IndisputableMonolith.Gravity.EnergyProcessingBridge
The EnergyProcessingBridge module defines the J-cost function and energy-to-processing mappings for gravity applications in Recognition Science. It supplies the explicit form of J together with distribution and gradient constructions that connect energy to processing fields. Researchers on acoustic levitation and weak-field superposition import these objects directly. The module consists of definitions and elementary algebraic properties with no complex proofs.
claimThe J-cost is the functional $J(x)=½(x+x^{-1})-1$ for $x>0$, forced by the Recognition Composition Law. Energy distributions are mapped to processing fields, and the equivalence states that any energy distribution creates a processing gradient that modifies gravitational behavior.
background
Recognition Science obtains all physics from a single functional equation whose solution is the J-cost. The module sits in the Gravity domain and imports the coherence-fall machinery to define how energy is re-expressed as a processing field. Key objects introduced are the J-cost itself, the EnergyDistribution structure, the map from energy to processing field, and the resulting gravity modifier. These rest on the Recognition Composition Law and the phi-ladder conventions already fixed in the foundational chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the energy-processing bridge required by AcousticPhaseLevitation and WeakFieldSuperposition. It operationalizes the J-cost inside the gravity sector so that downstream results can treat energy distributions as sources of processing gradients without re-deriving the cost functional each time.
scope and limits
- Does not derive the uniqueness of J from the composition law (that is upstream).
- Does not compute explicit numerical spectra for any energy distribution.
- Does not address quantum or higher-dimensional extensions.
- Does not contain the full gravitational field equations (those appear downstream).
used by (2)
depends on (1)
declarations in this module (11)
-
def
Jcost -
theorem
Jcost_nonneg -
theorem
Jcost_zero_iff_one -
theorem
Jcost_one_plus_exact -
theorem
Jcost_quadratic_ratio -
structure
EnergyDistribution -
def
energy_to_processing_field -
theorem
energy_creates_processing_gradient -
structure
EnergyProcessingEquivalence -
theorem
energy_processing_bridge -
theorem
energy_distribution_creates_gravity_modifier