The Governing Minimum: Multi-Domain Rate Asymmetry Under Challenge as Functional Reserve

1. Foundation

Functional reserve is the surplus capacity separating independent function from disability. It is demand-dependent. Prevailing operationalisations treat it as a stock measured at rest and combined by weighted summation. Three properties of that architecture are rejected: measurement at rest, substitutability across domains, and the use of levels rather than rates.

A companion paper defines a within-person gain–loss ratio for a single domain over a train–detrain window of weeks (O’Leary, 2026). The present paper defines a related quantity on the acute challenge–recovery cycle (seconds to minutes) and supplies the multi-domain aggregation rule. The two constructs share formal structure but differ in timescale and underlying physiology; this is not a direct generalisation of domain count alone.

Ontology

• Functional reserve — latent physiological construct
• Challenge response — observed perturbation trajectory
• Rate asymmetry — measurable kinetic phenotype
• Governing domain — the eligible domain with the smallest estimated ρ_d

2. Construction

Mandatory core. Force recovery, lactate clearance, and dual-task cost recovery are always required. They were chosen because each admits a matched instrument, none requires laboratory infrastructure beyond ordinary clinical equipment, they span three distinct rate-limiting physiologies, and each literature already contains established challenge protocols. The core is the minimum common panel specified for cross-person comparison; it is not claimed to be exhaustive.

Rate definition. For each eligible domain a standardised challenge is applied. Both rates are fitted constants obtained under the kinetic discipline of the companion paper:

• r_l — degradation rate under load
• r_g — restoration rate after load removal

ρ_d = r_g / r_l

Same-instrument rule. Both rates must be recorded by the identical instrument in identical units. Domains that cannot meet this rule are ineligible. No z-score substitution is permitted.

Primary quantity and uncertainty. ρ_min = min_d of the point estimates (ρ̂_d). Uncertainty is reported as a bootstrap or simultaneous interval for ρ_min itself. Taking the minimum of independent domain-wise lower confidence bounds is rejected: an imprecisely measured domain would systematically win the minimum.

Acute-window boundary. Plateau detection is an independent preprocessing step. After load removal the performance variable is examined for the earliest time t at which (i) the local first derivative is statistically indistinguishable from zero within the instrument noise model and (ii) the derivative remains non-positive for a consecutive confirmation interval of length τ. All data up to t are eligible for fitting r_g; data after t are excluded. Because the plateau is noisy, t is reported as a band. τ is a free parameter fixed before data collection; sensitivity of ρ_min and of domain ordering to reasonable variation in τ is a required reporting item.

Experimental isolation. Water immersion removes axial load while preserving graded muscular demand through velocity-dependent resistance and producing the same central fluid shift seen in bed rest. It isolates muscular work from joint loading.

3. Interpretation

Why the model predicts ρ < 1 on the acute cycle. Degradation under load is multi-factorial and parallel. Restoration after load is sequential and energy-constrained. The structural asymmetry predicts that the recovery limb will be shallower than the loss limb. The claim is restricted to the acute window.

Governing domain. The domain whose restoration is most constrained relative to its degradation yields the lowest ρ_d. Because domains are non-substitutable, that domain sets the recovery interval the person actually requires under the specified challenge. Asymmetry explains why ρ < 1; non-substitutability explains why the minimum is taken. These remain separate arguments. The governing domain is a rate-asymmetry bottleneck; it is not synonymous with the most clinically abnormal domain.

Timescale distinction. Net adaptation (supercompensation) lies outside the acute window. ρ therefore predicts the required recovery gap rather than the adaptive outcome. The required gap G is a monotonically decreasing function of ρ_min whose exact form is to be determined empirically.

Clinical consequence. Two patients can share the same rehabilitation programme and the same numerical minimum yet diverge. One recovers; the other plateaus. The under-recovered patient was re-challenged before the governing domain returned to baseline and therefore accumulated deficit under a programme that looked identical on paper. Intensity is measured. Volume is measured. Frequency is inherited.

4. Worked Illustration

Illustrative values only. Uncertainty intervals for ρ_min are omitted from this illustration; §2 requires that they be reported with any measured estimate.

5. Schematic

Figure 1. Acute cycle schematic. Steep loss limb under load, shallower recovery limb that decelerates into a visible plateau, acute-window boundary drawn as a band on that plateau, and supercompensation overshoot (lighter weight) outside the measured window.

Figure 1. Acute cycle schematic. Steep loss limb under load, shallower recovery limb that decelerates into a visible plateau, acute-window boundary drawn as a band on that plateau, and supercompensation overshoot (lighter weight) outside the measured window.

6. Relation to Prior Work

Convertino’s compensatory reserve is the closest precedent. It measures under progressive challenge and reports remaining margin to decompensation. It is the single-domain, single-limb, margin-to-threshold special case of the present framework. Convertino reports the level of remaining capacity; the slope of that trajectory is r_l.

Limiting-factor models already embody a bottleneck rule. The novelty claimed here is restricted to the quantity being minimised: a matched-instrument rate asymmetry rather than a peak level.

The stimulus-response programme in physical resilience is the nearest live work and shares this paper’s premise. Varadhan and colleagues (2008) proposed characterising loss of resilience in homeostatic regulation through the dynamics of response to a standardised stimulus rather than through resting level, and the Study of Physical Resilience and Aging has developed that proposal into an empirical programme (Walston et al., 2023). Bandeen-Roche and colleagues (2025) analysed multi-system stimulus-response data in the SPRING pilot — Holter time series, cortisol response to adrenocorticotropic hormone stimulation, and repeated diurnal salivary cortisol — and derived dynamic component scores intended to capture adaptive capacity across systems. Related work has applied provocative testing and orthostatic challenge in community-dwelling older adults toward the same end.

That programme and the present construct agree on the measurement condition and differ on the aggregation rule. Both hold that reserve is visible under provocation rather than at rest, and both measure response dynamics rather than levels. Three differences follow. The quantity extracted here is a ratio of two fitted rate constants, restoration against degradation, in the same instrument and identical units, rather than a component score derived across heterogeneous measures. Domains are combined by a minimum rather than by a composite or factor structure, on the claim that non-substitutable domains admit no averaging. And the window is the acute challenge-and-recovery cycle, seconds to minutes, whereas the resilience programme is anchored to major clinical stressors and to recovery trajectories over months.

The novelty claimed is therefore narrow. Not that provocation is the correct measurement condition, which that literature established. Not that multi-system dynamics carry information about reserve, which it has demonstrated. The claim is that the quantity to be minimised across domains is a matched-instrument rate asymmetry, and that the minimum rather than a composite is the governing figure.

Search statement. A targeted prior-art search was conducted in August 2026 using AI-assisted literature search across PubMed and Europe PMC. The nearest prior work identified is addressed above. No prior report was identified of a multi-domain minimum of matched-instrument gain-to-loss rate ratios under controlled acute challenge. This is a statement about the search rather than a claim that the construct is unoccupied: a systematic search with recorded databases, query strings, and hit counts has not been performed.

Novelty claim (modest form). We propose a multi-domain kinetic operationalization of functional reserve in which the smallest restoration-to-degradation rate ratio identifies the governing domain under a standardized acute challenge.

7. Falsification

The construct is falsified if, under measurement satisfying §2:

• ρ_min has no more predictive value than the mean of the eligible point estimates (ρ̂_d).
• The governing domain is unstable within persons across repeated equivalent challenges.
• ρ_min carries no relation to the recovery interval required for net adaptation.

8. Limitations

The construct is untested. The acute-window boundary rule remains to be validated across laboratories. τ is a free parameter whose influence must be reported. Standardised challenge protocols are not specified here. A systematic prior-art search with recorded databases, query strings, and hit counts has not yet been performed.