Conjugate-Half Mixing Correction to Observable Born Readout

T100 extends the observable-slice formulation of T99 by introducing weak coupling between the observable sector and its conjugate counterpart. While T99 established that the standard Born rule is recovered when the observable slice is perfectly closed, T100 derives the first-order correction that appears when a small amount of conjugate-sector structure mixes into observable measurement outcomes. The real symplectic state space is decomposed as \[R=O',\] where \(O\) is the observable sector and \[O'=JO\] is its conjugate counterpart under the complex structure \(J\). A state is written as \[v=o+h,∈ O,∈ O'.\] In the closed-sector limit, observable probabilities are given by the standard Born rule \[P_i⁽⁰⁾=\|Π_i o\|^2/\|o\|^2.\] To model weak communication between the sectors, the theorem introduces a small mixing parameter \(η\) together with a mixing operator \[C:O'→ O.\] The effective observable component becomes \[o_η=o+η Ch+O(η^2).\] The theorem derives the resulting first-order modification of Born probabilities. After normalization, the observable readout takes the form \[P_iᵒᵇˢ=P_i⁽⁰⁾+ηΔ_i+O(η^2),\] where the correction term is \[Δ_i=2Π_i o,Π_i Ch-P_i⁽⁰⁾∑_j2Π_j o,Π_j Ch.\] A central result is the conservation law \[∑_i Δ_i = 0.\] The conjugate sector, therefore, cannot create or destroy total probability. Any influence of the conjugate half appears only through the redistribution of probability among observable outcomes. This leads to a distinctive prediction. Deviations from the standard Born rule cannot manifest as a uniform probability increase or decrease across all outcomes. Instead, observable corrections must occur as correlated excesses and deficits: \[Δ_i > 0∃\,j such that Δ_j < 0.\] The theorem thus identifies differential probability redistribution as the characteristic signature of weak conjugate-sector mixing. Several limiting cases follow immediately. When \[η=0,\] The observable sector is perfectly closed, and the standard Born rule is recovered exactly. The theorem therefore preserves ordinary quantum mechanics as the zero-mixing limit while providing a controlled perturbative framework for possible departures from that limit. T100 serves as the first perturbative extension of the observable-slice Born framework. T99 identified the observable sector as the object being measured. T100 determines how those measurements change when the observable sector is weakly coupled to its conjugate counterpart. The result is a first-order correction theory in which probability remains globally conserved while being redistributed among observable outcomes through conjugate-sector mixing.