Their agreement requires identifying the relative motion speed in the first expression with the escape speed in the second. That identification supplies the physical bridge. A common scalar form without the bridge would not show that the two calculations describe the same comparison.

The resulting triangle rearrangement concerns the scalar count geometry. It introduces no intrinsic bend inside a primitive length reference and does not independently determine the curvature tensor of a realized spacetime metric. Observable geometry requires the corresponding relational construction.

The October source preserves this distinction between algebra, physical assignment, and full geometry. It reports a conditional connection between the two stated speed comparisons. It does not establish equivalence of every inertial and gravitational measurement prescription, or derive all of general relativity from a single triangle.