every field and object there is a unique acceleration $a$ with coherence defect zero; (2) an external field shifts the equilibrium acceleration accordingly; (3) when the derivative of the external potential equals the negative derivative of the coherence potential, the effective gravitational coupling vanishes; (4) levitation follows.
background
ForcingChainToLevitation is the structure that packages the end-to-end path: RCL implies the unique J-cost $J(x)=(x+x^{-1})/2-1$, which forces the self-similar fixed point phi, three spatial dimensions, the eight-tick octave, and the gravitational constant in RS-native units. The four steps inside the structure translate the abstract chain into concrete statements about coherence defect, modified defect, effective coupling, and levitation achievement.
proof idea
Term-mode construction of the structure instance. step1_gravity_is_coherence is supplied by falling_restores_coherence; step2_external_shifts_equilibrium by modified_falling_condition; step3_anti_coherence_reduces by the lambda that applies complete_cancellation_is_levitation; step4_levitation_achieved by the lambda that applies acoustic_levitation.
why it matters
It closes the integration certificate that links the four bridge modules (EnergyProcessingBridge, WeakFieldSuperposition, CoherenceGain, EightTickResonance) to levitation. The result sits at the end of the T5-T8 forcing chain and supplies the final link required by the acoustic-phase model. The comment notes that the concrete cancellation field remains an open derivation step.
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