# Three-Body Phase 16B - Radius Warning Re-Pose Spec Phase 16 answered the channel question: the frozen strict-oracle hazard label is warnable by an instantaneous geometric observable, and `radius` was the clean single-channel winner. Phase 16B is the narrow follow-on promised by Branch A: **would the Phase 15 warning-quality verdict have flipped if the warning score had been `radius` instead of energy?** This is a verdict-reconciliation replay, not a new discovery experiment. The channel was selected by Phase 16, so Phase 16B is explicitly post-selection. Its job is to re-pose the Phase 15 warning-quality readout with the right instrument, preserve the Phase 15 / 15B / 15C mechanism verdicts, and keep the claim boundary honest. The answer is already determined by the committed Phase 16 output: `hazard-channel-audit.csv` reports `radius` `perCellMeanAuroc = 0.996624` with `27/27` favorable cells defined, while the within-16B energy baseline is `0.655508` with `27/27` cells defined. Phase 16B formalizes that already-published number in Phase 15's verdict shape; it adds no statistical evidence beyond Phase 16's stronger pooled Branch-A result. ## 1. Decision Lock Operator lock: **2026-05-29**, after the dt-scope / decidability / already-known outcome amendment. Phase 16B implementation and run occurred after this lock; see `PHASE16B_RESULTS.md`. - **Frozen source receipt.** Use the already-completed Phase 16 lock receipt: `results/threebody/phase16-hazard-channel-audit-lock/trials-minimal.jsonl`. No new simulation is owned by this phase. If the source receipt is missing, malformed, or not paired with the Phase 16 Branch-A manifest, the run is void. The reducer must also read Phase 16's `hazard-channel-audit.csv` and verify that the `radius` row already carries `perCellMeanAuroc = 0.996624` and `perCellDefinedCount = 27`; any reproduction drift is a reducer bug. - **Frozen label and oracle.** Reuse the Phase 15 / Phase 16 strict forward-oracle label `hazardReached` unchanged. The hazard geometry remains `r3 > 4 OR minPrimaryDistance < 0.08`; no subtype relabeling is allowed. - **Frozen score.** Primary warning score is `radius`, direction `+` (larger radius means higher escape-hazard risk). Energy is recomputed only as the comparison baseline. - **Frozen slate.** Analyze the Phase 16 passive `off` grid at `dt=0.004`: mass ratios `0.01,0.3,1`, radius scales `1.025,1.05,1.075`, velocity scales `0.95,1.05,1.1,1.15`, eight seeds, duration `16`, audit cadence `240`. Primary favorable pocket is `velocityScale >= 1.05` (27 cells, 216 passive trajectories). `velocityScale = 0.95` is reported as a boundary control. - **dt scope.** Phase 16B is Phase-15-shaped, not Phase-15-identical: Phase 15's historical warning verdict spanned the five-timestep ladder (135 favorable cell rows), while Phase 16B is the Phase 16 `dt=0.004` passive receipt only (27 favorable cells). The baseline for 16B is therefore energy's `dt=0.004` per-cell mean `0.655508`, not the historical ladder mean `0.683`. - **Phase-15-style verdict.** The primary statistic is a per-cell warning-quality mean, matching the shape of Phase 15's warning verdict rather than Phase 16's pooled Branch-A statistic. Decidability is stricter than Phase 15's historical "samples present" coverage convention: a Phase 16B cell is defined only if it contains both label classes, because AUROC is otherwise undefined. - **No claim upgrade.** Phase 16B may repair the warning-instrument read. It does not revise Phase 15's Fail-Magnitude branch, retune the controller, alter the survival envelope, or convert the three-body claim to a full mechanism pass. ## 2. Scope Phase 16B owns: - a small offline reducer over the Phase 16 lock `hazardSamples` receipt; the reducer must reuse Phase 16's exact `computeAuroc` and `cellKey` logic (copying the helper implementations is acceptable; changing the estimator is not); - npm command: - `npm run threebody:phase16b:repose` - outputs under `results/threebody/phase16b-radius-warning-repose/`: - `radius-warning-quality-map.csv` - `radius-warning-summary.csv` - `manifest.json` - this spec and `PHASE16B_RESULTS.md`. Phase 16B does **not** own a harness change, a controller run, new oracle calls, new channel selection, guard retuning, subtype-specific hazard labels, or public copy changes. ## 3. Command Shape Runnable command: ```bash npm run threebody:phase16b:repose ``` Script shape: ```bash node scripts/threebody-phase16b-radius-warning.mjs \ --in results/threebody/phase16-hazard-channel-audit-lock \ --out results/threebody/phase16b-radius-warning-repose ``` This is an offline analysis over a 3.4 MB JSONL receipt and should run well under the ten-minute rule. No hard-void Phase 13 / 14 gates are required because no simulation or shared harness code is touched; instead, the reducer must verify the Phase 16 manifest branch is `A_hazard_warnable` and that the source contains 288 passive trials. ## 4. Metric Definition For each cell `(massRatio, radiusScale, velocityScale)` at `dt=0.004`, pool all passive `hazardSamples` from the eight seeds. For each score (`radius` primary, `energy` baseline): 1. Apply the pre-registered direction (`radius` positive; `energy` positive). 2. Compute Mann-Whitney AUROC against the boolean `hazardReached` label. 3. Mark the cell **defined** only if it contains at least one positive and one negative label. Primary readout: - `radiusDefinedCells / 27` in the favorable pocket (`velocityScale >= 1.05`); - arithmetic mean of defined favorable-pocket `radius` AUROCs; - the same mean and coverage for `energy`, as the baseline comparison. Reproduction targets from Phase 16's committed CSV: - `radius`: mean `0.996624`, coverage `27/27`; - `energy`: mean `0.655508`, coverage `27/27`. Secondary diagnostics: - median / min / max cell AUROC for `radius`; - per-velocity table, including the `v=0.95` control column; - pooled favorable-pocket AUROC for continuity with Phase 16; - subtype mix (`escape`, `close_approach`, `bounded`) copied from the Phase 16 manifest or recomputed from trial outcomes if present. No fitted combination, bootstrap threshold, or sign-agnostic discriminability can create a Phase 16B pass. This phase is specifically the Phase-15-style warning verdict with `radius` substituted for energy. ## 5. Pre-Registered Branches The Phase 15 warning-quality bar is reused: **mean favorable-pocket AUROC >= 0.70 with >= 2/3 favorable cells defined** (at least 18/27 cells). **(A) Warning verdict flips under radius.** `radius` clears the Phase-15-style bar. Interpretation: Phase 15's warning-quality miss was an instrument-choice failure; the frozen strict-oracle hazard label was warnable, but energy was the wrong instantaneous score. This still does **not** revise the Phase 15 Fail-Magnitude mechanism verdict. **(B) Warning verdict does not flip.** `radius` is decidable and misses the bar. Interpretation: Phase 16's pooled Branch-A result does not survive the Phase-15-style cell-mean readout; the warning repair is weaker than it looked. **(C) Mixed / provisional.** Coverage is below 18/27 cells, source receipt validation is incomplete, or `radius` passes only on pooled AUROC while the cell-mean readout is undefined or split. Interpretation: Phase 16B localizes the warning repair but does not cleanly flip the warning verdict. All branches preserve the controller-mechanism verdict from Phase 15 / 15B / 15C. ## 6. Readback Record: - source receipt path and Phase 16 manifest branch; - passive trial count, favorable-pocket trajectory count, sample count, and positive-label count; - `radius` favorable-pocket coverage and mean per-cell AUROC; - `energy` baseline coverage and mean per-cell AUROC under the same reducer; - per-velocity summary table; - branch (A/B/C); - exact prose boundary: warning-instrument repair only, no controller retune and no Phase 15 mechanism upgrade.