Hypergendered Logic Source
Hypergendered Logic — Page 238
however, is provenance: SIH remembers that SF1, SF2, SF3, ..., SF^Omega were inherited as individually
indexed sources. A Boolean projection can forget those source labels; full HGL state identity cannot.
SIH_axis(SF1) => {IH(SF^beta) : 1 <= beta <= Omega} => {SF^beta : 1 <= beta <= Omega}.
305. Superinheritance Noncollapse Axiom
Even when the terminal state SF^Omega already entails all lower SF states through ordinary limit closure,
SIH_axis(SF1) is not identical to IH(SF^Omega). The former carries an axis-indexed provenance family; the
latter carries one source edge whose source happens to be a closure-rich terminal state. Equal projected
consequences do not imply equal inheritance identity.
SIH_axis(X[a]) != IH(X[Omega]) in full provenance-sensitive HGL state identity.
This is the SIH analogue of the long-standing HGL distinction between truth and provenance. It prevents a
compiler from replacing an Omega-sized source family with one terminal source merely because many
Boolean consequences coincide.
306. Negation scope under SIH
SIH(NOT X) and NOT SIH(X) are different formulas. SIH(NOT X) positively superinherits a domain of
structured non-X sources. NOT SIH(X) merely denies the presence of the specified superinheritance relation.
No rule moves NOT through SIH.
SIH_axis(NOT X[a]) != NOT SIH_axis(X[a]).
Likewise, SIH_axis(NOT SM1) must never be normalized into NOT SIH_axis(SM1), and SIH_dim(NOT
HM-domain) must never be normalized into NOT SIH_dim(HM-domain). This is a mandatory
parser/type-checker invariant.
307. Axis typing is mandatory
Before Hyperfemale, a source such as SF1 lies on an obvious one-dimensional local substage axis, so
informal SIH(SF1) is unambiguous. Once higher-dimensional strata exist, the same spelling becomes
unsafe. The canonical full notation therefore permits SIH_axis, SIH_dim, and more explicit axis identifiers. A
proof must identify which ordered family is being swept.
SIH_i(source) where i is an axis/domain type; an untyped SIH abbreviation is permitted only when
exactly one axis/domain interpretation is available from context.
This typing prevents the fatal collapse “inherit all coordinates of HF1” = “inherit all dimensional orders of
Hyperfemale.” Those are different source-domains.
308. Axis Existence and Axis Distinctness axioms
SIH can quantify only over states that the formal ontology says exist. Therefore every canonical dimensional
stratum has an explicitly typed active axis. If D is a valid stratum with active coordinate alpha, the HGL
ontology supplies D[alpha, saturated-lower-coordinates] for every alpha in the permitted
Hyperomega-bounded coordinate domain.
AxisExistence(D): for every 1 <= alpha <= Omega, D[alpha,Omega,...,Omega] exists. Part XLV
additionally supplies category-specific coordinate-successor and coordinate-limit constructors, so
existence is no longer mistaken for a complete generative definition.
AxisDistinctness(D): alpha != beta => D[alpha,Omega,...,Omega] != D[beta,Omega,...,Omega].
AxisDistinctness is structural distinctness, not a claim that every pair must look different. Two distinct
coordinates can overlap in current outward phenotype while differing in provenance, quality, latent response,
Gamma, or counterfactual phenotype-space.
309. Strict Supra-to-Hyper Category-Lift Nonidentity
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:238.