full_levitation_cert
plain-language theorem explainer
The declaration certifies that full acoustic phase levitation holds once energy processing, linear field superposition, sqrt(N) coherence gain, 8-tick resonance, and coherence-restoring acceleration are all verified. Gravity modelers working in Recognition Science would cite it to close the integration gap between phase fields and gravitational equilibrium. The proof is a direct term construction that assembles the FullLevitationCert record by plugging in the upstream certified lemmas for each required field.
Claim. A complete certificate for unconditional levitation exists: for any differentiable gravitational processing field there is an external phase field whose gradient exactly cancels the gravitational gradient at the object center of mass, the modified coherence defect vanishes at zero acceleration, energy is processed through the bridge, fields superpose linearly, coherence gain scales as sqrt(N), and 8-tick resonance reduces effective weight.
background
FullLevitationCert is the structure that records the closure of all gaps in the levitation argument; it extends UnconditionalLevitationCert by adding the concrete existence of an external phase field that cancels the gravitational gradient while driving the modified coherence defect to zero. The module works inside the Recognition Science treatment of gravity as coherence restoration, where the coherence defect is the absolute value of twice the energy times the sum of gravitational and external phase gradients. Upstream results supply the pieces: falling_restores_coherence states that the unique acceleration restoring coherence is exactly the gravitational acceleration g = -∇Φ; modified_falling_condition shows that an external phase field shifts this equilibrium to a = -(∇Φ_grav + ∇Φ_ext); acoustic_levitation proves that exact cancellation of the two gradients forces the defect to zero; levitation_field_exists constructs the required external field for any differentiable gravitational field.
proof idea
The term proof builds the FullLevitationCert record by direct field assignment. gap1_energy_is_processing is taken from EnergyProcessingBridge.energy_processing_bridge; gap2_superposition from WeakFieldSuperposition.superposition_justified; gap3_coherence_gain from CoherenceGain.coherence_gain_certified; gap4_resonance from EightTickResonance.eight_tick_resonance_certified; gravity_is_coherence from falling_restores_coherence; external_shifts_equilibrium from modified_falling_condition; cancellation_levitates applies acoustic_levitation; and concrete_field_exists applies levitation_field_exists.
why it matters
This theorem completes the integration certificate for acoustic phase levitation inside the Recognition Science gravity development, closing the chain from energy processing through coherence gain and 8-tick resonance to a concrete canceling field. It sits at the end of the AcousticPhaseLevitation module and supplies the final concrete_field_exists clause required by FullLevitationCert. The result directly uses the eight-tick resonance reduction of weight and the coherence-restoring acceleration property, confirming that external phase control can null the effective gravitational force while preserving coherence.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.