# Locked analysis plan: regression-to-the-mean response length **Locked:** 2026-10-03T09:04:33Z, before inspecting any case-level audit row, implementing the analysis, or calculating a new aggregate. ## Status and claim boundary This is a dependent training-cohort analysis lock, not a preregistration. It was designed after the Project established that the raw fold distribution of follow-up word counts outperforms additive persistence and descriptively has lower mean CRPS than the inherited three-count source-form neighborhood. The known positive correlation between source and follow-up word count motivates one fixed regression-to-the-mean forecast, but no case-level result from the new comparison has been inspected. The analysis uses only the 150-row audit from the preceding training-only response-length decomposition. It will not read benchmark text, development or private-test rows; generate a text prediction; alter an existing method; or change the frozen submission. It can test whether one simple form of source- conditioned length forecasting beats a no-source baseline within this selected cohort. It cannot establish correct future identity content, population generalization, untouched confirmation, development performance, or private- test performance. ## Question Can a cross-fitted linear adjustment for earlier response length improve follow-up word-count CRPS beyond the raw fold distribution, after shrinking the unit-slope additive-persistence assumption toward the cohort's observed source-follow-up relationship? ## Fixed forecasts For outer held-out case `i`, let `x_i` be its source word count and `y_i` its follow-up word count. For each support case `j != i`, fit an ordinary least- squares slope `b_{-i,-j}` of follow-up count on source count using the other 148 cases. The slope includes the usual fitted intercept in its calculation, so it is covariance divided by source-count variance. If source-count variance is exactly zero, set the slope to zero. Do not constrain, transform, tune, or round the slope. The **cross-fitted linear-persistence distribution** for case `i` consists of 149 equally weighted support values: `max(0, y_j + b_{-i,-j} * (x_i - x_j))`. Thus support case `j` supplies an observed follow-up count, but its follow-up does not help estimate the slope used to transport that support value to the held-out source count. The fixed rule generalizes the two inherited comparators: slope zero corresponds to the **raw follow-up marginal**, whose support is `y_j`; slope one corresponds to **additive persistence**, whose support is `max(0, y_j + x_i - x_j)`. The inherited **source-form neighborhood** remains a contextual comparator and is not refit. Use the preceding audit's integer source and observed follow-up counts. Require 150 unique ordered case IDs and finite nonnegative counts. Recalculate raw and additive supports, CRPS values, medians, and central 80% interval diagnostics; require the raw, additive, and inherited source-form CRPS values to reproduce the stored audit case by case within its six-decimal storage precision. Hash- guard this plan, the corrected preceding plan and implementation, and the preceding complete audit. Write one complete machine-readable result and one 150-row audit without response text. Do not write any development or test artifact. Use the inherited equally weighted empirical CRPS, left-continuous weighted quantile, and central-interval-score definitions. The left-continuous empirical median is the point forecast for each distribution. ## Fixed evaluation The **primary outcome** is follow-up word-count CRPS. The **primary contrast** is raw-marginal CRPS minus cross-fitted linear-persistence CRPS; positive values favor the person-conditioned forecast. Report both means and paired case wins, ties, and losses. Prespecified secondary diagnostics are: - additive-persistence CRPS minus linear-persistence CRPS; - source-form-neighborhood CRPS minus linear-persistence CRPS; - raw-marginal CRPS minus source-form-neighborhood CRPS, closing the direct comparison left descriptive by the preceding plan; - raw-marginal absolute error minus linear-persistence absolute error; - raw-marginal central-80% interval score minus linear-persistence interval score, alongside each method's coverage and width; and - the distribution of the 22,350 support-specific fitted slopes, including its mean, standard deviation, minimum, quartiles, and maximum. For every paired effect, use a deterministic 20,000-resample percentile bootstrap over whole outer cases with seed `20261003`, restarting the seeded generator for each comparison. Report 95% intervals. The primary interpretation rests only on the one primary contrast; secondary intervals are unadjusted dependent diagnostics. ## Interpretation rules Describe linear source conditioning as improving response-length prediction beyond the no-source raw distribution only if the primary interval excludes zero in the positive direction. If the interval spans zero, conclude that this fixed analysis does not distinguish the methods. If it excludes zero in the negative direction, describe the raw marginal as better. A favorable primary result would show only that earlier response length carries incremental predictive information under this fixed regression-to-the-mean rule. It would not establish a lexical, semantic, causal, or ipseological mechanism, correct future signifiers, or justify development evaluation by itself. The secondary raw-versus-source-form interval is a delayed dependent comparison, not fresh confirmation. The support values and slopes come from heavily overlapping folds, the analysis follows known aggregate results, and the cohort is not a probability sample. Bootstrap intervals describe sensitivity to this cohort's case composition, not population generalization. Regardless of the result, do not run this count-only diagnostic on development data or make a private-test-performance claim in this iteration.