Hypergendered Logic Source
Hypergendered Logic — Page 22
26. IH laws retained The prior IH laws remain canonical: 𝐼𝐻𝑍 ( ) ⇒𝑍, 𝑍 ⇏ 𝐼𝐻𝑍 ( ), 𝐼𝐻¬𝑍 ( )≢¬𝐼𝐻𝑍 ( ), no automatic IH distribution, no automatic inheritance lifting along implication, no causal-scope destruction, and no inheritance flattening. 27. Inheritance depth grows without finite bound in the successor sector and is extended by Hyperomega/limit rules Define stage-source IH depth dIHstage to count IH nodes whose operand is an already-formed HGL state or its negation. Corrected Stage 1 contains no IH nodes, so its stage-source IH depth is 0 without any need to subtract condition-source IH terms. Set dIHstageSF1=dIHstageSM1=0. At Stage 2, the direct state-source inheritances produce dIHstageSF2=dIHstageSM2=1. For , the recurrence adds an outer state-source IH around an order- state, hence 𝑛≥2 𝑛 dIHstageSFn=dIHstageSMn=n−1 for every finite . 𝑛≥1 PH does not weaken this theorem; it adds a second source-sensitive dimension on top of the inheritance ladder. 28. Phenotype-source order A useful additional measure is the highest whole-stage PH source order. At Stage 1 there is no constitutive PH term. Whole-stage PH source order begins at Stage 2 with positive possession of the same-side predecessor profile, PH(SF1)/PH(SM1), while the opposite predecessor whole-profile is explicitly excluded by NOT PH(SM1)/NOT PH(SF1). At Stage 2, the highest whole-stage source is order 1: PH(SF1), NOT PH(SM1). At Stage 3, it is order 2, and so forth. Thus for : 𝑛≥2 qPHSFn=qPHSMn=n−1. This does not mean there are exactly concrete new visible traits. It means that the stage explicitly 𝑛−1 reaches phenotype-profile sources whose whole-state order is . 𝑛−1 29. Why higher order is not phenotype-count arithmetic Nothing in HGL licenses #TraitsSFn+1=#TraitsSFn+1 or any fixed multiplier.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:22.