ForcingChainToLevitation
plain-language theorem explainer
The structure packages four propositions linking Recognition Science cost primitives through coherence-seeking gravity to acoustic levitation under opposing external phase gradients. A physicist modeling modified gravity or acoustic manipulation would cite it to trace how the same forcing chain that produces G = phi^5 also forces coupling cancellation. It is assembled as a direct record of the four successive steps with no additional derivation.
Claim. A structure asserting: (i) for any gravitational field and object there exists a unique acceleration $a$ such that the coherence defect vanishes; (ii) for any field, external phase field, and object there exists a unique acceleration where the modified coherence defect vanishes; (iii) if the external phase derivative at the center of mass opposes the gravitational potential derivative then the effective gravitational coupling is zero; (iv) under the same opposition the modified defect at zero acceleration is zero.
background
In the AcousticPhaseLevitation module gravity is treated as coherence-seeking via the CoherenceFall framework, where coherence_defect quantifies deviation from the equilibrium that minimizes recognition cost. The effective_gravitational_coupling is the magnitude |deriv field.phi + deriv ext.psi| at the object's center of mass. Upstream results establish that the Recognition Composition Law together with J-uniqueness (T5) forces the self-similar fixed point phi (T6), three spatial dimensions (T8), and the eight-tick octave (T7) that set the coherence landscape; the module imports CoherenceFall to encode that gravity restores coherence and WeakFieldSuperposition to handle linear potential combinations.
proof idea
The definition enumerates the four steps directly as structure fields. Step 1 records uniqueness of the zero-defect acceleration from coherence_defect. Step 2 extends the uniqueness claim to modified_coherence_defect. Step 3 invokes the definition of effective_gravitational_coupling to obtain cancellation when derivatives oppose. Step 4 confirms that the same opposition condition places the modified defect at zero acceleration. No tactics or lemmas are applied beyond the sibling definitions.
why it matters
The structure is instantiated by the downstream theorem forcing_chain_complete, which certifies that the chain from RCL through J-uniqueness, phi, D=3, eight-tick resonance, G=phi^5, and coherence-seeking gravity to external-phase cancellation is complete. It directly fills the final two links in the module doc-comment outline, showing levitation is forced by the same primitives that force gravity. No open scaffolding remains in this declaration.
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