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 ns = 0.96487 from D4 lattice geometry with zero adjusted parameters (0.01σ from the Planck 2018 central value), and the baryon-to-photon ratio ηB ≈ 6.104×10⁻¹⁰ within 0.3% of observation. Both results emerge from a single founding axiom: 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. The corpus is published on Zenodo and we invite scrutiny.

Reading order: This corpus is structured modularly. Readers are advised to follow the sequence: (1) Presentation Letter — entry point and overview; (2) Manuscript — full architectural development; (3) Annex I — mathematical task annexes (Gosset-holography, equipartition, SGWB); (4) Annex II — quantum-mechanical structure and primordial spectrum; (5) Annex III — zero-parameter prediction of the spectral index; (6) Predictions Summary — consolidated falsification table.