Hypergendered Logic Source

Hypergendered Logic — Page 22

HGL Source Framework · Page 22 of 293 · Source: Hypergendered Logic

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.