The A-C Coupling Theorem – Solving Diophantine Systems in O(1)
The A-C Coupling Framework presents a general law for n-dimensional linear Diophantine systems of the form N = Σ cᵢ · xᵢ. Two structural conditions are identified as jointly sufficient for a direct, single-step determination of the minimum starting value A₀ = N mod c₂: Condition one (Foundation): th
The A-C Coupling Theorem – Solving Diophantine Systems in O(1) launched on June 13, 2026 with 5 votes, #2,466 of 22,647 launches that month and more than 75% of that year's launches.
What it does
The A-C Coupling Framework presents a general law for n-dimensional linear Diophantine systems of the form N = Σ cᵢ · xᵢ. Two structural conditions are identified as jointly sufficient for a direct, single-step determination of the minimum starting value A₀ = N mod c₂: Condition one (Foundation): the top coefficient must satisfy c₁ ≡ 1 (mod c₂). This renders the top layer transparent modulo c₂, ma
You are using an outdated browser. Please upgrade your browser to improve your experience. presents a general law for n-dimensional linear Diophantine systems of the form N = Σ cᵢ · xᵢ. Condition one (Foundation): the top coefficient must satisfy c₁ ≡ 1 (mod c₂). This renders the top layer transparent modulo c₂, making the steering value independent of the highest coefficient . Condition two (Chain): the remaining coefficients must form an exact divisibility chain cₙ | cₙ₋₁ | ... | c₂. This guarantees that every remainder at every layer is absorbable without gaps. the euro family (modulus 9, coefficients 19, 9, 3, 3, 1) where A₀ equals the digital root, and the clock…from zenodo.org
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