Corrections to the proposed plan

The following repairs are necessary.

1. Nonimplication is not nonexistence. A finite network with commuting channels need not determine a conformal net. This does not mean that no such network can occur inside a conformal-net model.

2. The circle already has a chiral interpretation. A circle net is an established mathematical model of chiral CFT, with spacetime interpretations obtained through additional constructions. The correct refusal is that the supplied VOA–net correspondence does not derive a gravitational spacetime. The categorical statement is not devoid of geometric or physical content CKLW,HenriquesTener.

3. En06-A's actual theorem has stronger hypotheses. The supplied :algmicro is a conditional observable-limit theorem, not a theorem deducing observable microcausality from channel commutation alone CheungEn06A. We retain its cross-product-preserving observable interface.

4. A finite-index sector is not a finite-dimensional quantum register. Categorical or statistical dimension is not the dimension of the sector Hilbert space. A qubit experiment requires its own finite encoding and output channel.

5. Fusion can describe categorical composition. Connes fusion composes correspondences. What it does not do by itself is specify the input, output, preparation, accessible factor, and complete decoder of a quantum-memory task ThomFusion,GuiUnbounded.

6. A preserved effect is weaker than recovery. A channel can preserve a named observable while destroying coherence needed to recover the full code.

7. The forty-shot statement is certificate-specific. We prove the limitation for the confidence procedures printed below. We do not claim a universal lower bound for every protocol, trusted noise model, or experimental design.

8. A sector tag is not sector identification. Attaching a channel certificate to a declared label does not prove that the device prepares or represents that superselection sector.

9. A source-level convention requires repair. Under the ordinary complex-linear contragredient convention, the Hermitian-dual evaluation in the supplied preprint has the opposite linearities to those printed there. Section sec:pairing records the precise correction without claiming that the remaining proof has thereby been verified.

10. The extension agenda contains open problems. Covering every stage of the comparison does not solve the non-strongly-rational locality conjecture, logarithmic extensions, or the inherited characteristic-map problem. Those questions are retained as separate programmes.