v0.10.0

Forecasts on the rate-limit gauges

Each gauge now shows a projection of where utilization will land at reset, with an 80% credible band, an ETA to threshold (default 100%), and a LOW/MED/HIGH confidence pill. This is an empirical Bayes forecast: the prior on the rate and the path-noise variance are both estimated from past data and plugged in to a posterior update, rather than being marginalized under a hyperprior. The full spec lives in internal/forecast/MODEL.pdf; the gist:

• Rate posterior. Inside the open window, utilization is modeled as u(t) = u_now + r·t + W(t), with r an unknown per-hour rate and W Brownian path noise with per-hour variance σ². The current rate is fit by OLS on the last 30 minutes of snapshots; that OLS slope and its standard error are treated as a Gaussian likelihood r̂_OLS | r ~ N(r, SE²_OLS), then fused with a Gaussian empirical prior on r (mean μ₀, variance τ₀²) via the standard conjugate normal-normal update. The prior is refit daily from up to 200 completed past windows.

• Closed-form projection. Both the rate-uncertainty and path-noise pieces are Gaussian, so projected utilization at reset is F ~ N(u_now + r̂·ΔT, ΔT²·τ_post² + ΔT·σ²). The 80% credible interval is F ± z₀.₉·σ_F, clipped to [0%, 100%] for display. (Surfaced to users as "80% CI" for brevity.)

• Path-noise calibration. σ² is recovered by replaying the forecaster across past windows: at each replay point, the squared forecast error e² against the actual u_final is regressed against [ΔT, ΔT²] with no intercept. The linear coefficient is path noise; the quadratic coefficient absorbs rate-uncertainty contamination and is discarded. This is a method-of-moments estimator, then plugged into the posterior; the prior is refit once more with the noise correction applied to its sample variance.

• Monte Carlo ETA. For each threshold, 500 trajectories of the SDE are simulated at 5-minute steps, drawing one rate sample per trajectory from the posterior. The reported ETA is the median first-passage time with the 80% CI from the 10th/90th percentiles. If at least half the trajectories never cross before reset, the threshold is reported as unreachable (p_inf is exposed on the API payload).

• Confidence tag. Derived from effective sample size n_eff = min(n_recent, τ₀²/SE_OLS² + N_sessions). n_eff ≥ 50 → HIGH, ≥ 15 → MEDIUM, else LOW. Falls back to the prior alone when fewer than three recent snapshots exist.

The forecast is computed once per poll and shipped inside the existing usage SSE event; the same payload is also exposed at GET /api/forecast for pull-style clients. It is suppressed when fewer than two completed past windows exist, when the window has just reset, or when a drop in the recent snapshot series indicates a missed reset between polls.

Fixes

• Canonicalize reset_at timestamps at write time. The Claude API returns reset_at recomputed as now + remaining on each poll, so the same nominal window drifts by hundreds of milliseconds across polls and occasionally straddles a minute boundary. Snapshots were being written with these drifting strings, so GROUP BY session_reset_at shattered every window into singletons and downstream aggregation lost track of session boundaries. Reset times are now rounded to the nearest minute on write, and a one-time idempotent migration canonicalizes existing rows on startup.