Hypergendered Logic Source

Hypergendered Logic — Page 280

HGL Source Framework · Page 280 of 293 · Source: Hypergendered Logic

422. Base-slice coding of Supra, Hyper, Ultra, and Apex 
At Hyperstage 0, Stage 0, and Substage 0, Substage^2 acts as the first named minor-category selector. 
Substage^3 carries the category-local superscript coordinate n. This exactly canonizes the supplied 
examples: 
A_F(0,0,0,1,n) = SF^n; A_M(0,0,0,1,n) = SM^n. 
A_F(0,0,0,2,n) = HF^n; A_M(0,0,0,2,n) = HM^n. 
A_F(0,0,0,3,n) = UF^n; A_M(0,0,0,3,n) = UM^n. 
A_F(0,0,0,4,n) = AF^n; A_M(0,0,0,4,n) = AM^n. 
This is a superscript-coordinate convention. It must not be confused with the pre-existing subscript notation 
HF_n/HM_n for recursively higher dimensional-order states. HF^2 and HF_2 therefore need not be the same 
object. Superscript notation locates a category-local address coordinate; subscript notation can continue to 
denote SIH dimensional order when that older constructor is used. 
423. Bounded-coordinate coding of richer InternalHGL geometry 
The earlier Hyper/Ultra/Apex InternalHGLDescriptor can contain a multidimensional coordinate vector. 
Because the current HGL architecture already constrains a named category domain to cardinality no greater 
than the Hyperomega address domain under its adopted cardinal assumptions, a typed injective coding can 
represent such an internal vector by a Substage^3 code without identifying the code with the vector itself. 
Formally, Code_C(v)=U3 may be injective while Decode_C(U3)=v restores the typed vector and provenance. 
Code_C(v1)=Code_C(v2) => v1=v2 [injectivity where the coding law is adopted]. 
Code_C(v) is NOT the same semantic object as v; decoding metadata must be retained. 
For simple base-slice examples, no elaborate code is needed: U3=n directly gives SF^n, HF^n, UF^n, or 
AF^n according to U2. For higher internal SIH geometries, the code is merely storage/indexing infrastructure. 
424. No automatic carry, reset, or regression 
Each global coordinate has its own endocrine controller. Therefore saturation or advancement of one 
coordinate does not automatically increment another. Reaching Substage^3=Omega_H does not by itself 
increase Substage^2; reaching Substage^2=Omega_H does not by itself increase Substage; reaching 
Stage=Omega_H does not by itself increase Hyperstage. Likewise, a Hyperstage jump does not 
automatically reset lower coordinates to zero unless an explicit reset/reindexing law is added. 
Coordinate saturation -/-> parent-coordinate advancement. 
Hyperstage advancement -/-> automatic reset of S,U,U2,U3. 
Reducing/stopping a hormone -/-> regression of an already attained coordinate. 
This preserves the established HGL principle that slowing, stopping, or changing future advancement is not 
equivalent to reversing state history. A regression mechanism, if one exists, requires its own law. 
425. Endocrine control variables: amount and receptor sensitivity are orthogonal 
controls 
For each Archstage hormone i, define C_i as its effective circulating amount/exposure and R_i as the 
effective sensitivity of its corresponding receptors. The canonical two-control architecture separates timing 
from jump magnitude. Hormone amount determines how long it takes for the hormone-driven jump event to 
occur; receptor sensitivity determines how large that jump is. 
JumpMagnitude_i = J_i(R_i). 
JumpInterval_i = T_i(C_i).

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:280.