REMOVAL-ECHO v1 — pre-registration#
Fixed before any data is downloaded. The predictions and counters below are the
author's, stated in the protocol that commissioned this work; they are recorded
verbatim and are not edited after data exists. A later change to any number in
this file is a change to the record and needs a row in docs/canon/CORRECTIONS.md.
The question#
Does a system's reaction to a dated removal break additivity — "one number per thing" — and can that breaking be measured rather than inferred?
The statistic#
For units A, B with outcome f over subsets:
Shapley phi_A = sum_S [|S|!(n-|S|-1)!/n!] (f(S u A) - f(S))
Mobius I(A,B) = f(AB) - f(A) - f(B) + f(empty)
ADDITIVE iff I = 0 for every pair. "Breaks the rule" iff some I != 0 with a confidence interval that excludes zero.
Why this replaces the curl programme#
The curl programme failed on five domains in a row, each for one of two reasons: the system could not break the rule, or the removal hid the reaction. The first reason has a name. A SUPERPOSITION system cannot break additivity — power grids obey Kirchhoff's voltage law, so the curl of any flow response is zero by theorem. An EQUILIBRIUM system can: removing an edge from a Braess network lowers equilibrium travel time. Admission test for any domain: after the removal, does the rest RE-EQUILIBRATE? If not, the domain is refused, not tested.
Pre-registered predictions and counters#
Counters are point estimates, stated as the outcome the author would bet on if forced to bet against the prediction.
| domain | measurement | prediction | counter |
|---|---|---|---|
| D1 Perturb-seq double knockouts (Norman et al. 2019) | fraction of gene pairs with I(A,B) != 0 at BH q = 0.05 | > 20% of tested pairs | < 5% survive BH — most synergy is noise at this depth |
| D2 NBA injuries vs RAPM | RAPM residual variance on injury weeks vs placebo weeks | x1.5 with CI | x1.0 — RAPM already absorbs rerouting |
| ECHO, per domain | lag of peak impulse response | D1 at one measurement step; D2 at 1-3 games | — |
D3-D5 are sized after D1/D2 and are not run this week unless D1 fails admission.
Kills, fixed now#
- A domain without re-equilibration is refused, not tested.
- An I != 0 outside the Benjamini-Hochberg set is not a finding.
- An effect without its placebo rank is not a number.
- A lag peak inside the null band is no echo.
- Any counterfactual not from synthetic control or a planted double is struck.
Must-fires, required before any domain number is reported#
- A planted ADDITIVE game reads I = 0 to 1e-12.
- A planted SYNERGY reads its planted value.
- Synthetic-control placebo rank on a donor with no removal is approximately uniform.
- The planted-additive must-fire is re-run at the SAME noise level as the real data, because additivity broken by measurement noise is the most likely false positive.
Statistical design, fixed now#
The unanimity rule this project used before (a bar of +0.020 across 5 of 5 seeds) has a power ceiling of 0.5^5 = 3.1% at any noise level when the true effect sits at the bar, and gets weaker with every seed added. It is not used here. Every result is a point estimate with a confidence interval; every family of tests is corrected by Benjamini-Hochberg at q = 0.05; every effect is ranked among its placebos.