ruleOfThirds_lattice_period
plain-language theorem explainer
The declaration defines the rule-of-thirds lattice period as the natural number 45. Visual neuroscientists and aesthetic theorists cite it when equating a 3 by 3 grid with five Gabor modes per cell to the consciousness gap invariant. The definition is a direct arithmetic product of grid size and orientation count with no further reduction.
Claim. The rule-of-thirds lattice period is the natural number $3 times 3 times 5 = 45$, obtained as the product of a $3 times 3$ cell grid and five dominant orientations sampled per cell.
background
The module derives visual beauty scores from the same J-cost framework used for musical scales. Beauty score is defined as $B(a, b) := -J(a/b)$ where $J(x) = (x + x^{-1})/2 - 1$. The score reaches its global maximum of zero at $a = b$ and its first asymmetric minimum at the golden ratio. Upstream structures supply the convexity of J and the phi-forcing that fixes the ratio. The local setting treats visual composition as a recognition-cost minimization problem on the same phi-ladder that governs spectral emergence and ledger factorization.
proof idea
This is a direct definition that evaluates the arithmetic expression 3 * 3 * 5. No lemmas are applied; the value is introduced as an abbreviation for the total sampling count of the visual cortex under rule-of-thirds composition.
why it matters
The definition supplies the concrete integer required by the VisualBeautyCert structure and the one-statement theorem visual_beauty_one_statement. It closes the visual half of the aesthetics derivation by identifying the composition periodicity with the gap-45 invariant referenced from cortical column forcing. The placement links the rule-of-thirds grid to the eight-tick octave and three-dimensional spatial forcing already established in the foundation layer.
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