theory: preregister mixed-traffic signal prediction

1 files changed, 10 insertions, 0 deletions

diff --git a/MIXED_TRAFFIC.md b/MIXED_TRAFFIC.md
index 0bc0ee2..521d108 100644
--- a/MIXED_TRAFFIC.md
+++ b/MIXED_TRAFFIC.md
@@ -37,6 +37,16 @@ matched:    u_l = ||r_l||_example / ||a_l||_example * a_l,
 innovation: u_l = r_l.
 ```
 
+The scale was chosen from a pre-endpoint signal calculation, not an accuracy
+pilot. If instruction and traffic are uncorrelated and the RMS ratio is
+`rho=4`, the instruction contributes only `1/(1+rho^2)=1/17=5.88%` of raw
+signal power. Ideal normalized LMS leaves coefficient fraction
+`(1-0.1)^20=0.12158` after warmup, so residual traffic has only
+`4*0.12158=0.4863` times the instruction RMS and innovation's instruction
+fraction rises to `1/(1+0.4863^2)=80.88%`. Ongoing neutral updates reduce it
+further. These are falsifiable scale predictions under the stated
+orthogonality idealization, not guaranteed accuracy outcomes.
+
 Norms are taken over every non-batch coordinate separately for each example
 and layer. Consequently the matched control has the innovation's update-signal
 norm but the raw signal's direction at the same network state. Every condition