Hypergendered Logic Source

Hypergendered Logic — Page 270

HGL Source Framework · Page 270 of 293 · Source: Hypergendered Logic

CUQB does not apply to a dimensional lift, category lift, or major-stage lift unless those relations are 
separately typed as coordinate succession, which canonical HGL does not do. SUQB remains the 
foundational Supra successor bridge, DUQB remains the dimensional-order bridge, CSQB remains the 
category-entry bridge, and Major Boundary bridges remain separate. 
400. Hyper dimensional coordinate-limit constructor 
Let lambda be a nonzero limit ordinal on the active coordinate axis of Hyper stratum n. The state 
HF<n>[lambda,Omega^n] is no longer merely guaranteed to exist by AxisExistence; it is now constructed as 
a typed Hyper coordinate-limit state HFLim(n,lambda). Its predecessor source domains are bounded prefixes 
rather than full SIH tails. 
HF<n>[lambda,Omega^n] := HFLim(n,lambda, OwnPrefix_HF(n,lambda), 
OppPrefix_HF(n,lambda)). 
OwnPrefix_HF(n,lambda) = {HF<n>[beta,Omega^n] : 1<=beta<lambda}. 
OppPrefix_HF(n,lambda) = {NOT HM<n>[beta,Omega^n] : 1<=beta<lambda}. 
For every beta<lambda the Hyper limit generates the five canonical predecessor roles: 
prefix-superinheritance of the own and structured non-opposite predecessor domains, positive possession of 
the own predecessor profile, exclusion of the opposite predecessor whole-profile, and own-side UD. In 
implementation, PSIH is a symbolic predecessor-domain descriptor; PH/NOT-PH/UD facts are generated 
lazily by queried beta membership. 
HF-limit roles for beta<lambda: PSIH/IH own, PSIH/IH NOT-opposite, PH own, NOT-PH opposite, 
UD own. 
No NOT-FD role is added. A Hyper limit can therefore be globally whole-form improving while local 
flaw-status of predecessor contributions remains unspecified unless another rule supplies it. 
401. Ultra and Apex dimensional coordinate-limit constructors 
UF<n>[lambda,Omega^n] := UFLim(n,lambda, OwnPrefix_UF(n,lambda), 
OppPrefix_UF(n,lambda)). 
AF<n>[lambda,Omega^n] := AFLim(n,lambda, OwnPrefix_AF(n,lambda), 
OppPrefix_AF(n,lambda)). 
For every beta<lambda, an Ultra coordinate limit generates the three Ultra roles: prefix inheritance of 
UF<n>[beta,...], prefix inheritance of NOT UM<n>[beta,...], and UD of the own predecessor coordinate. Apex 
does the exact AF/AM mirror with the same three-role topology. Hyper alone adds PH-own and 
NOT-PH-opposite among these higher named categories. 
Ultra/Apex limit roles for beta<lambda: PSIH/IH own, PSIH/IH NOT-opposite, UD own. 
402. Successor-after-higher-limit rule 
Once a higher-category coordinate limit has been constructed, its next coordinate is generated by the same 
category-specific coordinate-successor schema. Thus HF<n>[lambda+1,...] treats HFLim(n,lambda) as its 
immediate own-side predecessor and the mirror HMLim as its opposite predecessor. UF/AF behave 
analogously. There is no special ad hoc post-limit formula. 
HFLim(n,lambda) -> Hyper-ACSC -> HF<n>[lambda+1,Omega^n]. 
UFLim(n,lambda) -> Ultra-ACSC -> UF<n>[lambda+1,Omega^n]. 
AFLim(n,lambda) -> Apex-ACSC -> AF<n>[lambda+1,Omega^n]. 
403. Generalized Limit Quality Supremum Axiom 
LQSA is generalized from the Supra local axis to every canonically constructed active-coordinate limit. It 
remains a limit-continuity rule, not a successor-quality bridge.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:270.