Arch-Nullus: A Background-Independent Topological Framework for Emergent Gravity, Discrete Baryogenesis, and the Abolition of Metric Singularities

The Arch-Nullus framework derives the primordial spectral index n_s = 0.96487 from D4 lattice geometry with zero adjusted parameters (0.01σ from the Planck 2018 central value), and the baryon-to-photon ratio η_B ≈ 6.104×10⁻¹⁰ within 0.3% of observation. Both results emerge from a single founding axiom — the Arcus nullius: the substitution of the scalar zero, in those specific contexts where it produces formal absurdities, by a pre-metric topological state |O⟩. The framework is discrete and background-independent; it operates entirely within established formalisms (BF theory, Chern-Simons, Plebanski constraint); and it carries explicit epistemic markers on every claim, distinguishing what is computationally or algebraically verified from what is physically motivated, what is open, and what has been investigated and excluded. Version 2 (May 2026): the spectral index prediction chain n_s = 0.96487 is now complete with zero plausible links following rigorous closure of all six derivation steps (Annex IV). Readers familiar with v1 may go directly to Annex IV for the new results. The corpus is published on Zenodo and we invite scrutiny.