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Normative Response Learning
The learning problem is not to discover a hidden correct norm. It is to reduce a recurrent, publicly represented failure using responses that the practice can license independently of whether they happen to score well. The project calls this intended direction immanent self-correction.
The working pipeline is:
failure pattern → certified lawful edit → remediable pattern
→ filing → exposed failure → lesson
The word “lesson” is deliberately last. A lawful edit, a public filing, and an actual exposure must connect before a reduction in bad-response mass bears that interpretation.
The theorem consumes three primitives:
Due : S → D → Prop
Licensed : S → D → A → Prop
Loss : S → A → [0, L]
Due(S,d) says burden d calls for an answer in public pre-action state S.
Licensed(S,d,r) says response r is admissible for that burden, independently
of performance. Loss(S,r) measures bounded prospective performance. Coverage
is a quantitative property of Due, not a fourth normative primitive.
Given a due burden, a targeted source response, and a licensed alternative, the compiler produces a certified surgical repair: replace that one response on selected occasions and act as the identity elsewhere. The compiler must be protocol-legal, causal, prospective, loss-blind, and non-laundering.
The compiler does not prove that the licensed alternative performs better. A
positive margin δ_g is a separate joint hypothesis about the licensed response
and performance. Fixtures in both directions prevent licence and performance
from being identified.
The Blum–Mansour modification-regret engine supplies an upper bound on regret against the compiled surgical maps. Surgicality and a positive margin turn that into a bound on mixed mass assigned to the targeted inferior response. Dividing by the number of due occasions gives a conditional failure rate. If coverage grows faster than the learning scale, that conditional rate tends to zero.
This is an actual-trajectory theorem: the repair is scored against the loss on dates that really occurred. It does not show that the counterfactual trajectory generated by always applying the repair would be better.
A regenerating finite fixture repeatedly presents a due burden. Starting with substantial mass on an inferior response, the implemented learning dynamics shed that mass across four tested horizons while an uninformative matched control stays exactly flat. This is a witness that the fixed-point construction can show the intended feedback behavior, not a general convergence theorem.
| Component | Current research status |
|---|---|
| abstract response-learning theorem | settled at the stated conditional/interface level; unregistered |
| learning dynamics | witnessed on one regenerating fixture; unregistered |
substantive Due
|
no satisfactory instantiation |
Licensed |
interface discipline available; substantive soundness open |
| performance/loss | successful for the fixtures; general theory open |
| positive margin | hypothesis; derived only in fixtures |
| coverage | quantitative hypothesis, not a delivered conclusion |
No row is Established workspace state. In particular, the conditional theorem does not solve the normative-content problem exposed by its interfaces.