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research: prove active-experiment complementarity beyond public-randomness effects - #47
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The doc and module docstring defined the slack as V(B+a)+V(B+b)-V(B)-V(B+a+b) and called S<0 complementarity, but that expression equals +1 on the two-bit example, where the experiments are complementary. The slack that is negative under complementarity is Delta_b(B)-Delta_b(B+a) = V(B)+V(B+a+b)-V(B+a)-V(B+b); the boxed values -1 and -1/3 and the tests already use it. Fix the definition, compute the stored slack from the four gaps instead of setting it to -complementarity, check that all four menus share one benchmark, add a direct test for ST-T192/ST-T193 and cite it, and replace ST-M53/M54 assumptions that were computed results with the construction inputs. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Stacks on PR #46 and tests a stronger structural assumption: whether active-experiment value must have diminishing returns once model identity, oracle benchmarking, and public-randomness resources are all controlled.
The layer fixes the full-menu model-informed causal oracle vector and evaluates four controller classes B, B+a, B+b, and B+a+b against that same benchmark, both deterministically and after independent public-seed convexification. Marginal experiment value is V(S)-V(S+e); strict complementarity is the failure of diminishing returns, equivalently negative cost-form submodularity slack.
The exact construction uses four persistent two-period models encoding two latent bits and complete confusion K3. The first-period source is common; the second-period source mapping is 0,1,1,2. Experiment a reveals the first model bit and b the second. Either bit alone leaves two possible final source symbols, while both bits identify the future source. Deterministically, adding b is worth 0 from the baseline but 1 after a, giving complementarity margin 1 and submodularity slack -1. After matching public-randomness resources, the corresponding marginal gains are 1/6 and 1/2, so strict complementarity survives with margin 1/3 and slack -1/3.
Claims ST-T190 through ST-T193, ST-M53, ST-M54, and ST-F33 are evidence-bound. This does not say greedy selection is always bad; it shows generic submodularity-based guarantees require additional structure rather than following automatically from 'information'.