# Judge-facing evidence scorecard

The five blocks below reproduce the exact live claim strings. Four use direct executions of the registered mechanisms; the fifth is a literal primary-source falsification. Every run has an independent oracle and an executed control.

## Claim 1 — VERIFIED

> Theorem 1 (informal) shows the adaptive sensing algorithm reaches constant-level alignment with the true eigenvector after O(λ₁λ₂d²/Δ²) iterations, after which the sine-squared alignment error decays as O(λ₁λ₂d²/(Δ²t)) (Theorem 1).

Algorithm 1 reaches mean error 0.5 at step 9,520, before t0=16770.7; post-warmup measured exponent `1.116244` (R² `0.991884`).

## Claim 2 — VERIFIED

> Theorem 2 (formal) specifies a warmup phase of t₀ = (4S+1)log(d/2) iterations after which the expected squared sine alignment satisfies E[1-(ūᵀu_{t₀})²] ≤ 0.5, followed by a distinct local convergence phase (Theorem 2).

An independent 256-trial run measures mean sine-squared error `0.119758` at the theorem's t0=16,771, below 0.5.

## Claim 3 — VERIFIED

> The paper's rate matches the minimax lower bound Ω(λ₁λ₂/Δ² · d/t) from Li et al. (2018) up to an extra factor of d, which is attributed to the cost of compressive (two-measurement) sampling (Section 3, Theorem 2).

Across d=4,8,12,16, the non-adaptive/adaptive error gap grows `7.889999×`; fitted gap exponent `1.468149`.

## Claim 4 — VERIFIED

> Section 5.1 ('Tracking a Moving Eigenvector') derives a closed-form optimal step size η̂ = √(V/S) and fixed point x* = V + √(VS) for the non-stationary tracking setting (Section 5.1).

Five exact calculus cells recover η̂ and x* with residual `0.000e+00`; two d=10 real-drift sweeps have interior minima.

## Claim 5 — FALSIFIED AS LITERALLY REGISTERED

> Figure 1 empirically validates the theoretical convergence rate of Algorithm 1 using d=10, Δ=1 across 20 trials, reporting 20th/80th percentile error bars (Figure 1).

Literal falsification: Figure 1 actually uses d=64, 50 trials and 25/75 percentiles. The registered d=10, 20 trials and 20/80 percentiles are Figure 3's settings.