AI REASONING — FUTURE-FIELD GEOMETRY

Coarse-to-fine collapse

Legacy Case A supporting view. At each populated checkpoint, the original instrument sampled M=64 continuations and projected the resulting finite field four ways. The bands show the reported sequence under that declared instrument: residue, scaffold family, parameter, then answer.

Legacy Case AFinite-M / instrument-relative

target Y* = 532

25% PREFIX family-concentrated, parameter-diverse — the central decoupling

L1 Residue fiber q₁(Y) = Y mod 8 — —

L2 Scaffold family q₂(Y) = 𝟙[Y ∈ 8ℤ] — —

L3 Scaffold parameter q₃(Y) = Y / 8 — —

L4 Answer q₄(Y) = Y — —

wrong-fiber mass target Y* = 532 target-fiber escape M = 64 continuations per checkpoint

How to read. Each band is a different push-forward of the same sampled future-field measure μ_π^K,B through a coarsening map. Endpoint evaluation only sees L4. The earlier layers show a sampled target-excluding concentration before the answer projection concentrates. At 25%, the M=64 readout is family-concentrated and parameter-diverse; by 50%, the answer projection is concentrated. These are finite-sample observations under the declared instrument, not a proof that all continuations are impossible. Data: Qwen/Qwen2.5-Math-7B-Instruct on floor-sum target Σ_n=1..40 ⌊(3n+7)/5⌋ = 532. This page preserves the original 64-rollout Case A morphology; the 0% prompt-root state is not populated here. Use the current RC18 case page and RC18 evidence archive for current prompt-root and higher-M tables.