Cosmogenesis via Geometric Serialization: Inflationary Tilt and Duration from the Topology of the S15 → S8 Hopf Fibration

This work proposes a “geometric serialization” mechanism for the early universe in which inflation is not driven by an ad hoc scalar potential, but by a bounded, sequential projection of a high-dimensional coherence state onto an internal vacuum manifold. The framework models the vacuum using the octonionic Hopf fibration S7↪S15→S8 with an S8–based coherence network that has E8-like local connectivity. In this picture, time is the ordering parameter of projection/closure events, and the inflationary epoch corresponds to a finite “boot cycle” during which an S15 spinor state saturates this coherence network.

Within this setup, the paper advances two quantitative ansätze. First, the scalar spectral tilt is treated as a network “drag” set by a dimension-to-connectivity ratio d/k, giving ns≈1−8/240≈0.9667 for an 8-dimensional coherence manifold with E8 kissing number 240. Second, the duration of the inflationary phase is tied to the group-theoretic structure of E8: the Coxeter number h(E8)=30 implies N≈2h(E8) = 60 effective e-folds when spinorial 4π phase closure is taken into account. These are interpreted as capacity outputs of a bounded serialization process rather than as tuned features of a chosen inflaton potential.

The same geometric ratio d/k=8/240=1/30 is then used to define a core fraction fgeo that sets a geometric upper bound on how much of a coherence patch can collapse into a maximally locked core during the first closure event. This yields an initial black hole seed fraction M∙/M∗∼1/30≈3%, consistent with “heavy seed” supermassive black holes inferred in high-redshift AGN from JWST observations. Subsequent hierarchical growth of extended structure and comparatively channel-limited core growth naturally dilute this ratio toward the familiar local ∼10^−3 black hole–to–host mass relation.

To connect with standard cosmological observables, the paper recasts the serialization dynamics as a network transfer (graph-Laplacian) model acting as a low-pass filter on scalar perturbations. This leads to qualitative predictions of small tensor-to-scalar ratio rrr, small negative running αs\alpha_sαs, and near-Gaussian initial conditions consistent with current CMB bounds. The work explicitly lists falsifiers: a precise value of nsn_sns far from 1−8/240, a robust detection of large rrr, strong primordial non-Gaussianity, or high-redshift black hole demographics incompatible with a ∼3% heavy-seed phase would collectively or individually rule out the mechanism. The paper is intended as a mechanism-level proposal: it does not replace standard perturbation theory, but suggests that the apparent tuning of inflationary parameters and early black hole seeds may reflect a deeper constraint (finite closure bandwidth on a structured vacuum manifold) whose consequences are testable with current and upcoming data.