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Original file line number Diff line number Diff line change
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# A linear observable parameter is profilable only in the space its own noise family scores, so the log-family half is refused on the math and the linear-Gaussian half stays open on a measurement the corpus cannot make (issue #572)

**Status: Narrowed, not decided (2026-08-21).** ADR-0066/0099 profile a declared column's
**Status: Superseded in part by ADR-0129 (2026-08-25).** The two measurements this ADR named as
#572's gate have been taken, and they close it: see ADR-0129 for the decision, the numbers, and the
scope. **What still stands:** finding 1's log-versus-linear split, finding 2's double-binding
refusal and its two instances, and finding 5's census. **What ADR-0129 corrects:** finding 1's table
sorts families by the space their residual lives in, which is the wrong axis -- `laplace` scores a
linear residual but sums absolute values, so least squares is not its conditional optimum and it has
to be refused for the coupled form; and finding 3's reading of `Laske`'s `Int_nuc_off` ("profiles to
approximately 57.13 at essentially every box draw"), which is 9 of the 15 draws that integrate, with
five going to effectively zero -- the compression it reports does reproduce. **What ADR-0129
answers:** finding 4's redundancy question, and the "what would decide it" measurements at the end.

*(Originally -- Narrowed, not decided, 2026-08-21.)* ADR-0066/0099 profile a declared column's
optimal multiplicative **scale** out analytically, and ADR-0108 (#562) profiles out an
estimated **noise scale**. #572 proposed the third member — an additive **offset**, and the
coupled `(scale, offset)` pair — by variable projection, and asked for an evaluation before
Expand Down Expand Up @@ -244,6 +255,9 @@ If (1) shows the coupled pair behaves like `Int_nuc_off` did and (2) shows a ben
gate.
* Two reusable tools land in the corpus with their gotchas written down:
`Grein-2026-benchmark-subset-I/tools/linear_scope.py` and `.../linear_profile.py`.
**They were committed and not merged**, to `wshlavacek/BNGL-Models` branch
`tools/572-linear-observable-profiling`, so this ADR has been pointing at files that are not on
`main`. ADR-0129's branch merges them.

## Prior art

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