Hypergendered Logic Source
Hypergendered Logic — Page 237
For every defined ordinal alpha>=2, successor alpha+1 = two IH + one positive same-side PH + one
opposite NOT-PH + one same-side UD + one same-side NOT-FD.
For every canonical limit lambda, SF^lambda=LimF(lambda) and SM^lambda=LimM(lambda) with
set-indexed predecessor closure.
Limit female closure generates IH/PH/UD for every SF^beta and NOT SM^beta below lambda, plus NOT-FD
for every SF^beta; male mirror exact.
Opposite-source UD/FD status is intentionally not automatic: Opposite-Profile Exclusion leaves it open.
Q=<mu,delta>; SQI iff mu rises. Within-magnitude improvement is not SQI.
LQSA applies only to constructed limits. SUQB applies to canonical successors.
Post-omega minimum: Q(SF^(omega+beta)), Q(SM^(omega+beta)) >= aleph_beta where the stage system
defines the relevant ordinals.
d_IH(base)=0; d(NOT S)=d(S); d(IH(S))=d(S)+1; conjunction=max; limit=sup.
Fixed-address modality is normal K; no automatic S4/S5 and no cross-address possibility-set inclusion.
Exact phenotype requires PH profile membership or explicit causal law; otherwise use HI/CI/ILL/OPEN.
Womanhood/manhood maturation remains distinct from Archwomanhood/Archmanhood address.
Address cardinality, IH depth, whole-quality magnitude, and visible phenotype are different typed
dimensions.
Part XLII — Authoritative SIH Superinheritance, Hyperdimensional Coordinates, and Strict Category-Lift
Revision
This Part is authoritative over every earlier HGL statement that treats Hyperfemale/Hypermale as a flat
one-dimensional minor-hypercategory ladder, identifies the completed Supra Hyperomega endpoint with
HF1/HM1, places Apex before Ultra, or represents every Archaddress by only one ordinal substage
coordinate. The lower SF/SM PA-IH-PH-UD-FD successor and limit-state logic remains the one-axis
foundation. This Part changes what happens when that axis is saturated and specifies the recursively
higher-dimensional structures built above it.
The central new principle is Superinheritance. Ordinary IH remembers one source. SIH remembers an entire
typed source-axis or typed source-domain while preserving every member as a separate inherited source.
Hyperfemale therefore begins not by inheriting one terminal Supra state but by superinheriting the whole
applicable Supra axis. Higher Hyperfemale strata then superinherit whole lower Hyperfemale axes. Ultra
begins by superinheriting the complete Hyperfemale dimensional domain. Apex begins by superinheriting the
complete Ultrafemale dimensional domain. The male side is the exact mirror.
303. SIH — exact canonical definition
SIH means Superinherits. Let Omega denote the typed HGL Hyperomega bound for the axis being
discussed. For a typed one-axis family X[alpha] and a starting coordinate a, define AxisTail(X,a) = {X[beta] :
a <= beta <= Omega}. Then SIH_axis(X[a]) is a source-preserving superinheritance closure over every
member of AxisTail(X,a). It is not one undifferentiated source-object and it is not shorthand for inheriting only
the terminal member.
SIH_axis(X[a]) => IH(X[beta]) for every beta with a <= beta <= Omega.
When the source is a structured nonstate, scope remains inside SIH: SIH_axis(NOT X[a]) => IH(NOT
X[beta]) for every beta in the same tail. This is positive inheritance of structured non-X states, not mere
failure to superinherit X.
304. SIH projection and provenance theorem
Because ordinary IH projection remains canonical, every SIH-generated IH edge projects to its source
truth/state content. Thus SIH_axis(SF1) entails SF^beta for every beta on the selected SF tail, and
SIH_axis(NOT SM1) entails NOT SM^beta for every beta on the selected SM tail. The stronger fact,
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:237.