fix(ftip): prove the finite noiseless preference bound [AGENT] - #180
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Replace the inherited asymptotic assertion with a complete 1/80 lower bound for deterministic preference-only learners with stochastic output routing and pointwise response separation. Prove a simultaneous partition lemma using second moments and bounded differences, preserve the strict profile through query-dependent utility weights, and exhibit a feasible deterministic comparator. Handle finite boundary cases and carry the precise hypotheses into the square-root corollary, while distinguishing the reconstruction from the cited v1 proof and its broader claims.
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The noiseless preference bound previously quoted a rate whose displayed source proof drops logarithmic factors. This change supplies a complete finite proof with constant 1/80 for a deterministic preference-only learner whose returned router may be stochastic, under pointwise response separation. A simultaneous second-moment partition lemma, fixed strict ordinal profile and explicit attainable comparator establish the bound; the square-root corollary inherits every hypothesis.
The four changed sources distinguish this restricted reconstruction from the source's unrestricted claim and from extensions involving randomized learners, colliding responses or noisy preferences. Existing response separation, rate references and finite cardinal-query results remain intact.
Validation: analytic and finite controls, all 22 existing regressions, lint, source/rendered prose, full 2266-page build/output checks, nine local browser routes, all affected pages of the 241-page focused PDF, and complete source/HTML/PDF archive checks passed. A fresh independent adversarial review approved the exact candidate after checking the full finite proof, primary source, complete archived payloads and rendered proof continuations; no findings remain.