33.74 turns transition statistics into a tightening court: after freezing λ_std(P), the threshold-window width, the step-declaration rules, and a unified P→J calibration, δλ(P) must resolve into reproducible piecewise plateaus, multiple branching fractions bᵢ(P) must rewrite synchronously with a stable compensatory mode B_comp inside the same threshold windows, adjacent links in a decay chain must share the same threshold set or a calibrated convergent Δt_chain lag under one J family, and smooth-model / setting-label / up-down / chain-break / systematic-injection nulls must fail cleanly; under V08/V09-compatible tighten, this remains one rule-layer threshold-discreteness and chain-rewriting court rather than a new ontology of hidden allowed states.
Use this section as a compact machine-readable EFT reference.
33.74 turns transition statistics into one rules-layer tightening court. The admissible claim is that when an external control knob P—or its mapped tension index J—is scanned, the rate residual δλ(P) should not drift smoothly but should break into reproducible plateaus and short threshold windows, while branching fractions bᵢ(P) rewrite together in those same windows instead of wandering independently.
The measurement ledger keeps the threshold grammar explicit. It records λ(P) or τ(P), the frozen baseline λ_std(P), the rate residual δλ(P), at least two parallel branching fractions bᵢ(P) under a normalization that stays equal to one, a compensatory branch mode B_comp from the covariance of Δbᵢ inside threshold windows, the threshold set Pₖ or Jₖ with confidence intervals, a sparsity metric S_sp showing whether most variance is concentrated inside a small number of windows, and a chain-lag metric Δt_chain for adjacent links such as A→B and B→C.
The workflow is built so that real thresholds are not smoothed away. The study uses at least 6–10 settings, runs both upward and downward scans, interleaves baseline settings, measures λ or τ and multiple bᵢ in the same event windows, covers at least two adjacent links in the same scan sequence, blinds both setting labels and scan-direction labels, and freezes a plateau-plus-steps family, a smooth comparison family, the threshold-window width, and the step-declaration rule before unblinding.
The nulls are aimed at fake threshold structure. A smooth-model control tests whether continuous drift fits as well as steps, setting-label permutation must collapse both the threshold set and branch-compensation structure, up-scan versus down-scan consistency exposes thermal or stress-history hysteresis, chain-break controls remove the coupled-link relation, and systematic injections test whether efficiency or background drift can counterfeit synchronized compensatory rewriting.
Support requires all three lines to survive together: a reproducible threshold-discrete plateau set with high S_sp, a stable compensatory branch mode B_comp inside those windows, and adjacent-link threshold alignment under the same P scan or a convergent unified-J mapping. Falsification follows if thresholds do not replicate, if branch covariance drifts randomly, if links cannot share one threshold family, or if permutations, chain-breaks, and injections remain as strong as the nominal signal. The main systematics are counting-efficiency and dead-time drift, thermal or stress-history hysteresis, and branch-extraction dependence on fit prescriptions.
So the chapter closes only one tightened rule-layer threshold ledger aligned with the V08/V09 blind-freeze and null-separation lane. Pₖ/Jₖ, B_comp, and Δt_chain may survive only as the audited statistics of one threshold court, not as a rewritten micro-ontology of allowed states. Its clean onward value is to hand a hardened threshold grammar into the boundary-driven Sea State closure line of 33.75.