Representative adaptive-performance contract

This note formalizes Fixture F-006 from the sports expertise, adaptive performance, and team coordination audit. It supplies a comparison contract for Candidate 002, Candidate 004, Candidate 006, Candidate 007, Candidate 009, Candidate 012, Candidate 014, and Candidate 019. It creates no new candidate.

Versioned episode state

For agent $i$ in episode $e$, preserve

where:

• $X_e$ is the physical state, rules, task geometry, deadline, consequence, and hidden regime of episode $e$;
• $O_{i,e}$ is the information actually received by agent $i$, including source, support, latency in seconds, occlusion, noise, loss, and calibration;
• $A_{i,e}$ is the feasible action set under the current body, actuator, equipment, authority, rate, range, and safety constraints;
• $H_{i,e}$ is the timestamped acquisition and selection history: practice, feedback, opponents, teammates, injury or faults, prior exclusions, and opportunities that were offered or withheld;
• $M_e$ is the teammate and opponent roster, role assignment, policy history, turnover event, and communication topology;
• $F_{i,e}$ is the feedback channel, its delay in seconds, its information in bits, and the party choosing when it is supplied;
• $R_{i,e}$ is the resource and fatigue state, with each component stored in its native unit rather than collapsed into a readiness score;
• $D_{i,e}$ is the damage or fault state, diagnostic uncertainty, protected capability envelope, and current return stage;
• $G_{i,e}$ is the selection and opportunity policy that determines access to training, roles, observation, intervention, and later outcome measurement;
• $C_e$ is the randomized intervention, control, counterfactual pair, and stopping rule;
• $U_e$ is the sampling unit, such as action, possession, episode, agent, dyad, team, site, season, or cohort; and
• $B_e$ is the complete resource ceiling: events, bytes, seconds, person-hours, joules, damage, unsafe events, replacements, and opportunity.

The comparison estimand for method $m$ and literal outcome $k$ is

where $Y_k$ is measured in the registered unit for outcome $k$. A contrast $Q_{m,k}-Q_{b,k}$ against baseline $b$ is uninterpretable when any element of $\mathcal K$ differs without a registered intervention or adjustment.

Outcome firewall

No scalar “performance” score may replace the following vector:

The components and their units are:

Representative distance is a vector

Let $P_{\mathrm{tr}}$ and $P_{\mathrm{te}}$ be the training and target distributions. Register

where $d_O$ compares received information, $d_A$ feasible actions, $d_T$ deadline and consequence, $d_M$ teammate/opponent composition and policy, $d_F$ feedback, $d_R$ resource state, $d_D$ damage/return state, and $d_G$ selection/opportunity policy. Each $d_z$ is a declared divergence between the corresponding marginals or conditionals under $P_{\mathrm{tr}}$ and $P_{\mathrm{te}}$. It is dimensionless for a statistical divergence and has the registered ground-cost unit for optimal transport. No unreported weighted sum is a valid “representativeness” score.

For source stratum $s$ and target stratum $t$, preserve the transfer matrix

where both $Q^{\mathrm{tr}}$ and the transfer gap $G$ use the registered task unit. Report $G$ separately by cue, feasible action, opponent, feedback, resource, damage, and selection-policy changes.

Anticipation, interception, and cue use

For $N$ independent events, outcome $y_n$, actual observation history $o_{n,\le\tau}$ available by occlusion time $\tau$ in seconds, and predictive distribution $p_m$, define

where $L_m$ is log loss in bits per event. For information channel $c$, the registered causal cue value is

also in bits per event. Here $L_{m,-c}$ is measured under removal or neutralization of channel $c$, not inferred from gaze or saliency. Predictive regulation must additionally retain false-alarm action, reserve debit, recovery, and cumulative exposure instead of treating cue value as the whole outcome (C-1494).

Physical coupling is reported separately as

where $p_{\mathrm{hit}}$ is dimensionless interception success, $e_{\mathrm{end}}$ is endpoint error in metres, $t_{\mathrm{move}}$ is movement onset in milliseconds, and $p_{\mathrm{unsafe}}$ is dimensionless unsafe-event probability. Label or joystick accuracy cannot substitute for $I_m$.

Practice, retention, transfer, and exploration

Let $q_m(n,t)$ be literal task quality after attempt $n$ and exposure time $t$ in seconds. Keep three estimands:

where $\Delta t$ is the scaffold-free retention delay in hours or days. The first target trial $Q^{\mathrm{tr},1}_{m,s\rightarrow t}$ is frozen before any target update; later adaptation is a separate curve.

For action variable $A$ and reached-outcome variable $Z$, exploration is

where both entropies and mutual information are in bits, $K_m$ is coverage of the registered feasible region as a dimensionless fraction, $Q^{\mathrm{tr}}_m$ is later transfer in its task unit, and $C_m$ is the separate cost vector. Higher action entropy without outcome information or later utility is not useful exploration.

After a perturbation at time $t_0$, define recovery time

where $T^{\mathrm{rec}}_m$ and the stability horizon $h$ are in seconds, $q_m(u)$ is task quality in its registered unit, and $\mathcal A_q$ is the preregistered admissible quality envelope. Overshoot, recurrence, and damage are additional axes rather than hidden inside $T^{\mathrm{rec}}_m$.

Resource state, pacing, and readiness

Let external power $P(t)$ be in watts over event duration $T$ in seconds. The external work is

where $E_{\mathrm{ext}}$ is in joules. Metabolic, device, facility, embodied, and lifecycle energy use different boundaries and remain separate ledger rows.

A resource-qualified controller has the form

where $a_t$ is the commanded action or power target in its native unit, $o_{\le t}$ is causally received observation history, $\widehat r_t$ is the estimated resource/fatigue vector, $\widehat d_t$ is the estimated damage state, $s_t$ is remaining work in metres, seconds, events, or joules, $\widehat\pi_{\mathrm{opp},t}$ is the opponent-policy estimate, $\widehat b_{\mathrm{team},t}$ is the teammate-state estimate, and $f_t$ is available feedback. Each estimate and channel receives its own ablation.

Readiness is a calibrated action envelope rather than a score:

where $A_t$ is the feasible action set, $Z_{t:t+h}$ is the multidomain outcome vector over horizon $h$ in hours, $\mathcal Z_{\mathrm{safe}}$ is the registered safe envelope, $\mathcal I_t$ is information available at decision time, and $\alpha$ is the dimensionless tolerated risk. Empty envelopes require abstention or escalation.

Staged and reversible return

Let $g_t\in\{0,1,2,3,4\}$ denote protected, modified, controlled, full-load, and adversarial operation. Promotion is admissible only if

where $\mathcal A_g$ is the multidomain admissible envelope for stage $g$, $h$ is the follow-up horizon in hours or days, and $\alpha_g$ is its dimensionless risk tolerance. If the current envelope is violated, the gate must allow

Report false promotion, false withholding, dwell time in hours, recurrence, rollback count, availability, damage, and human adjudication hours separately.

Team coordination and shared information

For task variable $z(t)$ and agent contribution $u_i(t)$, perturb agent $i$ by $do(\eta_i)$ and estimate

where $\ell$ is lag in seconds and $X_t$ is task state. Compensation requires both a registered response in $\Gamma_{ij}$ and reduced task-variable error. Here $u_i$ and $u_j$ are recorded in their native contribution units, $\eta_i$ is a registered perturbation in the unit of agent $i$'s action or state, and $\Gamma_{ij}$ has the product unit of the two contributions; correlation or synchrony without intervention is insufficient. Common-drive and edge-intervention controls are therefore mandatory before mapped synchrony can be credited with useful coordination (C-1495).

For teammate $j$'s future action or intent $b_{j,n}$ and agent $i$'s predictive belief $p_i$, shared-information quality is

where $L_{i\rightarrow j}$ is in bits per event, $h_{i,n}$ is information actually available to $i$, and $N$ is the number of independent team events. Report it under message ablation, teammate turnover, role reassignment, and never-co-trained cross-play alongside messages, bytes, latency, repair, and task quality.

Deception and opponent adaptation

For opponent action $a^{\mathrm{opp}}_n$, available history $h_n$, and estimate $\widehat\pi_m$, define

in bits per opponent action. For matched genuine and deceptive interventions,

where $k$ names a literal outcome and the difference retains its unit. Report calibration, confidence, exploitability, regret, abstention utility, and adaptation time separately under known, held-out, changing, and colluding opponents.

Selection, opportunity, and prospective prediction

Let $S_i\in\{0,1\}$ denote selection, $Z_i$ preselection evidence, $O^{+}_i$ postdecision opportunity in hours or task exposures, and $Y^{\mathrm{future}}_i$ later capability in its task unit. The prospective selection-policy estimand is

It cannot be estimated by comparing selected survivors with excluded agents when selection changes $O^{+}_i$, coaching, opponents, follow-up, attrition, or injury exposure. Report prospective calibration in new cohorts, selection and opportunity rates, false-negative recovery, attrition, censoring, subgroup error, later capability, and complete development cost.

Complete efficiency and equal budgets

For method $m$, retain lifecycle energy

where every $E$ term is in joules under one declared service interval. The terms denote training, inference, sensing, actuation, communication, facility, recovery, maintenance, and amortized embodied energy, respectively.

Human effort is

where each term is in person-hours and roles are reported separately. The complete cost vector is

where the four $N$ terms count events, environment or optimization steps, queries, and bytes; $T_{\mathrm{wall}}$ is wall time in seconds; $H^{\mathrm{human}}$ is person-hours; $E^{\mathrm{life}}$ is joules; $N_{\mathrm{unsafe}}$ counts unsafe events; $D_{\mathrm{harm}}$ is damage in a registered physical or severity unit; and $C_{\mathrm{opp}}$ is withheld opportunity in task exposures or person-hours.

Method $m$ is feasible only if

where $\mathbf B$ is the preregistered componentwise ceiling with the same units. A complete efficiency claim requires non-inferiority on every protected outcome and a Pareto improvement on at least one preregistered resource axis. An over-budget run is infeasible, not a score to normalize afterward.

Confirmatory contrast and retirement

Let $b^*(t)$ be the strongest mature baseline for track $t$, selected on development data before confirmatory outcomes open. For protected outcome set $\mathcal P_t$, retain a residual only when

where $\delta_{t,k}$ is the preregistered improvement or non-inferiority margin in the unit of outcome $k$, and $\alpha_t$ is the dimensionless error budget. The contrast must survive actual-channel, feasible-action, history, opponent/team, feedback, resource, damage, selection, and complete-cost ablations on held-out task, model, site, and hardware strata. Otherwise retire the mechanism claim while preserving the measurement contract.