Skip to main content
This is where “the identity closes to 0.1 ms” stops being a claim about the SQL and becomes a property CI checks on every row, every build. Fourteen singular tests: thirteen run real logic today; one is a placeholder, documented honestly below rather than silently passing as if it were full coverage.

​
The shared closure macro

Most of these tests share one shape: a total column must equal the sum of named components plus a residual, within a tolerance. Rather than writing that comparison fourteen times, assert_additive_identity takes the model, the total column, the component list, and the residual column, and returns whichever rows violate the sum:
That’s the literal body of assert_lap_7term_identity, the “Lap 7-term residual identity” test below that enforces the seven-term identity itself. Three more of the fourteen tests below restate the same kind of sum-equals-total check by hand, at sector and qualifying grain, where the column lists differ enough that a direct SELECT reads more clearly than a macro call.
driver_skill_residual_s must equal pace_delta_s − total_explained_s, within 0.0001 s. This is the identity’s original two-term form total explained vs. residual that the seven-term test below further decomposes into six named physics components. track_unexplained_s is explicitly excluded from both sides: it’s the track-evolution model’s own internal residual, informational, not part of the closure. Guards int_lap_residual_decomposed. Active.
The headline test. After dirty_air_tax_s is extracted as its own term, the closure is:pace_delta_s=fuel+compound+rubber+ambient+constructor+dirty_air_tax+driver_skill_residual\text{pace\_delta\_s} = \text{fuel} + \text{compound} + \text{rubber} + \text{ambient} + \text{constructor} + \text{dirty\_air\_tax} + \text{driver\_skill\_residual}enforced via assert_additive_identity at 0.0001 s tolerance. Full derivation and the meaning of each term: the Seven-Term Identity. The model this closes: families/residual. Guards int_lap_residual_decomposed. Active.
The same identity, re-fit at qualifying grain rather than mirrored from the race-grain coefficients qualifying laps have their own fuel, compound, rubber, ambient, constructor, and dirty-air terms because a single push lap has a fundamentally different fuel and tyre-temperature profile than a race stint:quali_pace_delta_s=∑(6 quali-fit components)+quali_skill_residual_s\text{quali\_pace\_delta\_s} = \sum(\text{6 quali-fit components}) + \text{quali\_skill\_residual\_s}Same 0.0001 s tolerance as the race-grain test proof that the qualifying-specific coefficients are mathematically sound, not just plausible. Guards int_qualifying_decomposed. Active.
Each of a lap’s three sectors closes its own copy of the identity sector_pace_delta_s equals the sum of six sector-grain components plus sector_driver_skill_residual_s, at the same 0.0001 s tolerance the lap grain uses (the linear time-share allocation that produces sector components from lap components introduces no meaningful error). Guards int_sector_residual_decomposed. Active.
Checks whether SUM(sector_driver_skill_residual_s) over a lap’s three sectors equals that lap’s own driver_skill_residual_s from the lap-grain model. It doesn’t, today, by more than the 0.001 s tolerance and the gap is structural, not a bug: the sector-grain baseline (field_sector_pace_smoothed_s, a per-sector median) and the lap-grain baseline (base_track_pace_s, a trimmed-mean smoothed value) are fit independently, and the median of a sum isn’t the sum of medians. Closing this exactly would mean fitting a joint sector-grain baseline via panel regression instead of three independent sector medians a larger change than this test’s scope. Tagged placeholder; returns no rows by construction until that joint baseline exists. Placeholder.
braking_loss_s + mid_corner_residual_s + exit_residual_s must equal corner_residual_total_s within 0.001 s, checked only where all three phase residuals are non-NULL. Unlike the sector split, this isn’t a proportional time-share allocation of a known total each phase residual is measured independently against a field median so the sum equaling the total is a real, checked property rather than true by construction. Guards int_corner_skill_residuals. Active.
A degenerate-case identity rather than an additive one: when the ghost car’s ego driver and host constructor are the same (i.e. the counterfactual recombination is asking “what if this driver drove their own car”), predicted_lap_time_s must equal the driver’s own actual_lap_time_s exactly, within 0.0001 s. If recombination is mathematically correct, the self-case has to be a no-op; any drift here means the recombination formula itself is wrong, not just imprecise for genuine swaps. Guards fct_ghost_car_pace. Active.
The same macro call as the lap 7-term test above, byte-for-byte kept as a standalone, readable usage example of assert_additive_identity rather than removed once the canonical test existed. It doesn’t add coverage beyond what the lap 7-term test already enforces; its job is documentation-by-example for anyone adding a new closure test, not an independent guarantee. Guards int_lap_residual_decomposed. Active.
An internal-consistency check on the field-mean itself, not on any one constructor’s slope: the precision-weighted mean of (deg_slope_raw_s_per_lap − field_mean_slope_s_per_lap) must be exactly 0 within every (race_year, compound) cell, at 1e-9 s/lap tolerance (low-sample cells excluded they don’t enter the field mean). If this drifts, “deviation from the field-average compound curve” stops meaning what every downstream consumer of the centred slope assumes it means. Guards int_constructor_deg_sensitivity. Active.
The same centring property, applied to the post-cliff-onset hinge coefficient instead of the pre-cliff slope: the precision-weighted mean of (cliff_hinge_coef_s_per_lap − cliff_hinge_field_mean_s_per_lap) must be 0 within every (race_year, compound) cell, same 1e-9 s/lap tolerance, low-sample cliff cells excluded. Guards int_constructor_deg_sensitivity. Active.
Three tests below share one statistical property: Bayesian shrinkage toward a proper prior is convex, so the posterior (shrunk) mean is mathematically guaranteed to land between the raw observed value and the prior mean never outside either:shrunk∈[min⁡(raw,prior), max⁡(raw,prior)]\text{shrunk} \in \big[\min(\text{raw}, \text{prior}),\ \max(\text{raw}, \text{prior})\big]This one checks it for per-circuit driver affinity, at floating-point epsilon (1e-9 s). A violation isn’t a borderline statistical judgment it means the shrinkage formula itself is wrong, or the prior and observed values were mismatched (e.g. computed over different row sets). Guards int_driver_circuit_affinity. Active.
The same convexity bound, checked within each era cell instead of pooled across eras. Guards int_driver_circuit_era_affinity. Active.
The same convexity bound again, applied to era-normalized driver ratings: shrunk_residual_s must land between the driver’s raw residual mean and the season mean. Guards int_driver_season_ratings. Active.
A 95% credible interval built symmetrically around a posterior mean (mean ± 1.96·se) has to bracket that mean by construction ci_low ≤ mean ≤ ci_high. This test checks that property across both circuit-affinity models at once (era and non-era), wherever the standard error is estimable; degenerate single-observation cells carry NULL bounds by design and are excluded rather than flagged. A violation means the mean and the CI bounds were computed from mismatched intermediates a stale standard error, or low/high swapped. Guards int_driver_circuit_affinity and int_driver_circuit_era_affinity. Active.