IndisputableMonolith.LightCone.StepBounds
LightCone.StepBounds supplies saturation lemmas for step-wise bounds on light-cone reach time and radius. Researchers deriving propagation limits in Recognition Science cite the module to control equality cases in cone bounds. The argument reduces directly to the time quantum from the imported Constants module via algebraic comparison of summed bounds.
claimThe saturation lemma asserts that the light-cone bound holds with equality precisely when each step attains its individual bound: reach time and radius equal the sum of per-step maxima.
background
The module sits in the LightCone domain and imports Constants, where the fundamental RS time quantum is defined as τ₀ = 1 tick. It organizes step bounds that refine reachability after successive increments, using the time quantum to normalize displacements. The supplied saturation restatement gives the equality condition under which summed step bounds coincide with total reach.
proof idea
This is a lemma collection module whose main saturation result follows by direct algebraic comparison of the reach time and radius expressions against their per-step bounds.
why it matters in Recognition Science
The module supplies the saturation condition required by downstream light-cone reachability arguments. It fills the step-bound component that links individual increments to global cone limits, consistent with the eight-tick octave structure in the forcing chain.
scope and limits
- Does not derive the light-cone geometry itself.
- Does not treat non-saturating trajectories.
- Does not connect bounds to mass ladder or coupling constants.