QHCC: From Space to Matter, Three Geometric Regimes of a Single Informational Structure

This paper develops the QHCC account of space, radiation, and matter as different geometric regimes of a single relational information structure. Its governing principle is that relations carry physical information, while geometry is a read-out of those relations. An isolated degree of freedom or projected node carries no intrinsic physical information or private energy.

Starting from the FLiC identity $R_{\rm FLiC}^{3}=r_S\ell_P^{2}$ established in Paper I, the minimal symmetric rank-dependent read-out satisfies $L_k^{k}\ell_P^{3-k}=r_S\ell_P^{2}$ for $k=1,2,3$. This yields three canonical scales: $L_1=r_S$, $L_2=\sqrt{r_S\ell_P}$, and $L_3=R_{\rm FLiC}$. They describe progressively more complete geometric determination of the same relational capacity. Changing rank is neither physical compression nor the creation of additional information.

Quantum uncertainty is interpreted as the metric reading of geometrically incomplete relational information; entanglement corresponds to irreducibly shared relational content with a joint geometric read-out. A coarse-grained geometric-determination field provides a candidate bridge between discrete graph relations and a wave-function description. Photons are modeled as mobile correlation patterns without persistent localized anchors. Matter requires stable rank-three closure, while rank-two boundary structures can retain reconfigurability and quantum uncertainty.

The framework includes a symmetric mixed-rank matching prescription, $L_{km}=\sqrt{L_kL_m}$, which generates the interface scales $L_{32}$, $L_{31}$, and $L_{21}$. For the parent black-hole scale adopted from Paper 1.1, these are approximately $0.216\,\mathrm{fm}$, $64.4\,\mu\mathrm{m}$, and $0.431\,\mathrm{m}$.

Version 5 clarifies the classification of inherited relational channels through chordal admissibility, rotational orientation, and the two toroidal cycles. It distinguishes available correlations from their joint geometric and energetic realization. A minimal neutrino candidate has a Y-shaped rank-three anchor with three non-chordal outer sites and direct coupling to the spatial sector. A charged-lepton candidate adds three V-type valence branches. Jointly active short chordal correlations define a candidate strong-interaction sector; their contribution at the Y–V interface remains an open dynamical question.

A conditional inverse-length mode law gives $m_e/m_{\nu_i}=(C_e/C_{\nu_i})(r_S/\ell_P)^{1/6}$. Equal dimensionless mode factors, together with normalization to the observed electron mass, yield a reference neutrino estimate near $11.4\,\mathrm{meV}/c^2$.

The paper distinguishes inherited relations, conditional algebraic results, and proposed particle mechanisms. The microscopic matching dynamics, stable particle spectrum, mass normalizations, Schrödinger limit, and Born rule remain targets for subsequent derivation.