# Intervention model: reproducible methods appendix

CONDITIONAL MATHEMATICAL MODEL, NOT FITTED R104Q BIOLOGY.

## Variables and references

W and M denote WT and mutant synthesis divided by the same specified WT-only reference synthesis. The dimensionless parameters are survival u∈[0,1], competition b≥0, susceptibility λ≥0, capacity k≥0, mutant activity a≥0 and functional coupling γ≥0. All are explicitly assumed in the current calculations. The implementation bounds numeric inputs to [0,10⁶] and rejects nonfinite/negative outputs; this is a numerical domain, not a biological plausibility interval.

Additional WT partner penalty is q=b+λB, where the declared alternatives are B=0, u, 1−u or u(1−u). These alternatives encode distinct hypotheses; none is selected as the established R104Q mechanism. No sequence abundance score is converted into u.

## Surface and current equations

For W>0:

S_W = (1+k)W/[1+kH_W] × W/(W+qM)

S_M = u(1+k)M/[1+kH_M]

A_W = W/(W+γuM)

I = A_W S_W + a S_M.

The three delivery choices set (H_W,H_M) to (W,M), (W,W+M), or (W+M,W+M). The middle choice attenuates mutant delivery by total input but not WT delivery; it is not a shared-capacity model. The third uses common total-input attenuation, with an additional separate WT penalty. No conservation law is asserted for that penalty.

At W=0 the implementation defines S_W=A_W=0, retaining the mutant term. At W=M=0 total current is zero. At W=1,M=0, S_W=A_W=I=1, establishing the untreated WT-only reference. The modeled current is an additive nonnegative magnitude under the chosen protocol abstraction, not a voltage/time-dependent electrophysiological simulation.

## Actions and controls

An action changes W to α_W W+W_added and M to α_M M, with optional explicit changes to u, λ or γ. Other parameters remain fixed unless a separate model declares otherwise. Each intervention compares treated and untreated mixed-genotype outputs and applies the same action to the separate WT-only background. These controls are retained, not used to erase the mixed response.

The saved 9,072-row dose grid uses u=0.1/0.5/0.9, k=0/2, a=0/0.2/1, b=1, λ=2 and γ=1, across four burdens and three delivery laws. Dose definitions are authoritative in dose_response_v2.py. The expanded selectivity and factorial-combination grids have their own explicit domains and must not be described as the same experiment. Duplicate or parameter-equivalent grid members are not independent observations.

## Inference and numerical verification

The independent dose reconstruction verifies every saved dose result; the analytic review independently checks the monotonicity claims and model boundaries. The 96-group robustness matrix is an aggregation of this grid, not a proof over all parameter values. The proofs for proportional supply and isolated penalty/coupling reduction hold only under the fixed-action assumptions above. Counterexamples refute universal claims but do not estimate their frequency in biology.

The authenticated frozen partner-surface adapter has a different reference role from the current model. It explicitly converts empty-partner to WT-partner surface normalization and never converts surface into current. The integrated example preserves that separation. A tissue current-ratio mapping requires additional declared unchanged-kinetics/driving-force premises and remains uncalibrated.

## Reproduction and limitations

Primary implementation: forecast_v2.py and intervention_actions_v2.py. Source-grid generator: dose_response_v2.py. Verification: verify_dose_v2.py, verify_v2_analytic_review.py, test_forecast_v2.py and test_intervention_actions_v2.py. The machine results record source hashes; generators use exclusive output creation and must be reproduced in a fresh versioned directory. Preserve frozen predecessors rather than overwriting them.

This appendix states the equations needed to understand and reproduce the intervention results. It does not supply biological parameter estimates, confidence intervals, treatment ranking, toxicity, long-term kinetics or exact construct identity. Final package acceptance still requires the complete artifact manifest and report review.