Mathematical debugging ledger

Damping order. The noise term is multiplied immediately by $a$, giving $a^{4-r}$, not $a^{3-r}$.

Common noise cancellation. It applies only when the noise coefficient is common. Different damping gives a residual even at common $\sigma$.

L2 normalization. Norm divided by $N_W$ is not RMS.

Loss versus accuracy. A smooth loss descent theorem does not establish a held-out classification or stress ranking.

Gradient type. Ambient inactive-coordinate derivatives differ from derivatives blocked by an in-forward mask.

Zero regrowth. The repaired endpoint is exactly zero; hard count discontinuities elsewhere remain.

Density stage. Acute displacement is not paired with a post-challenge mask count.

Matching support. A span overlap or a pooled percentile is not finite-grid support.

Statistical units. Repeated noise draws do not multiply the number of independent population inputs.

Dephasing normalization. The generator $\gamma {\mathcal{D}}_Z/2$ gives off-diagonal decay $e^{-\gamma t}$.

Markov-rate orientation. $k_{ij}$ is the rate from $j$ to $i$, fixing both terms in (eq:markov).

Operational budget. A generator integral controls a specified interval channel. Complete histories need all interval and instrument errors.

Coherence and utility. The contrast is oriented and task-specific; its sign can reverse.

Graph versus subsystems. Node labels do not automatically define tensor-local interventions or a spacetime causal cone.

Source relations. Landmark comparisons are not carrier identifications or automatic premises.

Verification. Proof, compilation, numerical execution, regression, and clinical validation are distinct evidence types.