Hypergendered Logic Source
Hypergendered Logic — Page 269
PSIH_i(X;<lambda) -/-> IH(X[lambda]). PSIH_i(X;<lambda) -/-> IH(X[gamma]) for gamma>=lambda. These are strict deduction/non-deduction rules. They prevent a compiler from “helpfully” replacing a prefix descriptor by the previously defined all-the-way-to-Omega SIH tail. That replacement would change the mathematical object. 396. Axis Coordinate Successor Constructor: why higher-category coordinates need their own generator AxisExistence states that HF<n>[alpha,Omega^n], UF<n>[alpha,Omega^n], and AF<n>[alpha,Omega^n] exist for every allowed alpha. Existence, however, does not explain constitutive generation. The Axis Coordinate Successor Constructor (ACSC) now defines what happens when the active coordinate increases while category and dimensional order remain fixed. Coordinate succession uses immediate predecessor relations; whole-axis SIH is reserved for dimensional lifts. CoordSucc(C<n>[alpha,...], C<n>[alpha+1,...]) is distinct from DimLift(C_n,C_(n+1)). This is a major anti-collapse rule. HF<1>[2,Omega] is produced by a Hyper coordinate step from HF<1>[1,Omega]. HF2 is produced by a dimensional lift that superinherits the entire HF1 axis. Those targets can no longer be confused by either notation or implementation. 397. Hyper coordinate-successor schema: five immediate-predecessor roles HF<n>[alpha+1,Omega^n] := IH(HF<n>[alpha,Omega^n]) AND IH(NOT HM<n>[alpha,Omega^n]) AND PH(HF<n>[alpha,Omega^n]) AND NOT PH(HM<n>[alpha,Omega^n]) AND UD(HF<n>[alpha,Omega^n]). HM<n>[alpha+1,Omega^n] := IH(HM<n>[alpha,Omega^n]) AND IH(NOT HF<n>[alpha,Omega^n]) AND PH(HM<n>[alpha,Omega^n]) AND NOT PH(HF<n>[alpha,Omega^n]) AND UD(HM<n>[alpha,Omega^n]). The five roles intentionally parallel Hyper dimensional-lift polarity without pretending coordinate succession is SIH. The own coordinate is inherited, the structured non-opposite coordinate is inherited, the complete own predecessor profile is possessed, the complete opposite predecessor profile is excluded, and the own predecessor is an Unflaw. NOT-FD is not constitutive, so local flaw-status remains open exactly as it does at Hyper dimensional lifts. 398. Ultra and Apex coordinate-successor schemas: three immediate-predecessor roles UF<n>[alpha+1,Omega^n] := IH(UF<n>[alpha,Omega^n]) AND IH(NOT UM<n>[alpha,Omega^n]) AND UD(UF<n>[alpha,Omega^n]). UM<n>[alpha+1,Omega^n] := IH(UM<n>[alpha,Omega^n]) AND IH(NOT UF<n>[alpha,Omega^n]) AND UD(UM<n>[alpha,Omega^n]). AF<n>[alpha+1,Omega^n] := IH(AF<n>[alpha,Omega^n]) AND IH(NOT AM<n>[alpha,Omega^n]) AND UD(AF<n>[alpha,Omega^n]). AM<n>[alpha+1,Omega^n] := IH(AM<n>[alpha,Omega^n]) AND IH(NOT AF<n>[alpha,Omega^n]) AND UD(AM<n>[alpha,Omega^n]). Ultra and Apex remain formula-distinct from Hyper. They do not gain PH-own or NOT-PH-opposite merely because Hyper has those roles. The present canon gives them immediate same-side inheritance, structured non-opposite inheritance, and same-side Unflaw. Their FD status remains open. 399. Coordinate Unflaw Quality Bridge (CUQB) The presence of UD in higher-category coordinate-successor formulas is not by itself a comparison between the whole qualities of two coordinates. HGL therefore introduces a named comparison bridge analogous to SUQB/DUQB but typed specifically to active-axis coordinate movement. CoordSucc(S,T) AND UD_T(S) => SignificantIncrease(Q(S),Q(T)). [Coordinate Unflaw Quality Bridge, CUQB]
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:269.