Hypergendered Logic Source
Hypergendered Logic — Page 271
ConstructedCoordLimit(C,n,lambda) => Q(C<n>[lambda,Omega^n]) >= sup_{beta<lambda}
Q(C<n>[beta,Omega^n]).
This applies to H/HM, U/UM, and A/AM coordinate-limit constructors. Supra continues using its six-role
LSCC and the same supremum principle. Because the source state is now actually constructed at each limit,
quality is never evaluated on an undefined coordinate term.
404. Complete quality map after axis completion
The quality architecture now has a bridge for every currently defined kind of canonical movement. A single
word such as “advancement” is therefore insufficient for proofs; the proof trace must identify the movement
type.
Supra coordinate successor: SUQB.
Hyper/Ultra/Apex active-axis coordinate successor: CUQB.
Any constructed active-axis limit: generalized LQSA.
Hyper/Ultra/Apex dimensional-order lift: DUQB.
Named category lift: CSQB.
Adopted major-stage transition: Major Boundary Unflaw Bridge.
Once quality magnitude is transfinite, every SUQB/CUQB/DUQB/CSQB-qualified Significant Quality Increase
must cross to a strictly higher cardinal magnitude. Limits preserve at least the supremum of all lower attained
magnitudes. A coordinate limit itself need not add an extra successor jump merely by being a limit; its quality
guarantee is supremum preservation unless another explicit limit-quality axiom strengthens it.
405. Higher-category coordinate-depth rules
The inheritance-depth measure must also distinguish coordinate succession, dimensional superinheritance,
and limits. For active-axis immediate successors, one IH layer can be added relative to the deepest inherited
own/opposite source. For a coordinate limit, depth is the supremum of predecessor depths plus the closure
layer, represented ordinally. SIH/PSIH provenance depth can additionally be tracked in a separate
superinheritance-depth coordinate so that ordinary IH depth is not forced to encode every kind of
provenance.
d_IH(CoordSucc target) = max(d_IH(own predecessor), d_IH(opposite predecessor)) + 1, where
the category schema actually uses IH.
d_IH(CoordLimit(lambda)) = sup_{beta<lambda}(d_IH(C[beta]) + 1).
d_SIH and d_IH are typed depth measures and need not be numerically identical.
406. Strict category-lift map replaces all old endpoint identities
Completed(SF-axis) ->_SIH HF1; SF^Omega_H != HF1.
CompletedDimDomain(HF) ->_SIHdim UF1; completed Hyper endpoint/domain != UF1.
CompletedDimDomain(UF) ->_SIHdim AF1; completed Ultra endpoint/domain != AF1.
The current named order is exactly Supra -> Hyper -> Ultra -> Apex. Any occurrence of Supra -> Hyper ->
Apex -> Ultra is historical/superseded. Any formula equating a completed lower category endpoint/domain
with the new category seed is historical/superseded. Category-lift SQI is not a second jump attached to an
identity; it is a quality comparison between two distinct states linked by an explicit strict construction.
407. Logical deductions newly available
D-AXIS-1: If 1<=beta<lambda, PSIH_i(X;<lambda) entails IH(X[beta]) while not entailing IH(X[lambda]) or
any later coordinate.
D-AXIS-2: HF<n>[alpha+1,Omega^n] entails its five category-specific coordinate-predecessor roles; the
male mirror is exact.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:271.