Deeper power/pace science — W′ balance, TTE, critical speed, taper projection

[eschizoid]

Roadmap tier "deeper power/pace science", sequenced last deliberately: these refine numbers for athletes who already trust the engine. Umbrella for four related items that each build on the CP model the power-duration curve already fits: W′ balance (match-burning within rides), time-to-exhaustion from the fitted CP model, critical speed as the pace-sport analog of CP, and a taper projection on the same CTL/TSB arithmetic as event targeting. Split into per-item issues when the tier actually starts; until then this records the scope so it is not re-derived.

[eschizoid]

Split into per-item issues as this umbrella asked, now that the tier has started:

• W′ balance — match-burning within a ride, against the athlete's own CP fit #186 — W′ balance (match-burning within a ride, against the athlete's own CP fit)
• Time to exhaustion from the fitted CP model, with the model's own limits stated #187 — time to exhaustion from the fitted CP model, with the model's own limits stated
• Critical speed and D′ — the pace analog of the CP model #188 — critical speed and D′ (the pace analog)
• Taper projection — plan-conditional arithmetic, sequenced with event targeting #189 — taper projection (plan-conditional arithmetic, sequenced with Event targeting — projected CTL/TSB on a target date #138 because ADR 0010 deferred the command surface and hypothetical-plan format to whichever lands first)

Order of work: #186 and #187 first — both sit directly on Metrics.critical_power, which is already fitted and published by power-curve, so they are arithmetic over an existing model rather than new modelling. #188 needs a mean-max SPEED curve that does not exist yet plus a grade-adjustment decision. #189 waits for #138.

Leaving this umbrella open until all four close, as the scope record it was written to be.

[eschizoid]

Fully split — closing.

All four items this umbrella held are accounted for:

item	outcome
W′ balance	#186, shipped (Metrics.roc, ReportSessions.roc)
Time to exhaustion	#187, shipped (stride tte)
Critical speed / D′	#188, open
Taper projection	#189, open

The umbrella's stated job was to hold the scope "so it is not re-derived" until the tier started. It started: two shipped, two carry "Split from the #140 umbrella" in their bodies, so the trail back survives the close.

Worth recording for whoever picks up #188: ADR 0013 (#199) landed today and applies directly to it. D′ is the pace-domain analog of W′ and inherits the whole problem — same hyperbolic model, same dependence on short maximal efforts, same property that r² measures precision rather than plausibility. It should publish SE(D') from the start and must not adopt an r² gate on the strength of it looking like a quality signal.

And the practical blocker: this athlete has one Run on record, so CS/D′ cannot be fitted on his data at all. That feature gets validated against someone else's history or not at all.