module module high

`IndisputableMonolith.Gravity.CoerciveProjection`

The CoerciveProjection module defines the coercivity constant c = 49/162 for the ILG energy functional in Recognition Science gravity. The value arises from the eight-tick net constant and projection bound. It ensures the functional has a unique minimizer. Gravity researchers cite these definitions when setting up variational problems. The module consists of constant definitions and basic positivity properties.

claimThe coercivity constant satisfies $c = 49/162$, derived from the eight-tick net constant and projection bound. This value guarantees that the ILG energy functional admits a unique minimizer.

background

The module resides in the Gravity domain and imports IndisputableMonolith.Constants, whose core object is the RS time quantum τ₀ = 1 tick. It introduces definitions for c_coercive (the main value 49/162), K_net (net constant from eight ticks), C_proj (projection bound), defect_bound_constant, and the relation PressureEquivalence. These objects rest on the eight-tick octave (T7) and support coercivity for energy minimization.

proof idea

This is a definition module, no proofs. It organizes content as successive definitions of the constants c_coercive, K_net, C_proj and their positivity statements, ending with the PressureEquivalence relation.

why it matters in Recognition Science

The module supplies the coercivity constant that guarantees a unique minimizer for the ILG energy functional, matching the CPM paper statement. It draws directly from the eight-tick net constant in T7 of the UnifiedForcingChain. The definitions support parent gravity constructions by providing the required bound for energy minimization.

scope and limits

Does not prove existence or uniqueness of the minimizer itself.
Does not derive 49/162 from the Recognition Composition Law.
Does not extend coercivity beyond the ILG functional.
Does not supply numerical approximations or error estimates.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (22)

def c_coercive L34
theorem c_coercive_pos L36
theorem c_coercive_value L39
theorem c_coercive_approx L41
def K_net L48
theorem K_net_value L50
theorem K_net_gt_one L53
def C_proj L58
theorem C_proj_value L60
def defect_bound_constant L64
theorem defect_bound_constant_value L66
structure PressureEquivalence L82
theorem pressure_equiv_from_w L90
theorem operator_positivity_pointwise L100
theorem energy_bounded_below L105
def no_retuning L117
theorem no_retuning_consistent L124
def C_ilg_prefactor L132
theorem C_ilg_prefactor_pos L134
theorem ilg_alpha_is_alphaLock L139
structure CoerciveProjectionCert L143
theorem coercive_projection_cert L149