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

STATUS NOTE (July 2026). The core geometric thesis of this paper — the helix as the unification of cyclical, linear, and branching time, with the CMB temperature setting the revolution frequency — stands, and has been strengthened by subsequent work (the temperature identification is now shown to be dynamically self-maintaining). Several secondary elements have been corrected or superseded by the framework's continuing adversarial review, recorded here for the reader: (1) The coupling constant is refined to α = H_Λℏ/k_BT_CMB ≈ 5.1 × 10⁻³⁰, with H_Λ = H₀√Ω_Λ the de Sitter rate; the value quoted below uses the earlier H₀ convention. (2) The two observational predictions stated below are withdrawn: subsequent analysis shows the polarization rotation vanishes at leading order, and multi-messenger geometric delays are null at geometric-optics order. Details appear in the revised companion paper on the metric's geodesic structure. (3) The appendix's metric embedding is superseded as a fundamental description: later work establishes that the helical structure belongs in an internal fiber over a regular de Sitter base, within which the embedding's pathologies do not arise; the metric survives as an effective local chart and as the worked demonstration of why direct embedding fails. (4) The companion generation mechanism has been refined by subsequent boundary theorems: generation is confined to an initial genesis event, the black-hole return mechanism is an open question rather than an established component, and the gradual unwinding of cyclical structure is now a derived feature of the framework rather than a degeneration requiring prevention. A consolidated foundational paper and errata ledger documenting all corrections, with verification code, are in preparation. The text below describes the paper as originally deposited. This "version 2" is our internal v010. Version 1: 10.5281/zenodo.20944352 Version 2: 10.5281/zenodo.21250765