Recall these multiplication identities from the home page:

for septrights:
2 cos x cos y = cos (x − y) + cos (x + y)

not for septrights:
2 cosh x cosh y = cosh (x − y) + cosh (x + y)

The singletons Q through V are defined using cosine arguments from only the first quadrant (0, π/2). However, multiplication requires finding the cosines of arguments outside that domain, including the second quadrant (π/2, π).

This numerical table illustrates why the hyperbolic cosine cannot be substituted for the circular cosine in septright multiplication. With the circular function, the numbers in the second quadrant are the negatives of those in the first. On the other hand, with the hyperbolic function there is no particular relationship.

circular cosine,
doubled related
septright hyperbolic cosine,
doubled
2 cos ( 0π /14) = 2.000000 2 cosh ( 0π /14) = 2.000000
2 cos ( 1π /14) ≈ 1.949856 +Q first
quadrant 2 cosh ( 1π /14) ≈ 2.050567
2 cos ( 2π /14) ≈ 1.801938 +R 2 cosh ( 2π /14) ≈ 2.204824
2 cos ( 3π /14) ≈ 1.563663 +S 2 cosh ( 3π /14) ≈ 2.470572
2 cos ( 4π /14) ≈ 1.246980 +T 2 cosh ( 4π /14) ≈ 2.861250
2 cos ( 5π /14) ≈ 0.867768 +U 2 cosh ( 5π /14) ≈ 3.396611
2 cos ( 6π /14) ≈ 0.445042 +V 2 cosh ( 6π /14) ≈ 4.103728
2 cos ( 7π /14) = 0.000000 2 cosh ( 7π /14) ≈ 5.018357
2 cos ( 8π /14) ≈ −0.445042 −V second
quadrant 2 cosh ( 8π /14) ≈ 6.186749
2 cos ( 9π /14) ≈ −0.867768 −U 2 cosh ( 9π /14) ≈ 7.667984
2 cos (10π /14) ≈ −1.246980 −T 2 cosh (10π /14) ≈ 9.536964
2 cos (11π /14) ≈ −1.563663 −S 2 cosh (11π /14) ≈ 11.888199
2 cos (12π /14) ≈ −1.801938 −R 2 cosh (12π /14) ≈ 14.840581
2 cos (13π /14) ≈ −1.949856 −Q 2 cosh (13π /14) ≈ 18.543404
2 cos (14π /14) = −2.000000 2 cosh (14π /14) ≈ 23.183907

circular cosine, doubled	related septright		hyperbolic cosine, doubled
2 cos ( 0π /14) = 2.000000			2 cosh ( 0π /14) = 2.000000
2 cos ( 1π /14) ≈ 1.949856	+Q	first quadrant	2 cosh ( 1π /14) ≈ 2.050567
2 cos ( 2π /14) ≈ 1.801938	+R	2 cosh ( 2π /14) ≈ 2.204824
2 cos ( 3π /14) ≈ 1.563663	+S	2 cosh ( 3π /14) ≈ 2.470572
2 cos ( 4π /14) ≈ 1.246980	+T	2 cosh ( 4π /14) ≈ 2.861250
2 cos ( 5π /14) ≈ 0.867768	+U	2 cosh ( 5π /14) ≈ 3.396611
2 cos ( 6π /14) ≈ 0.445042	+V	2 cosh ( 6π /14) ≈ 4.103728
2 cos ( 7π /14) = 0.000000			2 cosh ( 7π /14) ≈ 5.018357
2 cos ( 8π /14) ≈ −0.445042	−V	second quadrant	2 cosh ( 8π /14) ≈ 6.186749
2 cos ( 9π /14) ≈ −0.867768	−U	2 cosh ( 9π /14) ≈ 7.667984
2 cos (10π /14) ≈ −1.246980	−T	2 cosh (10π /14) ≈ 9.536964
2 cos (11π /14) ≈ −1.563663	−S	2 cosh (11π /14) ≈ 11.888199
2 cos (12π /14) ≈ −1.801938	−R	2 cosh (12π /14) ≈ 14.840581
2 cos (13π /14) ≈ −1.949856	−Q	2 cosh (13π /14) ≈ 18.543404
2 cos (14π /14) = −2.000000			2 cosh (14π /14) ≈ 23.183907

As defined in this report, septrights are limited to the real numbers. In the context of complex numbers, however, the hyperbolic and circular cosines exhibit highly analogous behavior, and are a potential avenue for extending the septrights.