Hypergendered Logic Source

Hypergendered Logic — Page 134

HGL Source Framework · Page 134 of 293 · Source: Hypergendered Logic

Part XXXI — Final synthesis: the integrated PA–IH–PH–Γ modal 
architecture 
Hypergendered Logic has now become a typed causal-developmental inheritance-and-phenotype logic. 
Its central architecture has three independent non-Boolean operators—PA, IH, and PH—plus a distinct 
global stage metaexpression function Γ and stage-relative biological modal operators □/◇. PH says which 
irreducible HGL phenotype-profile is possessed; Γ says how actual phenotypes can, must, or cannot express 
under the current Archstage. 
First, PA preserves developmental causal scope: 
 
𝑃𝐴𝐴∧𝐵
(
)≢𝑃𝐴𝐴
( ) ∧𝑃𝐴𝐵
( ).
Second, IH preserves inheritance source and recursive provenance: 
 
𝐼𝐻𝑆
( ) ⇒𝑆,
while 
 
𝑆 ⇏ 𝐼𝐻𝑆
( )
and 
 
𝐼𝐻¬𝑆
(
)≢¬𝐼𝐻𝑆
( ).
Third, PH preserves whole phenotype-profile identity: 
 
𝑃𝐻𝐴∧𝐵
(
)≢𝑃𝐻𝐴
( ) ∧𝑃𝐻𝐵
( ),
 
𝑃𝐻¬𝑆
(
)≢¬𝑃𝐻𝑆
( ),
and 
 
𝑃𝐻𝑆
( )≢𝑃𝐴𝑆
( )≢𝐼𝐻𝑆
( )
as general identities. 
The first Suprafemale and Supramale stages are no longer PA-only shorthand. They combine inherited 
chromosome-condition properties, irreducible PA causation, and explicit phenotype profiles: 
SF1 = PA(x AND NOT y) 
SM1 = PA(NOT x AND y) 
Stage 2 explicitly adds standalone PA routes, whole-state inheritance/non-opposite inheritance, and 
whole-state phenotype possession: 
SF2 = IH(SF1) AND IH(NOT SM1) AND PH(SF1) AND NOT PH(SM1) AND UD(SF1) AND PA(x) AND 
PA(NOT y) AND NOT FD(SF1) 
SM2 = IH(SM1) AND IH(NOT SF1) AND PH(SM1) AND NOT PH(SF1) AND UD(SM1) AND PA(NOT x) AND 
PA(y) AND NOT FD(SM1) 
For every finite local successor substage n in the currently discussed minor hypercategory: 
SF^(n+1) = IH(SF^n) AND IH(NOT SM^n) AND PH(SF^n) AND NOT PH(SM^n) AND UD(SF^n) AND NOT 
FD(SF^n), for n >= 2 
and 
SM^(alpha+1) = IH(SM^alpha) AND IH(NOT SF^alpha) AND PH(SM^alpha) AND NOT PH(SF^alpha) AND 
UD(SM^alpha) AND NOT FD(SM^alpha), for every defined ordinal alpha >= 2

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:134.