extra_dim_eq_7
plain-language theorem explainer
The equality states that the number of extra dimensions reconciling superstring critical dimension 10 with Recognition Science spatial dimension 3 is exactly 7. Physicists examining compactification counts or structural matches between the two frameworks would cite this result. The proof is a one-line decision procedure that evaluates the definition extraDimensions := strCriticalDim - rsDimension directly to the integer 7.
Claim. Let $d_{RS}=3$ be the spatial dimension fixed by the forcing chain and let $d_{crit}=10$ be the critical dimension of superstring theory. The number of extra dimensions then satisfies $d_{extra} := d_{crit} - d_{RS} = 7$.
background
Recognition Science fixes three spatial dimensions at the T8 step of the unified forcing chain, where the self-similar fixed point phi together with the eight-tick octave forces D=3. Superstring theory requires a critical dimension of 10 for anomaly cancellation. The extra dimensions are therefore the difference 10-3=7, which equals the number of flip variants of the three-dimensional cube Q3 as described in the SpectralEmergence structure.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the concrete arithmetic expression in the definition of extraDimensions. No additional lemmas are invoked beyond direct evaluation of the subtraction 10-3.
why it matters
This theorem supplies the numerical value for the extra_dim field inside the SuperstringCert structure, which certifies the structural match between Recognition Science and superstring theory. It realizes the module observation that the seven compactified dimensions equal the seven flip variants of the 3-cube. The result closes the gap between the T8-forced D=3 and the string critical dimension without introducing new axioms.
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