Observable Deviation from Leakage Spectrum

This record presents TA19 (Observable Deviation from Leakage Spectrum), part of the Q5 Transport Architecture Series developed under the Zero-Point Hypothesis framework. TA19 closes the depth architecture arc TA14 through TA18 by connecting the leakage spectrum to observable probability deviations, and feeds back into the T71 through T79 experimental prediction arc. The depth program is no longer self-contained: it now connects the internal transport hierarchy to measurable interference structure. The full mechanism chain established across TA14 through TA19 is: depth mode n produces roughness scaling as n to the fourth power, which produces leakage amplitude scaling as n squared in the low-mode regime, which drives leakage return through the complement sector, which produces observable probability deviation. Each stage has its own object, its own scaling law, and its own epistemic status. The central result is that in the perturbative low-mode regime where c times n squared is much less than one, the depth-mode observable deviation scales as approximately eta times c times n squared. The full implied structure gives a deviation proportional to eta times cn² divided by (1 + cn²), which saturates to a global bound of eta as mode number increases. Observable anomaly; therefore, initially grows with depth-mode frequency before saturating; it does not grow indefinitely. The observable deviation is connected to the T71 quadrature deviation structure. The T71 interference deviation has the form involving coefficients A and B multiplying the cosine and sine of the phase angle. Under TA19, the depth-mode-dependent deviation coefficients scale as eta times n squared at low mode number, giving a depth-mode-refined interference prediction where the deviation amplitude carries an explicit n squared factor. Exact coefficients and phase prefactors are not computed here. Three lemmas establish the result: leakage return generates observable correction at leading order in the leakage coupling parameter eta (Lemma 1) ; the depth-mode deviation scaling follows as eta times n squared in the low-mode regime and eta times the square root of the roughness functional equivalently (Lemma 2) ; and the T71 quadrature deviation coefficients inherit the n squared scaling (Lemma 3). A critical epistemic note is maintained throughout: the theorem separates the robust qualitative claim from the model-dependent quantitative claim. The robust claim is that observable deviation increases monotonically with depth-mode frequency before saturating. The model-dependent claim is the specific n squared scaling, which requires the continuum depth approximation from TA15, the low-pass gate model from TA18, and the leading-order perturbative coupling assumed here. These must not be conflated in experimental interpretation. The leakage-deviation coupling is explicitly identified as a first-order perturbative ansatz rather than a structural inevitability, since probabilities are nonlinear objects and the full leakage return operator can contribute phase-sensitive cross terms at higher order in eta. Together, TA14 through TA19 form a complete emergence ladder: discrete adjacency transport, continuum evolution, smoothness selection, quartic roughness spectrum, leakage from admissibility misalignment, and perturbative observable consequences. This is a coherent multistage transport framework connecting discrete Q5 geometry to measurable interference deviations. The theorem chain progressively derives the structure of the effective transport generator \ Gₑff = PiY G PiY + K†BK \, from which observable phase, leakage, decoherence, and residual correction emerge as structural consequences of projected transport closure on Q5.