Numerator or Denominator Decomposing the successive transitions of the screening length into two mechanisms: a public analysis protocol for existing data

Abstract

Abstract The screening length can grow along two routes, a rise in transport capacity or a fall in local dissipation, and the two are fully separable observationally: the first is read from accessibility, the second from the relaxation curve of a disturbance. Every historical transition of the screening length altered transport capacity and never altered local dissipation. That is the strongest and least tested empirical claim in this body of work. This paper registers a public analysis protocol for existing historical data directed at that claim alone, and reports no results of any actual computation. The protocol fixes a two-mechanism coding procedure executed by hypothesis-blind coders on de-identified material, three hypotheses with their falsification conditions, and an exhaustive ex ante registry of all analytic degrees of freedom. The principal result produced here is a negative simulation of classifiability. At an equivalence bound of ln 1.5, a median log-scale standard error of 0.15 across the two observables yields a classifiable-period rate of 0.675 but a recall of only 0.570 for the dissipation-collapse type; at standard errors of 0.20 and 0.25 that recall falls to 0.301 and 0.131. Two parallel precision gates are registered accordingly, together with one fixed reading rule: failure to observe the dissipation-collapse type may never, at any precision, be read as the absence of that type. A second simulation prices the equivalence bound of the main setting: a pure mixed case in which both sides change by a factor of 1.4 is misclassified as one of the pure types in 11.3% of runs at a standard error of 0.15, rising to 36.3% if the bound is relaxed to ln 2. The same simulation narrows a clause the protocol had already registered, namely the magnitude-comparison gate intended to suppress such misclassification: at equivalence bounds of ln 1.25 and ln 1.5 that gate is logically redundant across the registered precision range, while at ln 2 it still produces a visible difference. One mandatory step precedes classification, namely deciding whether the field measured is of screening type at all, since the entire apparatus of this protocol holds only for such fields. The execution details of that step and its operating characteristics are borrowed from a methodological paper whose calibration conditions do not coincide with historical material, so the joint power of the two layers in series is given no numerical value here; it is only declared to lie below what the classification layer reports. This paper is an analysis plan and contains no empirical results. H1 to H3 constitute an executable and auditable testing framework and must not be cited as verified findings. The data on which it draws were already publicly available when it was written, so every test registered here is a post hoc test and provides exploratory evidence only.