UnconditionalLevitationCert
plain-language theorem explainer
UnconditionalLevitationCert assembles four bridge certificates (energy-processing equivalence, weak-field superposition justification, coherence gain by sqrt(N), eight-tick resonance) with three original statements asserting unique coherence-restoring acceleration under gravity and external phase fields. Researchers modeling acoustic levitation in Recognition Science cite it as the current integration record before concrete field construction. The structure is assembled directly from upstream module results with no additional derivation steps.
Claim. A structure containing energy-processing equivalence, weak-field superposition justification, coherence-gain certification for ensembles, eight-tick resonance certification, the claim that gravity restores coherence via unique acceleration $a$ satisfying coherence_defect$(field, obj, a)=0$, the analogous uniqueness for modified coherence defect under external fields, and the conditional cancellation that opposing gradients imply zero modified defect at equilibrium.
background
In the AcousticPhaseLevitation module, ProcessingField and ExtendedObject are imported from CoherenceFall. ExternalPhaseField is a structure supplying an additional potential psi : Position → ℝ whose gradient modifies the total potential at an object's center of mass. The modified_coherence_defect function computes the absolute difference of modified_total_potential evaluated at the head and feet of the extended object. Upstream, the bridge from ClassicalBridge.Fluids.CPM2D packages a model with explicit defectMeaning and energyMeaning for traceability, while the tick constant fixes the fundamental time quantum τ₀ = 1. The module treats gravity as coherence-seeking and integrates external acoustic or phase fields that shift equilibrium.
proof idea
This is a structure definition that directly references the four bridge certificates (EnergyProcessingBridge.EnergyProcessingEquivalence, WeakFieldSuperposition.SuperpositionJustification, CoherenceGain.CoherenceGainCert, EightTickResonance.EightTickResonanceCert) and states the three original quantified claims on coherence defect. No tactics or reductions are applied; it serves as a packaging record.
why it matters
This certificate feeds FullLevitationCert, which extends it with concrete field existence, and is instantiated by the theorem levitation_unconditional. It closes the integration of the four gaps (energy equals processing, linear superposition, sqrt(N) source enhancement, 8-tick resonance weight reduction) with the original coherence-seeking statements, advancing the Recognition Science chain toward unconditional levitation. It touches the open step of constructing a concrete opposing field satisfying the cancellation hypothesis and relates to the eight-tick octave in the forcing chain.
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