module module moderate

`IndisputableMonolith.Constants.CurvatureSpaceDerivation`

The CurvatureSpaceDerivation module fixes the configuration space dimension for the Recognition ledger as the effective dimension for curvature integration. Researchers building geometric constants from the cubic ledger would cite it when linking ledger structure to spatial forcing. The module organizes this via decomposition definitions and forcing lemmas that establish a 5D total with three spatial dimensions.

claimThe configuration space dimension satisfies $d = 5$, decomposed via canonical decomposition into three spatial dimensions, one temporal dimension, and a balance term, with the spatial count forced to equal 3 by the eight-tick octave and conservation.

background

The module sits inside the Recognition Science constants layer and imports the fundamental time quantum τ₀ = 1 tick together with the alpha derivation from the cubic ledger geometry. The latter supplies the structural 4π via Gauss-Bonnet on vertex deficits of Q₃. In this setting the central object is configSpaceDim, defined as the effective dimension for curvature integration over the Recognition ledger.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the dimensional scaffolding that feeds the T8 step of the unified forcing chain, forcing D = 3 spatial dimensions from the eight-tick octave. It directly supports the alpha derivation by furnishing the spatial geometry of the cubic ledger required for curvature integrals.

scope and limits

Does not derive numerical values for any RS constants.
Does not contain explicit curvature integral expressions.
Does not address extensions to higher-dimensional ledgers.
Does not prove the forcing lemmas; only states them.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Constants.AlphaDerivation module_import

declarations in this module (33)

def configSpaceDim L64
structure ConfigSpaceDecomposition L67
def canonicalDecomposition L74
theorem config_space_is_5D L77
def spatial_dims_forced L86
theorem spatial_dims_eq_3 L88
def temporal_dim_forced L95
theorem eight_tick_forces_temporal L98
def balance_dim_forced L106
theorem balance_from_conservation L109
def angular_contribution_per_dim L134
def total_angular_factor L137
theorem total_angular_is_pi5 L139
def seam_ratio L153
theorem seam_ratio_from_topology L155
def curvature_correction_derived L168
theorem curvature_correction_eq_formula L171
theorem curvature_matches_alpha_derivation L178
theorem pi3_incomplete L187
theorem pi4_incomplete L202
theorem pi6_excess L215
theorem pi_power_eq_pi5_iff L228
theorem curvature_power_family_eq_canonical_iff L244
theorem curvature_power_family_matches_derived_iff L271
theorem curvature_denominator_at_pi5_eq_canonical_iff L281
theorem curvature_numerator_at_pi5_eq_canonical_iff L318
theorem curvature_tuple_uniqueness_bundle L339
theorem curvature_tuple_uniqueness_bundle_vs_derived L352
theorem pi5_uniquely_forced L380
theorem curvature_term_complete_derivation L390
def dual_balance_codimension L417
theorem balance_constraint_codim_1 L419
theorem config_space_complete L423