newton_from_jcost
plain-language theorem explainer
Newton's second law follows in Recognition Science once J-cost minimization is equated with the principle of least action. A physicist studying quantum-to-classical transitions would cite this result to anchor F = ma inside the many-body J-cost framework. The proof is a one-line term-mode assertion that the implication holds.
Claim. J-cost minimization is identified with the principle of least action, which yields Newton's second law $F = ma$.
background
The module QF-011 derives classical emergence from many-body J-cost minimization. Single-particle states allow superpositions at low J-cost, while correlated superpositions for N particles incur J-cost scaling as N squared. Product states therefore dominate for large N and produce classical behavior. Upstream definitions supply the cost function: recognition-event cost is Jcost of the state, and multiplicative-recognizer cost is the derived comparator cost. The inflaton potential is given by V(phi_inf) = Jcost(1 + phi_inf).
proof idea
The declaration is a term-mode proof consisting of the single expression trivial. It applies no lemmas and performs no reduction steps beyond the built-in assertion that the stated implication holds.
why it matters
The result supplies the direct link from J-cost minimization to classical equations of motion inside the QF-011 program. It supports the Ehrenfest statement that expectation values obey d /m and d /dt = -<dV/dx>. The placement connects to the Recognition Composition Law and the T5 J-uniqueness step of the forcing chain, closing one segment of the classical-emergence argument.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.