GitHub - A19dammer91/the-exact-algebraic-condition-for-clock-behaviour.: This paper analyses the linear Diophantine system N = 25A + 12B, where p ≡ 1 (mod q) — the exact algebraic condition for clock behaviour. · GitHub
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A19dammer91
the-exact-algebraic-condition-for-clock-behaviour.
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p ≡ 1 (mod q) is the exact algebraic condition for clock behaviour in linear Diophantine representation systems.
A clock does not count indefinitely — it resets. That reset is not coincidental but a structural property: 13 ≡ 1 (mod 12), so after 12 steps the system returns to its starting point. This same mechanism underlies every system N = pA + qB where p ≡ 1 (mod q): every p steps the A-coordinate restarts modulo q, making the minimal coordinate A₀ directly readable as N mod q — without search, without iteration.
The clock is therefore not a metaphor. It is a special case of the same mathematical structure.
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This paper analyses the linear Diophantine system N = 25A + 12B, where p ≡ 1 (mod q) — the exact algebraic condition for clock behaviour.
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