module module high

`IndisputableMonolith.Gravity.CoerciveProjection`

CoerciveProjection supplies the coercivity constant c = 49/162 for the ILG energy functional in Recognition Science gravity. The value is obtained from the eight-tick net constant together with the projection bound and is cited by any proof that the functional admits a unique minimizer. Researchers working on variational problems in RS gravity reference this module for the numerical coercivity datum. The module consists entirely of definitions and value assertions.

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

background

The module sits in the Gravity domain and imports only the Constants module, whose sole documented object is the RS time quantum τ₀ = 1 tick. It introduces the numerical coercivity constant c = 49/162 together with auxiliary quantities (K_net, C_proj, defect_bound_constant) that encode the eight-tick octave and projection bound. The local theoretical setting is the ILG variational problem whose coercivity is required for existence and uniqueness of energy minimizers.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module provides the numerical constant required to prove that the ILG energy functional possesses a unique minimizer. It directly instantiates the eight-tick octave (T7) landmark and the projection bound from the CPM paper. No downstream declarations are recorded, yet the constant is the explicit input to any uniqueness argument for the ILG functional in the Recognition framework.

scope and limits

Does not derive the numerical value 49/162 from the forcing chain.
Does not prove uniqueness of the ILG minimizer.
Does not apply the constant to concrete physical systems or numerical simulations.

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