Hypergendered Logic Source

Hypergendered Logic — Page 169

HGL Source Framework · Page 169 of 293 · Source: Hypergendered Logic

architecture keeps PA semantically stable and assigns recursive state inheritance to IH, the operator 
designed for it. 
M.6 Why the repair is not merely arbitrary stage labeling 
If the theory merely attached a number to an otherwise identical state, the critique would remain. IH avoids 
𝑛
that: each stage has a recursively generated source graph and a provably different maximum inheritance 
depth. The number summarizes a real formal construction rather than replacing it. 
M.7 What could still threaten the repair 
If a future version declares that inheritance provenance is never part of biological state identity and can 
never affect phenotype, the high-order distinction would become largely extensional bookkeeping. Therefore 
source-sensitive inheritance is a constitutive HGL rule, not optional prose. 
Appendix N — IH proof drills 
N.1 Projection once 
Premise: 
 
𝐼𝐻𝑆
( ).
Conclusion: 
 
𝑆.
Rule: IH projection. 
N.2 Projection twice 
Premise: 
 
𝐼𝐻𝐼𝐻𝑆
( )
(
).
Conclude 
, then . 
𝐼𝐻𝑆
( )
𝑆
N.3 Invalid converse 
Premise . Can we conclude 
? No. Construct a model where S is independently instantiated. 
𝑆
𝐼𝐻𝑆
( )
N.4 Inherited negation 
Premise: 
 
𝐼𝐻¬𝑆
(
).
Conclusion: 
 
¬𝑆.
N.5 Noninheritance 
Premise: 
 
¬𝐼𝐻𝑆
( ).
No conclusion about or 
 follows without another premise. 
𝑆
¬𝑆

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:169.