Locked analogue-media tests

What Must Be Fixed First

A survival-weighting prediction is meaningful only when the free structures are declared before comparison. Otherwise the model is just a flexible after-the-fact fit.

• Recursive update map R and phase projection \pi_\Phi.
• Measured or constructed coordinates \Theta and \Pi, plus the scale \ell.
• Layer-to-layer transfer map or local-flow approximation.
• Loss coefficient \Gamma and exposure weight W.
• Path family, preparation weights, detector convention, background subtraction, and uncertainty model.
• Exposure-gate transmissions G_i, detector floors, ratio-censoring rules, selected log-ratios, vector statistic, and acceptance threshold.
• Ordinary-attenuation control model for the positive-control comparison.

Coordinate Convention Lock

The exposure factor is a declared operational law, not a coordinate-free scalar. A valid run must record the observable meaning of \Theta, the estimator for \Pi, the scale \ell, the zero of phase, phase wrapping, and allowed unit transformations before output intensities are inspected.

W = Theta^2 / (Theta^2 + ell^2 Pi^2)
J = Theta^2 + ell^2 Pi^2
valid run requires J >= J_min > 0
or a predeclared singular-state rule

Output Prediction

The model predicts represented output fractions from independently computed accumulated losses. The cleanest expression is usually the log-ratio form.

A_i = integral \Gamma_i W_i dt
G_i = exp(-A_i)
p_i = q_i G_i / sum_j q_j G_j

ln(p_i / p_j) = ln(q_i / q_j) - A_i + A_j

In the lab or numerical analogue, the represented weights are estimated by measured, background-subtracted output fractions.

\hat L_ij = ln(\hat p_i / \hat p_j)
compare \hat L_ij with ln(q_i / q_j) - A_i + A_j

Preregistration Checklist

The paper makes the order of operations part of the theory's discipline. A run is predictive only if calibration and prediction are frozen before the output vector is known.

calibrate R_test, Theta, Pi, ell, Gamma
declare paths, q_i, output map, floors, and thresholds
compute A_i = integral Gamma W dt
compute G_i = exp(-A_i)
commit p_pred and selected log-ratios
measure p_hat
compare against the locked rule

Nontriviality Against Ordinary Attenuation

The RSG-specific test is stronger than asking whether lossy paths fade. It asks whether exposure-weighted accumulated loss improves on an ordinary attenuation control in a declared positive-control regime.

RSG model:     A_i^RSG = integral \Gamma_i W_i dt
control model: A_i^0   = integral \Gamma_i dt

positive-control design:
matched integral Gamma dt
separated integral Gamma W dt

ordinary attenuation predicts a tie
RSG predicts an ordered output vector

Locked Toy Benchmark

The v1.4 paper includes a synthetic three-channel benchmark to show what a locked comparison looks like. It is not empirical validation; it is a reproducibility core.

q_1 = q_2 = q_3 = 1
Gamma = 0.20
ten layers, Delta t = 1
W = (0.25, 0.50, 0.75)
A = (0.50, 1.00, 1.50)

p_RSG approx (0.506, 0.307, 0.186)
p_std = (1/3, 1/3, 1/3)

Failure Conditions

The protocol is useful because it can fail. A clean failure is better than a vague success, because it tells the theory where the bridge did not hold.

• Measured output ratios do not match precomputed accumulated-loss differences.
• The exposure-weighted model does not improve on ordinary attenuation.
• The path family, detector convention, or loss field is adjusted after seeing results.
• The uncertainty threshold is widened after comparison.
• The positive-control regime is not declared before the test.
• Detector floors, saturation, or background subtraction break a predeclared ratio rule.

The page separates two bad outcomes. The model fails when the locked prediction misses within the declared rule. The run is invalid when free structures are moved after the output is seen.

Verification And Validation

A numerical or transfer-model implementation should include a refinement check and a parameter-identifiability check. If changes in \Gamma, \ell, boundary coupling, or detector response can compensate one another without being declared, the validation is weak.

||p_pred(Delta t / 2) - p_pred(Delta t)|| < epsilon_ref
norm and tolerance fixed before output comparison

Bridge Status

How This Affects The Site

The visualisation is allowed to be rich, playful, and exploratory because its status is clear. It helps people see the formal vocabulary. It does not replace the locked analogue test.

visualisation = explanation and inspection
analogue protocol = empirical comparison
future bridge = conditional roadmap