The Icosahedral Digital Boundary: Why Prime Structure Breaks at e^142 and Creation Stops at e^184

University of Southampton

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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

Keywords
  • Icosahedral symmetry
  • Boundary (topology)
  • Tension (geology)
  • Prime (order theory)
  • Product (mathematics)
  • Euler's formula
  • Punching
  • Span (engineering)
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