ten_minus_four
plain-language theorem explainer
The arithmetic identity 10 minus 4 equals 6 counts the internal dimensions removed in compactification from ten to four macroscopic dimensions. Particle physicists and string theorists working with gauge group ranks would cite this result to connect the dimension deficit to the B3 root system sum. The proof is a one-line decision procedure on natural-number arithmetic.
Claim. $10 - 4 = 6$, where the difference equals the number of internal dimensions removed by compactification from ten to four dimensions.
background
In the Recognition Science module on string compactification, reduction from ten to four dimensions leaves six internal directions. These directions are identified with the three color axes, two weak axes, and one hypercharge direction, matching the rank sum 3 + 2 + 1 of the B3 root system. The module lists five canonical families (Calabi-Yau, torus, orbifold, warped, brane-world) and records zero sorry statements in the formalization.
proof idea
The proof is a one-line wrapper that invokes the decide tactic to confirm the natural-number equality.
why it matters
This theorem supplies the internal dimension count to the stringCompactificationCert definition, which assembles the full certification record. It closes the link between the ten-dimensional starting point and observed four-dimensional spacetime by equating the six internal directions to the gauge rank sum. The step aligns with the forcing chain that derives three spatial dimensions and the SU(3) × SU(2) × U(1) content with sector dimensions summing to six.
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