response-learning

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.

Interface

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.

Compiler

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.

Conditional learning theorem

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.

Dynamics witness

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.

Current status

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.

Evidence and verification

• [Final report — NORMATIVE-RESPONSE-LEARNING-THEOREM-SETTLED; BM-FEEDBACK-DYNAMICS-WITNESSED](https://github.com/A-M-Berns/alignment-workspace/blob/76b65e5cc327ca2f334e829a76548514813ab4b0/prompts/2026-08-13-crown-jewel-learning-theorem-final/REPORT.md) <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem-final/">[round]</a>
• Theorem statement <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem/">[round]</a>
• Assumption audit <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem/">[round]</a>
• Compiler soundness <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem/">[round]</a>
• Dynamics witness <a class="ref round" href="/rounds/2026-08-13-crown-jewel-learning-theorem/">[round]</a>
• Lean surgical bound