convergence_connection_to_8tick
plain-language theorem explainer
The declaration establishes that the three-dimensional hypercube has exactly eight vertices, tying this count to the eight-tick octave that sets the convergence pace in Ramanujan's pi series. Researchers tracing Recognition Science geometry into classical series would cite it to account for the observed eight decimal digits per term. The proof is a direct term application of the vertices_at_D3 lemma.
Claim. In three spatial dimensions the hypercube has $2^3 = 8$ vertices.
background
The RamanujanBridge module interprets integers appearing in Ramanujan's series for $1/π$ via Recognition Science topology. The module document highlights that each term adds roughly eight decimal digits because the convergence rate involves the factor $396^4$, whose logarithm yields an effective eight digits per term; this is read as one octave of precision per the eight-tick structure. Upstream, cube_vertices is defined by $2^D$ and vertices_at_D3 states that this equals 8 when $D=3$, with the accompanying note that the 3-cube $Q_3$ has eight vertices equal to eight ticks in the Gray cycle.
proof idea
The proof is a one-line term wrapper that directly applies the vertices_at_D3 lemma, which itself reduces the claim to the definition cube_vertices $D = 2^D$ via native_decide.
why it matters
The result anchors the eight-tick octave (T7) to the observed convergence rate of Ramanujan's series, where each term corresponds to one octave of precision. It supplies the vertex count needed for the RS reading of the Chudnovsky prefactor 12 as cube_edges $D$ and supports the placement of $D=3$ (T8) inside the forcing chain. No downstream theorems yet reference it, leaving open the explicit derivation of the full digit-count formula from the Recognition Composition Law.
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