aligned_collective_cost_zero
plain-language theorem explainer
The result shows that J-cost vanishes exactly at unit ratio. Researchers deriving the Global Co-Identity Constraint from the forcing chain cite it as the base case establishing zero collective cost at alignment. The argument is a direct one-line reduction to the unit lemma for the squared-ratio definition of J.
Claim. When the ratio equals one, the J-cost satisfies $J(1)=0$.
background
J-cost is defined by the squared-ratio expression $J(x)=(x-1)^2/(2x)$. The module derives the Global Co-Identity Constraint from the RS forcing chain with no empirical axioms: T5 (J-uniqueness) implies ratio rigidity at J=0, which combines with compact phase from T6+T7 to yield uniform phase at stationarity. The upstream unit lemma states that J-cost at argument 1 is zero by direct simplification of the definition.
proof idea
One-line wrapper that applies the unit lemma Jcost_unit0, which itself follows by simplification from the definition $J(x)=(x-1)^2/(2x)$.
why it matters
This supplies the zero-cost base case required by gcic_from_forcing_chain and phase_alignment_minimizes_Jtilde. It closes the alignment step in the T5-to-GCIC chain, confirming that collective J-cost reaches its global minimum precisely when phases are uniform. No open scaffolding remains at this node.
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