The Helical-Resonant Time Model: A Geometric Framework Reconciling Cyclical, Linear, and Branching Temporal Descriptions

What if the ancient debate between cyclical and linear time — does history repeat, or does it progress? — was never actually a contradiction? This paper proposes that cyclical, linear, and branching descriptions of time are not competing theories but different two-dimensional views of the same three-dimensional geometric object: a helix. Viewed from the front a helix looks like a circle (cyclical time). Viewed from the side it looks like a wave with net forward progress (linear time). Viewed in full three dimensions it contains both simultaneously. This geometric unification — what we call the Helical-Resonant Time Model — also connects to a companion paper on continuous spacetime generation, proposing that the same substrate mechanism driving cosmic expansion determines the pitch of the temporal helix, that the cosmic microwave background encodes the helix's revolution frequency, and that black holes function as the return mechanism that prevents temporal structure from degenerating into pure linear progression. An appendix proposes a candidate spacetime metric embedding of the helical geometry, motivated by analogy with the Kerr metric for rotating black holes. The coupling constant connecting helical geometry to spacetime (α ≈ 6.4 × 10⁻³⁰) is derived from two existing cosmological measurements — the Hubble parameter and CMB temperature — without introducing free parameters. Two new observational predictions follow: cumulative polarization rotation of light from distant quasars and anomalous geometric time delays in multi-messenger signals. This is a speculative framework paper, not a completed theory. Limitations are explicitly acknowledged throughout.