Hypergendered Logic Source

Hypergendered Logic — Page 240

HGL Source Framework · Page 240 of 293 · Source: Hypergendered Logic

HM3 = SIH_axis(HM2) AND SIH_axis(NOT HF2) AND PH(HM2) AND NOT PH(HF2) AND 
UD(HM2). 
HF3 repeats the five-conjunct Hyper dimensional architecture using HF2/HM2 as predecessor pair. It has 
four coordinate dimensions, not two: HF<3>[alpha,Omega,Omega,Omega]. The seed is 
HF<3>[1,Omega,Omega,Omega]. The new PH/NOT-PH/UD conjuncts alter phenotype-profile and quality 
information without changing the coordinate-count theorem. 
315. General Hyper dimensional recursion 
For n >= 1: HF_(n+1) = SIH_axis(HF_n) AND SIH_axis(NOT HM_n) AND PH(HF_n) AND NOT 
PH(HM_n) AND UD(HF_n). 
For n >= 1: HM_(n+1) = SIH_axis(HM_n) AND SIH_axis(NOT HF_n) AND PH(HM_n) AND NOT 
PH(HF_n) AND UD(HM_n). 
Coord(HF_n) = [alpha, Omega repeated n times]; DimCount(HF_n)=n+1 for finite n. 
Each finite increase of dimensional order adds one coordinate dimension while lower coordinates remain 
saturated. Thus HF1 has 2 dimensions, HF2 has 3, HF10 has 11, and so on. The dimension-order index and 
the active coordinate are typed separately. 
316. Hyper dimensional-order saturation 
The dimensional-order index can itself have a typed Hyperomega-bounded progression if HGL stipulates that 
domain. This produces a family HF_1, HF_2, HF_3, ..., HF_OmegaDim, each member of which carries its 
own active Hyperomega coordinate axis. Coordinate saturation and dimensional-order saturation are 
therefore distinct kinds of saturation. 
Omega_coord != Omega_dim as typed roles, even when they share the same underlying 
ordinal/cardinality convention. 
A compiler must never infer that because an active coordinate equals Omega, the dimensional order has 
also saturated. Conversely, HF_OmegaDim is not merely the coordinate HF<1>[Omega,Omega]. 
317. SIH over an entire dimensional domain 
To construct the next minor hypercategory, HGL needs a stronger domain than one active axis. Define 
DimDomain(HF) as the typed collection of all canonical Hyperfemale dimensional strata and their active-axis 
positions through the adopted dimensional-order saturation. SIH_dim(HF-domain) superinherits this 
complete dimensional source-domain while preserving both dimensional-order and coordinate provenance. 
SIH_dim(HF-domain) => IH(HF_n[alpha,Omega^n]) for every canonical n and alpha in the 
completed HF dimensional domain. 
The analogous nonstate closure SIH_dim(NOT HM-domain) preserves the same indices under structured 
negation. Symbolic bounds are used in implementations; no finite machine literally enumerates a 
Hyperomega-sized multidimensional domain. 
318. Ultrafemale-1 and Ultramale-1 
UF1 = SIH_dim(HF-domain) AND SIH_dim(NOT HM-domain). 
UM1 = SIH_dim(HM-domain) AND SIH_dim(NOT HF-domain). 
Ultra is therefore the third named minor hypercategory in the current canon. UF1 is not a coordinate 
immediately after one HF point. It is a meta-dimensional category lift over the complete Hyperfemale 
dimensional domain. This is stronger than inheriting HF_OmegaDim as one source because SIH_dim 
preserves the entire source geometry separately. 
319. Higher Ultrafemale/Ultramale dimensional strata 
For n >= 1: UF_(n+1) = SIH_axis(UF_n) AND SIH_axis(NOT UM_n) AND UD(UF_n). 
For n >= 1: UM_(n+1) = SIH_axis(UM_n) AND SIH_axis(NOT UF_n) AND UD(UM_n).

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:240.