IndisputableMonolith.Foundation.CostFirstExistence
The CostFirstExistence module defines recognition existence by the vanishing of J-cost. It states that an object x exists precisely when J(x) equals zero and supplies immediate consequences such as cost positivity for non-existence. The module rests on the imported Cost and Constants modules to anchor the criterion in RS-native units.
claimAn element $x$ exists if and only if $J(x)=0$.
background
The module belongs to the Foundation domain and imports the J-cost function from the Cost module together with the base time quantum from Constants. The Constants module supplies the RS-native time quantum τ₀ = 1 tick. J-cost measures multiplicative deviation from unity under the Recognition Composition Law, and the module uses this to equate existence with zero cost.
proof idea
This is a definition module, no proofs. It introduces the predicate RSExists via the J-cost condition and records direct equivalences together with the positivity statement for non-existent objects.
why it matters in Recognition Science
The module supplies the existence criterion that supports the forcing chain (T0-T8) and later results on the phi-ladder. It implements the recognition existence step that precedes J-uniqueness and the derivation of spatial dimensions.
scope and limits
- Does not derive the explicit algebraic form of J.
- Does not address numerical evaluation of costs.
- Does not connect existence to physical constants or mass formulas.
- Does not treat multi-object compositions or the RCL.