Hypergendered Logic Source

Hypergendered Logic — Page 235

HGL Source Framework · Page 235 of 293 · Source: Hypergendered Logic

Appendix AN — Limit/Transordinal Conformance Tests for AI 
Test L1. “SF^omega exists because omega is written as a superscript.” Expected: Reject; require LSCC. 
Test L2. “After LSCC constructs SF^omega, LQSA may evaluate Q(SF^omega).” Expected: Accept. 
Test L3. “SF^(omega+1) uses the same six-conjunct successor schema with alpha=omega.” Expected: 
Accept. 
Test L4. “SF^omega has one immediate predecessor.” Expected: Reject. 
Test L5. “SF^omega entails SF37.” Expected: Accept via closure IH + projection. 
Test L6. “SF^omega entails NOT SM37.” Expected: Accept via closure IH + projection. 
Test L7. “SF^omega entails NOT FD(NOT SM37).” Expected: Reject absent strengthening axiom. 
Test L8. “A huge delta improvement inside m7 is SQI.” Expected: Reject if mu stays m7. 
Test L9. “m7 to m8 is SQI.” Expected: Accept. 
Test L10. “aleph_0 to aleph_0 with larger delta is transfinite SQI.” Expected: Reject. 
Test L11. “aleph_0 SQI successor must be at least aleph_1.” Expected: Accept. 
Test L12. “d(SF^omega)=omega under canonical closure.” Expected: Accept. 
Test L13. “d(NOT SF^omega)>d(SF^omega).” Expected: Reject; negation adds no IH depth. 
Test L14. “Later Gamma must include every earlier possible phenotype.” Expected: Reject. 
Test L15. “K axiom is valid at one fixed address under normal Kripke semantics.” Expected: Accept. 
Test L16. “Actual p implies Box p.” Expected: Reject. 
Test L17. “SF^(omega+3) can share current outward phenotype with SF5.” Expected: Accept as 
model-consistent possibility, not deduction of actual similarity. 
Test L18. “Limit profile equals union of predecessor profiles.” Expected: Reject absent an explicit reduction 
axiom. 
Test L19. “Limit closure may generate emergent whole-limit phenotypes.” Expected: Accept as CI/ILL. 
Test L20. “Address cardinality aleph_omega and quality aleph_omega are the same variable.” Expected: 
Reject. 
Appendix AO — Expanded Quality and Aleph Proof Catalogue 
AO.1 Base finite ascent: repeated SUQB + unified SQI makes mu strictly rise at every canonical finite 
successor. 
AO.2 Omega limit: LSCC constructs the limit; LQSA takes the supremum; minimum lower bound aleph_0. 
AO.3 Omega successor: successor schema + UD + SUQB + successor-cardinal minimality -> aleph_1 
minimum. 
AO.4 Finite post-omega induction: omega+n -> aleph_n minimum. 
AO.5 Omega+omega: LSCC + LQSA + continuity sup_n aleph_n=aleph_omega. 
AO.6 Omega*2+k: successors continue at least aleph_(omega+k). 
AO.7 General beta: transfinite induction yields at least aleph_beta where local stage construction is defined. 
AO.8 CH-independence: no-cardinal-between aleph_alpha and aleph_(alpha+1) is definitional 
successor-cardinal structure, not CH. 
AO.9 Boundary construction rule: current named hypercategory boundaries are strict nonidentity 
constructions. Therefore there is no identity-boundary double-count problem. CSQB compares the 
completed lower category/domain with the newly constructed higher-category seed only because they are 
distinct typed states. A compiler must reject any proof that simultaneously assumes endpoint identity and a 
nontrivial category-lift SQI.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:235.