Hypergendered Logic Source
Hypergendered Logic — Page 240
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.