Papers

Academic papers on mathematics, systems theory, and structural analysis.

2026-03-10•Mathematics

Scale-Relative Primality and the Structural Determinism of Transcendental Digits

Using scale-relative primality — a factorization framework in which powers of τ act as units of scale and primality is defined by integer content — this paper argues that the digit sequence of τ is the unique trace of a maximally constrained geometric-arithmetic object, and therefore nonrandom in the deepest available sense.

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2026-03-07•Mathematics

Tau, Pi, and the Choice of Generator: Full Closure, Half Closure, and the Arithmetic Shadow of a Quotient

The constants π and τ represent two normalizations of the same circular structure. Starting from the reciprocal relation 1/π = 2/τ, we show that the π-lattice is the index-2 sublattice of the τ-lattice—and that this arithmetic fact is the fingerprint of a deeper structural distinction between identity-level closure and antipodal quotient.

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