Episode 11: From Algebra to Algorithm: Multenions and Program SynthesisThe research record sharpens Episode 10’s proposal. McAulay’s Multenions is an associative, noncommutative, graded algebra: in the general n = 4 case it has sixteen scalar components, explicit grade projections, and named linear operations. It is not already a program, and it is not an eight-component octonion machine. An algebra gives computing a vocabulary and a discipline—what objects exist and what operations are lawful—but an algorithm supplies the missing temporal rule: which lawful operation happens next, under what condition, with what state, trace, halt, or error. Drawing on Trakhtenbrot’s labyrinth and machine arguments, this episode asks how a program can retain an Ariadne thread: an ordered record of the permitted choices that led to a result, a failure, or an exhausted bounded search. That thread extends Episode 4’s architectural vocabulary of activities, modes, transitions, and conditions by preserving the route through that structure.