module module high

`IndisputableMonolith.Gravity.EnergyProcessingBridge`

This module defines the J-cost functional and supporting energy-processing maps for gravity models. Gravity researchers cite it when linking recognition costs to field gradients and coherence. The module consists entirely of definitions and supporting lemmas with no proofs.

claim$J(x) = \frac12(x + x^{-1}) - 1$ for $x > 0$, the unique cost functional forced by the Recognition Composition Law. Related maps include energy-to-processing-field conversion and energy-distribution creation of gravity modifiers.

background

Recognition Science derives physics from the Recognition Composition Law, which forces the J-cost as the unique functional satisfying J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The supplied DOC_COMMENT states that J(x) equals half the sum of x and its reciprocal minus one. The module sits in the Gravity domain and imports CoherenceFall to supply coherence properties used by the energy maps.

Sibling definitions introduce Jcost_nonneg, Jcost_zero_iff_one, EnergyDistribution, energy_to_processing_field, energy_creates_processing_gradient, EnergyProcessingEquivalence, and energy_distribution_creates_gravity_modifier. These objects translate recognition costs into processing gradients that modify gravitational behavior.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the J-cost and energy-processing bridge used by AcousticPhaseLevitation and WeakFieldSuperposition. It fills the step that converts recognition costs into gravity modifiers within the T5-T8 forcing chain.

scope and limits

Does not derive the Recognition Composition Law.
Does not compute numerical values of physical constants.
Does not address quantum corrections to the classical J-cost.
Does not prove uniqueness of J beyond the RCL hypothesis.

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Gravity.AcousticPhaseLevitation module_import
IndisputableMonolith.Gravity.WeakFieldSuperposition module_import

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Gravity.CoherenceFall module_import

declarations in this module (11)

def Jcost L33
theorem Jcost_nonneg L35
theorem Jcost_zero_iff_one L45
theorem Jcost_one_plus_exact L60
theorem Jcost_quadratic_ratio L69
structure EnergyDistribution L79
def energy_to_processing_field L87
theorem energy_creates_processing_gradient L93
structure EnergyProcessingEquivalence L108
theorem energy_processing_bridge L121
theorem energy_distribution_creates_gravity_modifier L137