Why we tried it
Study exterior control of finite-rank matrix Hamiltonians and the local/global analytic inputs required for zero-mode decay conclusions.
What the evidence shows
The manuscript leaves substantive analytic inputs for specialist verification and claims neither independent human nor proof-assistant validation; the coefficient audit and clarification must be read together.
Where the work stands
Finite symbolic free-channel diagnostics do not close the full interacting estimates; existence, uniqueness, endpoint and rank-uniform conclusions are not established.
Possible next steps
Fix operator, trace and coefficient conventions, and audit the local estimates, cluster localization and rotation argument individually; retain conditional status until those inputs are checked.
Suggested next steps are untested research questions, not new experimental results. The archive records manuscript provenance, licensing and status.