Declarations

. The author is Ngo Cheung. The title metadata and declarations are consistent. No empty-author boilerplate is retained.

and novelty. The fixed-input sharp-width theorem is attributed to X-D, version 3. The predecessor scalar maps and classical handoff are attributed separately. The claimed contribution is the supported proof, topology and defect audit, and finite encoding interface, not a new general singular-product theorem.

status. X-D and the Enter background are cited as source records. Comparisons available here as supplied excerpts are identified as such; no catalogue-wide proof verification is asserted. Internal publication dates and DOIs are not invented.

scope. The metric coefficients are fixed smooth classical inputs. The limit is in a named scalar compact-test topology, then its unchanged free quotient. No joint sharp metric admission or characteristic quantum composition follows.

scope. The clock consumes a finite encoding, not geometric time. The finite dictionary does not acquire a continuum field. Transport uses declared regular finite-operation permissions.

. No successful execution, proof-assistant verification, symbolic-program execution, numerical evaluation, hardware synthesis, experiment, independent referee review, journal acceptance, or external registration is asserted. The mathematical claims are the explicit definitions and written proofs in this source.