Experimental Higher-Dimensional Discrete State: 49 Lattice Successive Cubits Control Scalar

I’ve been building a personal experimental framework for turning geometric / multi-face measurements into a higher-dimensional discrete state. The goal is to keep everything reproducible, append-only, and isolated from any production systems. Sharing the core data structures and math in case others have tried similar patterns.

1. Lattice A cubic lattice with 49 cells on each edge (49³ = 117 649 cells). Cells are addressed by 1-based triples $(i,j,k)$ or by a linear index: $$n = (k-1)\cdot49^{2} + (j-1)\cdot49 + (i-1) + 1$$ Inverse conversion is the usual integer division / modulo.
2. Face Mapping Six faces of the cube (+X/−X, +Y/−Y, +Z/−Z). Mapping one face to another is an affine transform $$\mathbf{x}' = R\mathbf{x} + \mathbf{t}$$ where $R$ is a permutation/reflection matrix with entries in ${-1,0,1}$ and $\mathbf{t}$ is an integer translation that lands on the target face index (1 or 49). The inverse is exact: $$\mathbf{x} = R^{-1}(\mathbf{x}' - \mathbf{t})$$ (with $R^{-1}=R^{T}$ for pure rotations/reflections). After the inverse, coordinates are rounded and clamped to $[1,49]$. Polarity (normal vs inverse face) and crop-circle harmonic sign/phase can be flipped under the same transform.
3. Per-Face Feature Vector For each face $k=1\dots6$ a 7-component vector is extracted: $$\mathbf{f}{k} = (T{k},\, U_{k},\, \Phi_{k},\, E_{k},\, P_{k},\, S_{k},\, G_{k})$$ Typical components (all normalized to convenient ranges):

$T$ – torque / shear index across triangulated face
$U$ – uplift / asymmetry
$\Phi$ – phase from dominant harmonic of any crop-circle pattern
$E$ – energy sign (+1 normal, −1 inverse)
$P$ – pivot / corner coherence
$S$ – seam strength
$G$ – gap / topological-defect measure (the “remainder” cells)

1. Successive Cubits Averages across the relevant faces produce nested cubits:

$c^{(4)} = (\overline{T},\overline{U},\overline{\Phi},\overline{E})$
$c^{(5)} = c^{(4)} + \overline{P}$
$c^{(6)} = c^{(5)} + \overline{S}$
$c^{(7)} = c^{(6)} + \overline{G}$ (full 7-component vector)

Each is then normalized to unit length:
$$\hat{c}^{(n)} = \frac{c^{(n)}}{|c^{(n)}|}$$

1. Master Projection & Control Scalar The normalized cubits are concatenated, projected by a matrix $M$ (PCA or hand-tuned) into a 7-dimensional master vector, then renormalized. A fixed realization axis $\mathbf{r}$ yields the control scalar $$\lambda_{0} = \mathbf{r}\cdot\hat{c}^{\text{master}}, \qquad \lambda = a\lambda_{0}+b$$ where $a,b$ are affine calibration constants chosen so that $\lambda$ sits on a convenient scale (in my experiments I use a reference value near 3.9). A simple decision rule can be attached: if $\lambda$ crosses a threshold and a decoherence proxy $\Gamma$ (derived from seam/gap strength) also rises, a “branch” flag is raised. This is treated purely as an experimental indicator, not a physical claim.
2. Ledger Discipline Every run is recorded as a new, append-only entry containing:

Mapping ID + version + timestamp
Full face-to-cell lists and the affine $R,\mathbf{t}$ used
Raw $\mathbf{f}_{k}$, aggregated cubits, normalized forms, projection $M$, $\lambda$, $\Gamma$
Previous entry hash (for auditability)
New entry hash computed locally after append

The production / “quake” ledger is never modified; this experimental series lives in its own isolated stream.
Why I’m sharing
The interesting engineering pieces are:

treating geometric remainders / mismatches as first-class components rather than noise,
a clean invertible face-mapping algebra on a discrete cubic lattice,
successive dimensional aggregation followed by a single scalar projection,
strict append-only versioning so experiments never contaminate earlier results.

I’m not claiming predictive power or a finished theory—only that the data structures and the projection pipeline are reproducible and may be useful to others who are exploring higher-dimensional discrete states or multi-face geometric feature aggregation.
If anyone has tried similar lattice → vector → projection pipelines, better ways to keep the ledger strictly append-only, or suggestions for scaling the 49³ representation, I’d be glad to hear them.