The bar grid from the recording alone: the sanity gate caught the bench, the decision gate failed everywhere, and the real limit is the ruler

Validation, instrumentation

Study Overview

The Sanity Gate Did Its Job, On the Bench

The study registered three arms (a least-squares ceiling, a declared-tempo arm with a blind downbeat phase, and a fully blind detector arm) plus a sanity gate: the pipeline on each chart's synthetic reference render, whose true bar starts are exact, must hit at least 95 percent. The first run scored zero on all four renders. The cause was the bench's own registered metric: it paired grid index to bar index, but a blind phase estimate exists only modulo the period, so a comb that had landed 68 milliseconds from the render's downbeats scored nothing, one bar shifted. Per the program's rules the metric was replaced (lattice distance, each truth bar start against the nearest lattice point, with each arm's period reported beside its rate so a half-period lattice cannot take silent octave credit), the defective run's numbers disclosed as seen, and the re-run passed at 100.0 percent on all four renders.

The Decision Gate, and the Ruler

On the real recordings the declared-tempo arm read 8.5 to 68.8 percent against the registered 80 percent line, and the ceiling arm read 27.3 to 37.9 percent. When the best uniform grid that can be fit to the truth itself misses two-thirds of that truth at fifteen percent of a bar, with around 400 milliseconds of mean error against tolerances of 122 to 280, no derivable grid could have passed and none did. The mechanism is the program's own instrumentation: the chart-anchored DTW truth is quantized at 93 milliseconds and its path wanders, so consecutive truth bar durations swing by hundreds of milliseconds. Per-bar chord grading tolerates that, which is why Study 21 read 97 percent roots on these exact grids, but a bar-position gate is finer than the ruler, and whether the bands also genuinely drift cannot be separated from the ruler's wander. One blind-arm result stands cleanly: the shipped detector's tempo landed on a Study 11 ladder rung of the declared tempo on all four songs, and the raw-octave grids score under 30 percent, so the ladder fold is load-bearing for any future grid work.

What Stands

The registered decision: the end-to-end draft study runs grid-given, taking its bars from the chart-anchored alignment like every chord study before it, and the no-chart grid is recorded as open, unmeasurable until the program owns truth finer than a few hundred milliseconds per bar. Human-tapped downbeats on one or two songs would unlock it. Predictions: two right, two wrong (one decisively, the ceiling), one not evaluable, and the first prediction wrong as registered then right after the amendment its failure forced.