The Time-Symmetric Parity Constraint or The Twin-Time Theory of Cosmology

Summary description — This compendium brings together the complete sequence of papers defining the Time-Symmetric Parity Constraint (TSPC): a geometric framework in which the universe’s observed anomalies are re-expressed as structural consequences of a fixed algebraic condition on the spacetime metric. TSPC imposes a parity constraint that forbids geometries with an absolute direction of time, requiring mirrored temporal domains evolving from a shared low-entropy origin. Without adding new fields or particles, the condition modifies curvature coupling through a single bounded parameter αλ. The suite traces the resulting implications for late-time acceleration, dark matter, inflation, entropy symmetry, and the correlated H₀ and S₈ tensions. It extends to empirical tests in lensing, gravitational-wave populations, and sky-wide dipoles. Together these papers form a single argument: that geometry and baryonic matter alone account for the phenomena attributed to the dark sector. The hypothesis is parsimonious, coherent, and falsifiable; if any of the correlated signatures fail, the framework is excluded. Three supplements have been added in response to recent research: (1) a comment on the interpretation of the recently reported γ-ray excess from the Galactic Centre (Paper 14); (2) a review of the new analysis of the radial-acceleration relation in extremely low-mass dwarf galaxies (Paper 15); and (3) a comparative analysis of several recent interpretations of the DESI DR2 data (Paper 16). Substantive updates — v7 (2025-11-26). New paper 17 added: Undressing the Emperor - A historical and conceptual dismantling of the FRW ansatz, with consequential amendments to the Preface and the Introduction. v.9 (2025-11-27) - Corrections to Paper 14: The Galactic-Centre Gamma Excess Reconsidered, clarifying the findings of Muru et al. (2025) on the morphology of the Galactic-centre γ-ray excess, together with the addition of a footnote noting recent claims by Tomonori Totani (2025) of a high-latitude annihilation signal. Explaining why these claims do not affect the analysis presented. v.10 (2025-12-04) Paper 2, Sections 2–3 updated to state Π as fixed and primitive, and to clarify the resulting exclusions for admissible metrics (e.g. Gödel, anisotropic cases). v.11 (2025-12-05) Paper 8 udated with ACT DR6 constraints on early-Universe models; Paper 14 adds recent mid-IR flare and extinction results, further tightening the astrophysical interpretation of the Galactic-Centre excess. No changes have been made to the core TSPC framework. v.13 (2025-12-11) Minor revisions: added rebuttal of the ΛCDM timing argument in Paper 9 and clarified the Bullet Cluster discussion in Paper 10, removing dark-halo assumptions. v. 18 (2026-01-03) New Paper 2: Reassessing late-time cosmic acceleration in light of supernova progenitor age bias, has been added.This paper re-examines the empirical status of late-time acceleration using progenitor-age–corrected Type Ia supernova analyses, showing that the inferred acceleration signal is transient and weakening, and consistent with BAO geometry without invoking dark energy. The ordering of papers has been finalised to reflect the intended logical progression:introduction → evidential reassessment → core framework → theoretical consequences → empirical tests → conclusion → supplements. Cross-references between papers have been corrected and standardised to reflect final numbering and titles. The Preface and concluding material have been updated to align with the completed contents and empirical scope. No substantive changes have been made to the underlying theoretical framework or to previously published empirical analyses.