Description: This working paper establishes the Generative Time Circuit Theorem (GTCT), the fifth operator T in the TOGT generative chain C→K→F→U→T. Building on the dm³ contact‑geometric framework of Principia Orthogona Volumes I–II, the paper proves the spiral return x0→G64(x0)→G64(x64)=x0′ with x0′≠x0, derives the stability radius ε0=1/3, formalizes the g‑series taxonomy, and provides complete derivations of the action‑variable dissipation encoded in the contact form α=dz−λ. The document includes six graded exercises, three falsifiability conditions, and a set of open problems linking dm³ to TSVF, delayed‑choice experiments, and entanglement swapping. This is Ring 5 of the Principia Orthogona series.

Keywords: dm³, TOGT, GTCT, generative transitions, contact geometry, spiral return, stability radius, operator algebra, Principia Orthogona, AXLE, Lean 4

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