# Separating two assigned cue contributions

Run `python reproduce.py` with numpy and matplotlib. Standalone assigned model,1,764 CSV rows:441 coefficient pairs times four cue conditions. Two original scientific figures in PNG/SVG/PDF; recorded runtime, generator SHA256 and validation. No animals, people or empirical responses were measured.

`reading(a,v,A,V,b=0)` returns y=b+aA+vV. A is binary acoustic-cue presence and V is binary support-vibration presence; each equals0 or1. Coefficients a,v are assigned0..1 by0.05, and the exported baseline b=0. Output is a continuous instrument reading in arbitrary units, not a behavioral probability. Values can reach2 at a=v=1 when both cues are present; do not interpret this as200% likelihood. The figures deliberately select examples whose combined reading is1.

When only neither cue (00) and both cues (11) are observed, their difference identifies a+v under the additive model, but cannot identify a and v separately. The assignments(0.8,0.2),(0.2,0.8),(0.5,0.5) all give readings0 and1 in those conditions. Off-diagonal conditions separate these examples: y10-y00=a and y01-y00=v. The interaction contrast y11-y10-y01+y00 is zero by construction. A nonzero observed contrast would challenge this additive model; these synthetic data cannot test whether the assumption holds in reality.

The independent algebra checks all441 coefficient pairs, including endpoints, using contrasts and the additivity identity. A design-matrix check gives rank2 for rows[1,0,0] and[1,1,1], compared with rank3 for all four conditions when estimating baseline and two coefficients. Vector[0,1,-1] changes the separate contributions but leaves the paired readings unchanged. With baseline fixed at zero the analogous coefficient ranks are1 and2; the identifiability conclusion is the same. Seven invalid guards pass.

The figures show the four-condition matrix for assigned a=0.8,v=0.2 and the three indistinguishable paired-condition explanations side by side. This is not causal proof from real observations: calibrated measurements, actual manipulation, controls, uncertainty, repeatability and possible interactions would still matter. The model does not measure hearing, neural function, animal behavior or covert control. Its practical lesson is why changing two inputs together can leave their contributions ambiguous.