# Stage 1 Steady-State Acceptance Protocol Status: implemented model-assessment protocol, 2026-08-25. This protocol defines what the equilibrium software can assess before any structure or sequence search begins. It does not define biological success. Every value below is conditional on a declared model, parameter set or stress box, concentration windows, and concentration units. ## Regional quantities For XOR region `r`, let ```text L_r = minimum modeled P_on over the declared region and parameter box U_r = maximum modeled P_on over the declared region and parameter box. ``` The software reports the four quantities needed for acceptance separately: ```text input_a_only_on_floor = L_10 input_b_only_on_floor = L_01 basal_off_activity_ceiling = U_00 joint_high_off_activity_ceiling = U_11 ``` Aggregates are then ```text on_floor = min(L_10, L_01) intended_off_activity_ceiling = max(U_00, U_11) separation = on_floor - intended_off_activity_ceiling. ``` `intended_off_activity_ceiling` is modeled ON-macrostate occupancy in the two intended OFF regions. It is not off-target binding, reporter leakage, or cross-talk. ## Single-high balance The narrow descriptive statistic is ```text single_high_floor_imbalance = abs(L_10 - L_01). ``` This compares two modeled regional floors. It is not full molecular symmetry and does not bound pointwise A/B exchange symmetry across a parameter box. In particular, the statistic need not worsen monotonically when a stress box is widened. The software also reports the stronger response-envelope quantity ```text single_high_response_gap_upper_bound = max(U_10 - L_01, U_01 - L_10). ``` In the mathematical interval model, it bounds the absolute difference between any two values drawn from the complete single-high response envelopes. The reported binary64 value is an approximation, not an outward-rounded certified upper bound. The quantity also penalizes variation within each region, so failure does not by itself demonstrate A/B asymmetry. A future pointwise symmetry claim would require a declared mapping between normalized A and B concentrations and a separately reviewed optimization method. ## Criteria and outcomes The API accepts four optional criteria: - a fixed output threshold `t`; - a minimum separation `S_min`; - a maximum intended OFF activity `L_max`; - a maximum single-high floor imbalance `D_max`. No criterion has a scientific default. Each present criterion uses a strict binary64 decision convention: ```text threshold passes when min(on_floor - t, t - intended_off_activity_ceiling) > tau separation passes when separation - S_min > tau intended OFF activity passes when L_max - intended_off_activity_ceiling > tau floor balance passes when D_max - single_high_floor_imbalance > tau tau = 64 * binary64 epsilon. ``` Equality and positive clearance within `tau` fail. Here `tau` is a fixed operational deadband applied to already-rounded binary64 values. It is not a bound on accumulated floating-point error, measurement uncertainty, or a certified interval-arithmetic error bound. `pass` means only that the computed clearance exceeded this software convention; it does not certify the corresponding real-arithmetic inequality. Each component and the overall result has one of three outcomes: - `not_assessed`: no criterion was supplied; - `pass`: the criterion was supplied and cleared strictly; - `fail`: the criterion was supplied but did not clear. Overall acceptance is `pass` only when all four criteria are present and pass. Any observed component failure makes the overall result `fail`; otherwise a missing component keeps it `not_assessed`. Scientific failure is a valid program result and does not produce a process error. ## Criterion provenance A scientific criteria profile must be identified, versioned, and locked before candidate screening. Its record must include its basis, units, model version, operating windows, parameter provenance, and the commit that evaluated it. Changing a limit creates a new profile; it must not overwrite the earlier result. Before real candidate screening, the numerical implementation must add validated, outward-rounded bounds (or an equivalently reviewed certification method). The present binary64 engine is suitable for transparent model development and software regression, not certified decisions near an acceptance boundary. The checked command-line example uses this post hoc software-regression profile: | Profile | Threshold | Minimum separation | Maximum intended OFF activity | Maximum floor imbalance | | --- | ---: | ---: | ---: | ---: | | `illustrative-regression-v1` | `0.5` | `0.30` | `0.15` | `0.05` | These values were selected around an already constructed mathematical fixture. They have no empirical or biological basis and must not be reused as candidate acceptance criteria. ## Coupling audit The `coupling-audit` command evaluates a paired ablation: 1. the declared state-specific double-binding model; 2. the same apo and dissociation-constant boxes with only both `omega` intervals forced to exactly one. There is no refit. This tests whether the declared result depends on the coupling terms for this parameterization and these apo/dissociation-constant boxes. It is not a likelihood-ratio test, a family-wide necessity result, a ranking of biological mechanisms, or evidence that the declared coupling is physically realizable. Run the raw audit without acceptance criteria: ```sh bash container.sh exec make coupling-audit ``` Run the regression-only protocol explicitly with: ```sh bash container.sh exec make coupling-audit \ AUDIT_ARGS='--criteria-label illustrative-regression-v1 --criteria-threshold 0.5 --criteria-min-separation 0.30 --criteria-max-intended-off 0.15 --criteria-max-floor-imbalance 0.05' ``` `AUDIT_ARGS` is shell-parsed and is intended only for trusted, developer-supplied values. ## Evidence outside the equilibrium model Missing evidence is never serialized as a zero or a favorable Boolean value. The coupling audit currently records cross-talk, response time, and reset as `not_assessed`. Cross-talk requires a versioned off-target panel, identities, concentrations, context, controls, response definition, replicates, and an aggregation rule. Any future conclusion is conditional on that panel. Response time must be recorded for every relevant directed transition. A future kinetic protocol may define ```text T_i_to_j = first time the output enters the destination acceptance band and remains there for a declared dwell time. ``` Sampled trajectories require interval or right censoring and a declared observation horizon. Reset requires more than observing an OFF output. Output recovery and functional recovery must be recorded separately, followed by a standardized rechallenge showing that the expected single-high ON response returns. ## Next mechanism-capability audit The current bilinear response family is not a fair implementation of every competitive-binding architecture. A literature-grounded candidate for a future comparator is the asymmetric `Q_UW` heterodimer described by de Ronde, ten Wolde, and Mugler, in which one ligand can bind either subunit and the other competes for one of those sites. That theoretical result motivates a model; it is not experimental evidence for a realizable XOR protein. [Biophysical Journal 103, 1097–1107 (2012)](https://doi.org/10.1016/j.bpj.2012.07.040) With cooperative factors fixed to one, a provisional mathematical form is ```text Q_s = (1 + a/K_AU,s) * (1 + a/K_AW,s + b/K_BW,s). ``` Before adding that comparator, the project must review its partition polynomial, analytic stationary-point bounds, parameter-count parity, and parameter provenance. A sampling grid will not be accepted as proof of a regional bound. A two-input equilibrium “conformational parity” interpretation whose ON and OFF partition polynomials are already restricted to positive bilinear form collapses algebraically into the current response family. In this abstraction, that restriction permits at most one binding event per input and excludes terms such as `a^2`, `b^2`, and higher occupancies. Positivity alone does not impose the restriction. Such a bilinear parity model will therefore be treated as an interpretation or identifiability audit, not scored as an independent mechanism unless structural constraints or additional observables make it distinguishable. Specifically, each output partition has the form ```text Z_y = c_y,00 + c_y,10*a + c_y,01*b + c_y,11*a*b, ``` which maps to the present binding polynomial by scaling out `c_y,00` and setting `K_A,y = c_y,00/c_y,10`, `K_B,y = c_y,00/c_y,01`, and `omega_y = c_y,11*c_y,00/(c_y,10*c_y,01)`. Zero coefficients are boundary limits rather than an additional positive-coefficient response family.