Hypergendered Logic Source
Hypergendered Logic — Page 262
A limit is not an ordinary immediate successor, so LSCC cannot simply copy one predecessor formula.
Nevertheless its closure roles must agree with the semantic polarity of the current ladder. The limit
accumulates the current same-side and opposite-side relations over every beta below lambda; it does not
reach backward into a superseded dual-UD/profile-of-nonstate era.
LC-IH-Own-F: SF^lambda & beta<lambda => IH_(SF^lambda)(SF^beta).
LC-IH-Opp-F: SF^lambda & beta<lambda => IH_(SF^lambda)(NOT SM^beta).
LC-PH-Own-F: SF^lambda & beta<lambda => PH_(SF^lambda)(SF^beta).
LC-NOTPH-Opp-F: SF^lambda & beta<lambda => NOT PH_(SF^lambda)(SM^beta).
LC-UD-Own-F: SF^lambda & beta<lambda => UD_(SF^lambda)(SF^beta).
LC-NFD-Own-F: SF^lambda & beta<lambda => NOT FD_(SF^lambda)(SF^beta).
The male laws are exact mirrors. In particular, no constitutive LC-PH-Opp-of-Nonstate and no LC-UD-Opp
exists. This does not prohibit a later causal law from assigning some opposite structured nonstate an Unflaw,
Flaw, or profile relationship; it means those facts are not generated by LSCC itself.
374. PH-9 after harmonization: positive own-profile closure plus opposite-profile exclusion
PH-9 is retained as the name Limit Profile Closure, but its current content is Profile-Exclusion-aware. A
female limit positively possesses every complete lower SF profile as an explicit whole-profile source and
explicitly does not possess every complete lower SM profile as a whole. It also inherits every structured
non-SM state through IH. The three facts—IH(NOT SM^beta), PH(SF^beta), and NOT
PH(SM^beta)—remain noncollapsed.
PH-9 does NOT entail PH(NOT SM^beta).
PH-9 does NOT reduce Profile(SF^lambda) to Union_{beta<lambda} Profile(SF^beta).
A limit can therefore have emergent whole-limit phenotype organization arising from relations among an
unbounded family of positively possessed own-side profiles, excluded opposite profiles, and inherited
structured non-opposite states.
375. Corrected limit deductions
Strictly deductive consequences include: existence of typed LimF/LimM states at canonical limits; IH
projection to every lower own-side state and every structured non-opposite state; positive PH possession for
every lower own-side profile; negative PH status for every complete opposite predecessor profile; UD and
NOT-FD for every own-side predecessor contribution; LQSA quality lower bounds; and successor-schema
applicability at lambda+1. Opposite-source PH-of-nonstate, UD, FD, or NOT-FD remain open unless another
axiom explicitly supplies them.
376. Why a precedence note was not sufficient
A formal reader or compiler should not have to encounter LC-UD-Opp in one Part and discover hundreds of
pages later that Single-UD superseded it. Precedence resolves legal interpretation but does not produce
local logical transparency. HGL therefore uses direct historical migration: superseded formulas may be
discussed as superseded history, but no active theorem catalogue, closure law, machine specification, or
worked proof may assert them as current canon.
377. Ultra and Apex receive same-side UD without becoming copies of Hyper
UF_(n+1) = SIH_axis(UF_n) AND SIH_axis(NOT UM_n) AND UD(UF_n), n>=1.
UM_(n+1) = SIH_axis(UM_n) AND SIH_axis(NOT UF_n) AND UD(UM_n), n>=1.
AF_(n+1) = SIH_axis(AF_n) AND SIH_axis(NOT AM_n) AND UD(AF_n), n>=1.
AM_(n+1) = SIH_axis(AM_n) AND SIH_axis(NOT AF_n) AND UD(AM_n), n>=1.
This strengthening is deliberately narrow. Hyper remains five-role because it additionally carries PH-own and
NOT-PH-opposite. Ultra and Apex are three-role internal dimensional recurrences: own-axis
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:262.