The Icosahedral Digital Boundary: Why Prime Structure Breaks at e^142 and Creation Stops at e^184
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Abstract
We show that icosahedral geometry creates two fundamental boundaries that bracket physical reality. At the digital boundary (e^142), mod 3 collapses and the Ramanujan tension transforms from −1/12 to −1/4. At gravitational closure (e^184), mod 5 locks out and tension transforms from −1/12 to −5/12. The operating physics lives between these boundaries where both mod 3 and mod 5 function, with tension −1/12 = −5/|A₅|. The prime product digit gaps discovered in our companion paper occur at these scales: staggered gaps requiring factor 3 at e^142, coincident gaps requiring factor 15 = 3 × 5 at e^184. We derive that the gap 55 − 53 = 2 equals the Euler characteristic χ because the icosahedron's triangular faces…
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Topics
Keywords
- Icosahedral symmetry
- Boundary (topology)
- Tension (geology)
- Prime (order theory)
- Product (mathematics)
- Euler's formula
- Punching
- Span (engineering)
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