Biomarker-like surface-state gating for patient-selection analog: A2C-controlled scanning achieves ≥30% time reduction only when a measurable pre-scan 'surface controllability index' (SCI) exceeds a threshold, where SCI is computed from a 1–2 second pilot scan (e.g., power spectral density of height/current noise, drift rate estimate, and tip stability metric). Hypothesis: selecting samples/conditions with SCI>τ enables reliable A2C resource allocation without loss of atomic resolution, while SCI≤τ triggers a fallback deterministic scan. Test by prospectively stratifying experiments by SCI and comparing time-to-resolution and failure rate (tip crash, loss of atomic contrast) across strata.

For scanning probe microscopy (STM/AFM) sessions on a given sample-tip-instrument configuration, define a Surface Controllability Index (SCI) computed from a 1–2 second pilot scan as a weighted function of: (a) power spectral density (PSD) of height/current noise in a defined frequency band, (b) estimated drift rate (nm/min) from short-baseline repeated line scans, and (c) a tip-stability metric (e.g., variance of setpoint current/force error under feedback). The falsifiable claim is: there exists a threshold τ on SCI such that (1) for sessions with SCI>τ, an A2C-controlled adaptive scanning policy achieves ≥30% reduction in time-to-resolution versus a deterministic raster baseline, with atomic-resolution contrast (as measured by a defined lattice-fidelity metric) statistically indistinguishable from baseline (non-inferiority margin ≤5% contrast loss), and tip-crash/failure rate not exceeding baseline failure rate by more than 2 percentage points; and (2) for sessions with SCI≤τ, the same A2C policy shows either no significant time reduction (<10%) or a significantly elevated failure rate (≥2x baseline), justifying a deterministic fallback. The hypothesis is disprovable if no such τ exists that separates these two regimes with statistical significance.

Minimum viable test: single-instrument, two-arm stratified prospective study.

1. Instrument: one STM or AFM system with programmable scan control and API access to raster parameters and feedback signals.
2. Samples: 3–5 calibration-grade samples spanning a controllability gradient (e.g., freshly cleaved HOPG = high SCI expected; aged/contaminated Au(111) or samples with known drift issues = low SCI expected), plus intermediate cases (partially contaminated surfaces).
3. For each of N=90 scan sessions (30 per SCI tertile, randomized sample/session order to avoid time-of-day confounds): run 1–2s pilot scan, compute SCI in real time, then run assigned arm (A2C-adaptive vs. deterministic-raster) blind to a human evaluator for outcome scoring.
4. Record: time-to-resolution (wall clock to reach pre-defined resolution criterion), final lattice-fidelity score, binary failure flag, and full pilot-scan raw data for SCI recomputation/audit.
5. Primary analysis: stratify by SCI tertile; compare time reduction and failure rate between A2C and deterministic arms within each stratum using paired/unpaired tests as appropriate; fit logistic/segmented regression to locate optimal τ.

# 1. SCI computation
def compute_sci(pilot_scan_data, weights):
    psd_feat = welch_psd_band_power(pilot_scan_data.height, band=(0.1,10))
    drift_feat = estimate_drift_rate(pilot_scan_data.repeated_lines)
    stability_feat = rolling_variance(pilot_scan_data.feedback_error)
    norm = [normalize(f) for f in (psd_feat, drift_feat, stability_feat)]
    return weighted_sum(norm, weights)  # weights frozen from calibration set

# 2. Session runner
for session in randomized_session_queue:
    pilot = run_pilot_scan(duration=1.5)
    sci = compute_sci(pilot, FROZEN_WEIGHTS)
    stratum = assign_stratum(sci, tau_candidates)
    arm = session.assigned_arm  # A2C or deterministic, randomized a priori
    if arm == "A2C":
        result = run_a2c_policy(frozen_policy, sample)
    else:
        result = run_deterministic_raster(sample)
    log(session_id, sci, stratum, arm, result.time, result.fidelity, result.failure_flag)

# 3. Analysis (post-hoc, offline)
grid_search_tau(sci_values, outcomes, metric="time_reduction_and_failure_rate")
mixed_effects_model(outcome ~ sci_stratum * arm + (1|sample) + (1|instrument))
bootstrap_ci(tau_optimal, n_boot=10000)