Hypergendered Logic Source
Hypergendered Logic — Page 213
𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦 𝑚𝑒𝑚𝑏𝑒𝑟𝑠ℎ𝑖𝑝 𝑖𝑠 𝑏𝑖𝑛𝑎𝑟𝑦; 𝑜𝑟𝑑𝑖𝑛𝑎𝑙 𝑎𝑑𝑣𝑎𝑛𝑐𝑒𝑚𝑒𝑛𝑡 𝑖𝑠 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑚𝑒𝑛𝑡𝑎𝑙, 𝑛𝑜𝑡 𝑠𝑐𝑎𝑙𝑎𝑟 𝑚𝑒𝑚𝑏𝑒𝑟𝑠ℎ𝑖𝑝 Γ 𝑔𝑜𝑣𝑒𝑟𝑛𝑠 𝑝ℎ𝑒𝑛𝑜𝑡𝑦𝑝𝑒−𝑠𝑝𝑎𝑐𝑒; 𝑝ℎ𝑒𝑛𝑜𝑡𝑦𝑝𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑠 𝑝ℎ𝑦𝑠𝑖𝑐𝑎𝑙𝑙𝑦 𝑎𝑛𝑑 𝑜𝑓𝑡𝑒𝑛 𝑣𝑖𝑠𝑖𝑏𝑙𝑦 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑒𝑑 𝑠𝑎𝑚𝑒 𝑎𝑑𝑑𝑟𝑒𝑠𝑠 ⇏ 𝑠𝑎𝑚𝑒 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑜𝑟 𝑝ℎ𝑒𝑛𝑜𝑡𝑦𝑝𝑒 ℎ𝑖𝑠𝑡𝑜𝑟𝑦 ℎ𝑖𝑔ℎ𝑒𝑟 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦/𝑚𝑎𝑗𝑜𝑟 𝑠𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒𝑠 𝑟𝑢𝑙𝑒 𝑎𝑟𝑐ℎ𝑖𝑡𝑒𝑐𝑡𝑢𝑟𝑒, 𝑛𝑜𝑡 𝑚𝑒𝑟𝑒𝑙𝑦 𝑡ℎ𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑙𝑑 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦 𝐻𝑦𝑝𝑒𝑟𝑜𝑚𝑒𝑔𝑎 𝑎𝑛𝑑 𝑚𝑎𝑗𝑜𝑟−𝑠𝑡𝑎𝑔𝑒 𝑙𝑖𝑚𝑖𝑡𝑠 𝑎𝑟𝑒 𝑒𝑥𝑝𝑙𝑖𝑐𝑖𝑡 𝐻𝐺𝐿 𝑎𝑥𝑖𝑜𝑚𝑠, 𝑛𝑜𝑡 𝑐𝑜𝑛𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒𝑠 𝑜𝑓 𝑛𝑒𝑠𝑡𝑒𝑑 𝑃𝐴 LEGACY-CONSISTENCY SWEEP: obsolete five-part Stage-1, six-term Stage-2, nine-conjunct dual-UD Stage-2, four-term Stage-3+, seven-conjunct dual-UD Stage-3+, and incompatible De Morgan expansions have been rewritten to the current Profile-Exclusion canon. LIMIT-STATE PRECEDENCE NOTE: Part XLI below is authoritative over any earlier wording that treats successor recursion as finite-only, invokes Q(SF^lambda)/Q(SM^lambda) without first constructing the corresponding limit state, treats Significant Quality Increase as transfinite-only in precision, or copies obsolete opposite-source quality assumptions into limit closure. The current limit canon uses a typed Limit-State Closure Constructor, ordinal-general successor recursion, unified finite/transfinite magnitude semantics, and—under the later Profile-Exclusion revision—IH(NOT opposite) plus NOT PH(opposite) with no constitutive opposite-side UD/FD status. Part XL — Authoritative Unflaw/Flaw and Transcardinal Whole-Quality Revision This Part is authoritative over every earlier incompatible statement. It does not discard PA, IH, PH, Gamma, hypercategories, Hyperomega, or major stages. It changes the canonical finite SF/SM base formulas and successor formulas by adding the FD/UD quality layer, and it makes explicit the bridge axioms required to turn UD from a feature-level predicate into stage-to-stage whole-quality theorems. 237. Canonical fixed recursion: final current form Let x denote XX and y denote XY in the fictional HGL condition language. The first local Suprafemale/Supramale states are PA-only and remain PA-irreducible. SF1 = PA(x AND NOT y) SM1 = PA(NOT x AND y) The second local stages are special base cases because they add standalone primitive PA routes in addition to the recursive IH/PH/UD/FD architecture. 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) 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) For every already-defined ordinal alpha >= 2, finite or transfinite, the ordinary successor rule is: SF^(n+1) = IH(SF^n) AND IH(NOT SM^n) AND PH(SF^n) AND NOT PH(SM^n) AND UD(SF^n) AND NOT FD(SF^n), for n >= 2 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 Stage 2 therefore has eight outer conjuncts. Every ordinary successor from Stage 3 upward, including a successor whose predecessor is a limit ordinal stage, has six outer conjuncts. Limit stages themselves are not generated by this successor formula; they are constructed by the Limit-State Closure Constructor. The female and male sides are exact structural mirrors. No formula may silently omit UD, omit NOT FD of the
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:213.