Hypergendered Logic Source

Hypergendered Logic — Page 5

HGL Source Framework · Page 5 of 293 · Source: Hypergendered Logic

These definitions restore the PA-only Stage-1 base as canonical. SF1 and SM1 each contain one irreducibly 
compound developmental-causal basis; no condition-source IH or Stage-1 PH term is constitutive of 
SF1/SM1. 
De Morgan remains valid inside the PH source when logical-equivalence substitution is used: 
 
¬ ¬𝑥∧𝑦
(
) ≡𝑥∨¬𝑦,
so 
 
𝑃𝐻¬ ¬𝑥∧𝑦
(
)
(
)
may be Boolean-normalized to 
 
𝑃𝐻𝑥∨¬𝑦
(
)
while retaining provenance that it arose from negating the Supramale inner condition. Crucially, neither form 
is equivalent to 
. 
𝑃𝐻𝑥
( ) ∨𝑃𝐻¬𝑦
(
)
The canonical second-order states are special eight-conjunct base cases. They add same-side inheritance, 
opposite-side structured-nonstate inheritance, positive same-side whole-profile possession, explicit exclusion 
of the complete opposite whole-profile, one same-side UD relation, two standalone PA routes, and a 
same-side NOT-FD safeguard. The opposite-side source has no constitutive UD or FD status. 
SF2 = IH(SF1) AND IH(NOT SM1) AND PH(SF1) AND NOT PH(SM1) AND UD(SF1) AND PA(x) AND 
PA(NOT y) AND NOT FD(SF1) 
and 
SM2 = IH(SM1) AND IH(NOT SF1) AND PH(SM1) AND NOT PH(SF1) AND UD(SM1) AND PA(NOT x) AND 
PA(y) AND NOT FD(SM1) 
PHSF1 does not mean merely “repeat every PH term visibly written inside the Stage-1 formula.” It means 
possession of the complete phenotype-profile of the whole SF1 state as a whole, including any phenotype 
that canonically belongs to the interaction/organization of its components. This is the phenotype-level version 
of the principle that the whole need not reduce to the sum of the parts. 
For every finite n >= 2, the canonical higher successor ladder is the six-conjunct IH + PH + UD + NOT-FD 
recursion shown immediately below. 
SF^(alpha+1) = IH(SF^alpha) AND IH(NOT SM^alpha) AND PH(SF^alpha) AND NOT PH(SM^alpha) AND 
UD(SF^alpha) AND NOT FD(SF^alpha), for every defined ordinal alpha >= 2 
and 
SM^(alpha+1) = IH(SM^alpha) AND IH(NOT SF^alpha) AND PH(SM^alpha) AND NOT PH(SF^alpha) AND 
UD(SM^alpha) AND NOT FD(SM^alpha), for every defined ordinal alpha >= 2 
Thus each higher Archwomanhood successor stage from Stage 3 onward does six formally distinct things: 
(1) inherits the previous same-side whole; (2) inherits the structured non-state of the previous opposite-side 
whole; (3) possesses the complete phenotype-profile of the previous same-side whole; (4) explicitly does 
NOT possess the complete phenotype-profile of the opposite-side predecessor as a whole; (5) treats the 
previous same-side whole as an Unflaw; and (6) explicitly denies that the previous same-side whole is a 
Flaw. Archmanhood mirrors all six relations exactly. 
This makes the antithetically productive zig-zag literal at the inheritance level while keeping 
phenotype-profile status deliberately asymmetric. Opposite-side non-state structure is positively inherited 
through IH(NOT opposite), but the complete opposite predecessor phenotype-profile is excluded through 
NOT PH(opposite). HGL therefore carries positive provenance about the structured non-opposite source 
without positively possessing a phenotype-profile of that nonstate as a constitutive successor rule. 
The ladder still preserves female/male typing:

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:5.