Hypergendered Logic Source

Hypergendered Logic — Page 275

HGL Source Framework · Page 275 of 293 · Source: Hypergendered Logic

now advance in the same order: define the state, derive its constitutive relations, then evaluate quality or 
phenotype consequences. 
Appendix BO — Axis-Complete Machine-Readable Core 
BSIH_i(X;[a,b)) := bounded source-preserving superinheritance over a<=beta<b. 
PSIH_i(X;<lambda) := BSIH_i(X;[1,lambda)). PSIH excludes beta=lambda and all beta>lambda. 
SIH_i(X[a]) remains tail-oriented through the canonical Omega endpoint. 
HYPER COORD SUCCESSOR (5): IH-own + IH-NOT-opposite + PH-own + NOT-PH-opposite + 
UD-own. 
ULTRA/APEX COORD SUCCESSOR (3): IH-own + IH-NOT-opposite + UD-own. 
HYPER COORD LIMIT: PSIH-own + PSIH-NOT-opposite + PH-own(beta) + 
NOT-PH-opposite(beta) + UD-own(beta) for each beta<lambda. 
ULTRA/APEX COORD LIMIT: PSIH-own + PSIH-NOT-opposite + UD-own(beta) for each 
beta<lambda. 
GENERALIZED LQSA: constructed active-coordinate limit quality >= supremum of all prior 
coordinate qualities. 
CUQB: CoordSucc(S,T) AND UD_T(S) => SQI(Q(S),Q(T)). 
ORDER: Supra -> Hyper -> Ultra -> Apex. STRICT LIFTS: no category endpoint identity. 
Appendix BP — Axis-Complete AI Conformance Tests 
Test AX1. Input: “PSIH(HF;<omega) inherits HF[37] when 37<omega.” Expected: Accept. 
Test AX2. Input: “PSIH(HF;<omega) inherits HF[omega].” Expected: Reject; upper bound is exclusive. 
Test AX3. Input: “PSIH(HF;<omega) inherits HF[omega+1].” Expected: Reject. 
Test AX4. Input: “PSIH(NOT HM;<lambda) equals NOT PSIH(HM;<lambda).” Expected: Reject. 
Test AX5. Input: “SIH(HF[1]) can replace PSIH(HF;<lambda) in a limit constructor.” Expected: Reject; SIH tail 
reaches lambda/future. 
Test AX6. Input: “HF<1>[2,Omega] is HF2.” Expected: Reject. 
Test AX7. Input: “HF<1>[2,Omega] is generated by the Hyper coordinate-successor schema from 
HF<1>[1,Omega].” Expected: Accept. 
Test AX8. Input: “HF2 is generated by a whole-axis dimensional SIH lift.” Expected: Accept. 
Test AX9. Input: “Hyper coordinate successor has five constitutive roles.” Expected: Accept. 
Test AX10. Input: “Ultra coordinate successor has five Hyper roles.” Expected: Reject; Ultra has three. 
Test AX11. Input: “Apex coordinate successor contains UD of its own predecessor.” Expected: Accept. 
Test AX12. Input: “Hyper coordinate successor contains NOT-FD of its own predecessor.” Expected: Reject 
absent strengthening. 
Test AX13. Input: “HFLim(n,lambda) is a first-class limit coordinate.” Expected: Accept. 
Test AX14. Input: “HFLim inherits future coordinates through its prefix closure.” Expected: Reject. 
Test AX15. Input: “HFLim has PH-own and NOT-PH-opposite predecessor roles.” Expected: Accept. 
Test AX16. Input: “UFLim has PH-own by analogy with Hyper.” Expected: Reject. 
Test AX17. Input: “UFLim has UD-own over lower coordinates.” Expected: Accept.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:275.