Hypergendered Logic Source

Hypergendered Logic — Page 37

HGL Source Framework · Page 37 of 293 · Source: Hypergendered Logic

𝑑𝐼𝐻𝐼𝐻𝑆
( )
(
) = 1 + 𝑑𝐼𝐻𝑆
( ).
Therefore 
 
𝑑𝐼𝐻𝐼𝐻𝐼𝐻𝑆
( )
(
)
(
) = 2 + 𝑑𝐼𝐻𝑆
( ),
which differs from 
. Hence the two expressions are not identical under inheritance-sensitive state 
𝑑𝐼𝐻𝐼𝐻𝑆
( )
(
)
identity even though both project down to . 
𝑆
Proposition 20 — Inheritance depth of a finite local successor substage 
Theorem. For every finite 
, 
𝑛≥1
dIHstageSFn=dIHstageSMn=n−1. 
Proof. Corrected SF1 and SM1 contain no IH nodes, so their stage-source IH depth is 0. Stage 2 contains 
IH(SF1)/IH(SM1) plus inherited opposite-side non-state sources, so its stage-source depth is 1. Each 
Stage-(n+1) successor adds an outer state-source IH layer around Stage-n sources, increasing maximum IH 
depth by one. PH, UD, and FD remain separate typed relations. Hence d_IH(SF^n)=d_IH(SM^n)=n-1 for 
finite n. QED. 
Proposition 21 — The hierarchy does not truth-functionally need to be novel at 
every step in order to be a new full HGL state 
A later ¬SMn can be truth-functionally implied by an earlier stronger exclusion. Nevertheless IH¬SMn has a 
different source label and inheritance depth from IH¬HMk for k<n. Since source and depth are part of full 
HGL state identity, the stage can be new even when its Boolean shadow is partly redundant. 
This proposition is not a trick. It states the explicitly intensional nature of HGL: developmental provenance is 
modeled as biologically relevant state structure, not discarded commentary. 
Proposition 22 — Female typing does not entail standalone 
 
𝑃𝐴𝑥
( )
The axiom 
FemaleTypeSF1 
is a category assignment. It does not permit 
SF1⇒PAx. 
Therefore the theory can consistently maintain both PA irreducibility and the claim that Stage-1 Suprafemale 
is female. 
Proposition 23 — Exact local-substage predicates are coherent in the finite 
strict-depth sector 
Define 
ExactSFn:=SFn∧¬SFn+1. 
Since SFn+1 has inheritance depth n and SFn depth n−1, the full HGL states are not identical. The same 
applies to ExactSMn. Thus the earlier saturation problem caused by purely Boolean componentwise 
recursion is avoided.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:37.