On this page
Question
What does marked refinement rigidity add, and is it a dependency of the reconstruction proof?
What the note explains
The source labels ARR a proved external companion and records that it is not imported into the eight-stage reconstruction chain. Mathematical usefulness and logical necessity are different questions.
Example
Perform the source's counterfactual deletion test: remove ARR from the dependency diagram and ask which named hypotheses, constants, or operator inputs are actually lost.
What the approach gains
The note supplies a separate rigidity result, a selected SU(3) coefficient-line analysis, and a record of where reverse comparisons fail. It also identifies which attractive interpretations lack a quantitative bridge.
Reading route
Begin with the status page and exact theorem statement. Read the typed hypothesis ledger before the selected-SU(3) clauses, and finish with the import audit and counterexamples.
Scope and limits
Retain PROVED_EXTERNAL_COMPANION, NOT_IMPORTED, and NOT_A_DEPENDENCY as source dispositions. This production pass does not re-audit the five-paper proof or turn a rigidity slogan into a mass-gap estimate.