Venus Self Similar Structure

The Maya canonical Venus synodic (584 days) and Haab' (365 days) are linked by 5 Venus = 8 Haab' = 2,920 days — exact in Maya canonical arithmetic and observable by naked-eye astronomy. This paper establishes that the 5:8 ratio is a feature of three independent mathematical systems. (i) Integer arithmetic: Venus (584 = 2³ × 73) and Haab' (365 = 5 × 73) share the Calendar Round prime 73; their quotients generate 5:8 as a pure LCM identity. (ii) Musical harmony: The ratio 8:5 is the exact just-intonation minor sixth — the unique such interval in the Maya canonical corpus — corroborated by Kepler, who in Harmonices Mundi (1619) identified 5:8 as the Earth-Venus interplanetary harmonic ratio. Both describe the same Earth-Venus relationship through different methodologies. (iii) Fibonacci: The integers 5, 8, 13 are F(5), F(6), F(7); 5:8 approximates 1/φ within 1%. The ratio persists across five attested scales centred on the Dresden Venus Table as fundamental observational unit: the base LCM unit (2,920 days), the Mam Year-Bearer cycle (13 Haab', 1/8 of a Dresden, 0.65 d drift), the Dresden Venus Table (65 Venus, 104 Haab', 2 CR, 5.20 d drift), the Powell 6-CR closure, and the Venus Mega-Cycle (50 Dresden Tables, 100 CR, raw drift = 1 Cholqi'j). The numerical self-similarity 0.65 ↔ 65 ↔ 5.20 ↔ 260 reflects the prime-factor structure of the Maya canonical system. The convergence of three independent mathematical structures on the same ratio, documented by two civilizations independently, constitutes a scientific observation of the Maya canonical corpus.