module module high

`IndisputableMonolith.Gravity.CoerciveProjection`

The module defines the coercivity constant c = 49/162 for the ILG energy functional in Recognition Science gravity models. Researchers analyzing variational problems with unique minimizers cite this value to close coercivity arguments. It assembles the constant from the eight-tick net constant and projection bound as a pure definition module with no proofs.

claim$c = 49/162$, the coercivity constant arising from the eight-tick net constant and projection bound that guarantees the ILG energy functional has a unique minimizer.

background

Recognition Science gravity rests on the forcing chain through T7, the eight-tick octave of period 2^3, whose net constant combines with a projection bound to produce coercivity. The module imports the base time quantum τ₀ = 1 tick from Constants and introduces supporting quantities such as K_net, C_proj, and defect_bound_constant to enforce a positive lower bound on the energy functional.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

Supplies the numerical constant required for the uniqueness claim on the ILG energy functional minimizer stated in the CPM paper. It encodes the projection bound that follows from the eight-tick structure in the forcing chain and feeds any later theorem that invokes coercivity of the functional.

scope and limits

Does not derive 49/162 from the forcing chain axioms.
Does not prove uniqueness of the energy minimizer.
Does not relate c to other RS constants such as G or alpha.
Does not apply the constant to explicit physical solutions.

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