IndisputableMonolith.Foundation.ThreeSubstrateValidationCert
The module certifies that all three validation substrates share the J-cost fixed point at x=1. Researchers validating multi-substrate consistency in the Recognition Science J-cost model would cite it. The argument applies the multi-channel J-cost extension independently to each substrate to establish the common fixed point.
claimThe three validation substrates satisfy the fixed-point condition $J(1)=0$ under the multi-channel extension $J_n(x)=∑_i J(x_i)$.
background
The module imports the J-cost definition from IndisputableMonolith.Cost and the multi-channel generalisation from MultiChannelJCost, where $J_n(x)=∑_i J(x_i)$ for $x∈ℝ^n$ with all $x_i>0$. This additive extension of J-cost to n independent channels is the setting for the ALEXIS B5 formalisation. The module introduces sibling objects including ValidationSubstrate, shared_fixed_point, and ThreeSubstrateCert to encode the uniform fixed point at x=1 where J(1)=0.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supports ThreeSubstrateCert in the foundation layer. It fills the validation step showing uniform J-cost fixed points across substrates, consistent with the multi-channel extension in the ALEXIS B5 formalisation and the J-uniqueness step of the forcing chain.
scope and limits
- Does not derive the functional form of J itself.
- Does not address numerical evaluation of J at points other than x=1.
- Does not extend the certification to four or more substrates.
- Does not prove invariance under channel coupling.
depends on (2)
declarations in this module (13)
-
inductive
ValidationSubstrate -
theorem
validationSubstrateCount -
theorem
shared_fixed_point -
theorem
shared_descent -
theorem
shared_symmetry -
def
languageModelAlignmentFraction -
theorem
lm_fraction_eq -
theorem
lm_above_threshold -
def
photonicCodeRate -
def
photonic_code_rate_rfl -
theorem
seven_eighths_from_F2_cube -
structure
ThreeSubstrateCert -
def
threeSubstrateCert