Figure — Annotated readout

What the instrument reveals: staged-collapse signature

A single reach-scan readout from the floor-sum case study, annotated with the structural features that emerge when the future field is profiled along the commitment axis. The same readout would be unreadable as a single number; it becomes legible as a profile.

FLOOR-SUM CASE STUDY · Qwen2.5-Math-7B-Instruct · M=64 per checkpoint · target = 532 7 6 5 4 3 2 1 0 residue (mod 8) 0% 2.5% 5% 10% 15% 20% 25% 50% 75% commitment fraction (sweep axis) target residue (Y ≡ 4 mod 8) — copper row wrong fiber (Y ≡ 0 mod 8) — teal row target-fiber extinction target residue mass → 0/64 at 25% wrong-fiber closure numeric mass in 8ℤ → 64/64 at 25% answer-basin lock 63 of 64 → Y = 56 at 50% terminal: 50% ≈ 75% JS sim 0.984 (answer projection) ~25% of trace residue closure precedes answer lock
Feature 1 — copper

Target-fiber extinction

The target residue class disappears from the sampled numeric field by 25% of the trace. The model can no longer reach an answer in the right family under the declared instrument.

Feature 2 — teal

Wrong-fiber closure

The wrong residue class (0 mod 8) reaches full numeric support by 25%, in lock-step with target extinction. At this depth, the future field is confined to a target-excluding answer fiber.

Feature 3 — light

Answer-basin lock

By 50% of the trace, 63 of 64 continuations produce the same wrong answer (Y = 56). The 75% checkpoint is empirically indistinguishable from 50% on the answer projection.

Why this readout matters. Endpoint evaluation reduces the entire run to a single bit: wrong. Process supervision reduces it to a sequence of step scores. Neither captures the staged structure visible here — that residue closure happens at 25%, while answer-basin lock happens at 50%, with a measurable interval between the two events. This interval is the in-flight observability signal: the future field has lost its connection to the target before any answer has been emitted. Indexed to: Qwen2.5-Math-7B-Instruct · target Y* = 532 · policy T=0.7, top-p=1.0 · budget B = 2048 · M = 64 (256 at 0%) · finite-M, instrument-relative. Cell intensity is gamma-scaled for visibility; raw values are reported in the paper's future-field profile table.