Declarations

and identifier. Oai212-A is the requested manuscript identifier. No authorship, approval, or endorsement by N. Cheung or by the authors of the external papers is asserted.

dependency. The standard FPP shape theorem and the cited cone classification are external established mathematical inputs. The regularity claims of 212-02 are separately marked conditional. Cheung manuscript comparisons do not identify distinct models.

changes. The controlled CNOT circuit, independent-pair quench, monitored quench, and advertised serial repeater are explicit engineered models. Their exact identities do not substitute for missing reductions of generic models.

scope. No invariant physical speed, Lorentzian metric field, Einstein dynamics, thermodynamic optimum, Page curve, holographic dictionary, or standing quantum-gravity solution is claimed.

scope. No full characteristic cross-line product, interacting Ward datum, or inherited gravitational quantum coefficient is admitted. O.1 remains NOT_CLOSED; the downstream admission exit remains closed.

and verification. No successful pdflatex execution, proof-assistant run, independent numerical execution, referee approval, or journal acceptance is asserted. The source is provided as one self-contained pdflatex file. The claimed new results are the explicit proofs above, with their stated hypotheses.