pythagorean-comma

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thefalsework / papers

An open-source research programme on structural incompleteness in domains organized around a minimal generative operation. CC-BY-4.0. Validation, corrections, and Lean formalization welcome.

reproducible-research open-science category-theory music-theory formal-methods digital-humanities papers open-research structural-analysis falsework philosophy-of-mathematics lean4 spencer-brown pythagorean-comma epistemic-dependency ai-assisted-scholarship distinction-operation kernels-and-commas canonical-analysis

Updated Aug 28, 2026
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Fifth-Initiate / pythagorean-twin-primes

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every prime >3 lies on one of two explicit irrational straight lines of slope κ = log₂(3¹²/2¹⁹) in the covering space of ℝ²/(12ℤ×6ℤ). Twin primes are simultaneous integer points on both lines. Irrationality implies infinite recurrence. A live browser implementation is provided. The pattern has been verified to N>10⁸ and holds

twin-prime-conjecture octatonic-scale pythagorean-comma prime-geometry

Updated Dec 29, 2025
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