unity_config
plain-language theorem explainer
The unity configuration is the ledger state in which every one of N entries equals exactly 1. Cosmologists working within Recognition Science cite it as the forced zero-defect initial condition of the universe. The definition constructs this state directly by the constant map to 1 together with a normalization check that all entries remain positive.
Claim. Let $N$ be a positive integer. The unity configuration is the element $u_N$ of the space of configurations of $N$ ledger entries such that $u_N(i)=1$ for every index $i$, where each entry satisfies the positivity requirement $0<u_N(i)$.
background
A configuration of $N$ ledger entries is a map from the finite index set to the positive reals whose total defect is the sum of the individual defect values. The defect of an entry $x$ is given by the function $J(x)$, which vanishes precisely at unity. The module F-005 formalizes the low-entropy initial condition as the unique zero-cost ledger state forced by the cost axioms rather than an extra postulate.
proof idea
The definition is a direct construction that assigns the constant function with value 1 to the entries field and discharges the positivity predicate by norm_num.
why it matters
This definition supplies the concrete initial state required by the Past Theorem, the no-singularity theorem, and the statement that the initial state has minimum entropy. It realizes the F-005 claim that the universe begins at the global minimum of total defect, converting the traditional Past Hypothesis into a derived theorem within the Recognition framework.
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