IndisputableMonolith.Engineering.IdentityTickBioremediationPilot
The module defines the J-cost reduction factor as 5/2 - φ together with its elementary inequalities for identity tick bioremediation pilots. Engineers applying Recognition Science cost models to bioremediation would cite these definitions to bound savings at the golden ratio. The module consists of direct definitions followed by short algebraic verifications of positivity and monotonicity.
claimThe J-cost reduction factor is defined by $1 - J(φ) = 5/2 - φ$, where $J(x) = (x + x^{-1})/2 - 1$ and $φ$ satisfies $φ^2 = φ + 1$.
background
Recognition Science obtains the J functional equation from the forcing chain T0-T8 and uses it to define cost via the composition law. The module imports the RS time quantum τ₀ = 1 tick from Constants and the cost primitives from the Cost module. It specializes these to the reduction factor 5/2 - φ for identity-tick bioremediation calculations.
proof idea
This is a definition module, no proofs. reductionFactor is set directly to 5/2 - φ; the remaining declarations verify positivity, the bound less than one, and strict anti-monotonicity by direct substitution and arithmetic.
why it matters in Recognition Science
The module supplies the reduction factor used by IdentityTickBioremediationPilotCert and the surrounding engineering certificates. It applies the core J-cost and φ fixed point to bioremediation pilots, closing the step from abstract cost definitions to concrete engineering bounds.
scope and limits
- Does not compute numerical values for specific bioremediation parameters.
- Does not address experimental validation or field data.
- Does not extend the reduction factor to other engineering domains.
- Does not incorporate higher rungs of the phi-ladder or gap(Z) corrections.
depends on (2)
declarations in this module (13)
-
def
reductionFactor -
theorem
reductionFactor_pos -
theorem
reductionFactor_lt_one -
theorem
reductionFactor_band -
def
residualFraction -
theorem
residualFraction_zero -
theorem
residualFraction_pos -
theorem
residualFraction_lt_one_of_pos -
theorem
residualFraction_strict_anti -
theorem
residualFraction_succ -
structure
IdentityTickBioremediationPilotCert -
def
identityTickBioremediationPilotCert -
theorem
bioremediation_one_statement