Technical and documentary clarifications

Product completeness. The finite ledger is complete for Assumption ass:product, not for every self-adjoint extension of the full three-dimensional minimal operator. Non-product boundary data are infinite dimensional.

Positivity and infrared behaviour. The nonnegative extension condition, the compact-test covariance estimate, and thermal infrared behaviour are separate questions.

Boundary relations. A finite Hermitian matrix is one chart, not the entire extension space. Compression in (eq:CW) supplies the remaining charts.

Transverse versus longitudinal spectrum. A transverse bound eigenfunction gives a longitudinal continuous branch. The instability proof uses that branch rather than an invented full-space eigenvector.

Analytic branch versus physical flux periodicity. The shifted formulas refer to a fixed entire geometric branch. They do not eliminate the extension change by integer flux relabeling.

Complex first jet. Taking a real part is appropriate for the stress prescription but destroys the current information if done before its first jet.

All diagonal cone parameters. Joint ellipticity proves the regular representative even where individual image sectors jump.

Projection versus original CCR. The principal-value reference is not positive; the projected positive covariances have projected commutators and do not solve the original local-state problem.

Completion terms. Vanishing local curvature ambiguities on $M$ does not classify worldsheet-supported terms or stress-correlation contacts.

Transfer versus covariance. Supported equality of Green operations does not identify their symmetric states.

Finite arrays versus continuum normalization. A finite report, finite normal-jet array, or small numerical residual is not automatically a finite-dimensional exhaustive normalization class or a continuum identity.

External programme boundaries. The supplied XIV-H/I/J and XV-B excerpts describe different objects, fields, domains, contacts, and quantum gates. Internal retarded-kernel reconstruction, characteristic composition, output wavefront control, and quantum admission remain distinct there. No theorem here supplies a missing graph product or promotes a classical master-equation result to quantum closure.

Verification status. No successful compilation, independent execution, machine-checked proof, referee acceptance, or journal acceptance is claimed. The mathematical assertions released here are the displayed proofs with their explicit hypotheses.