totalCost
plain-language theorem explainer
The total J-cost of a ledger is defined by summing the J-costs of its entries. Cosmologists deriving dark energy densities and quantum modelers working with ledger superpositions cite this when aggregating recognition costs. The definition is realized as a direct summation after mapping each entry to its cost function.
Claim. Let $L$ be a ledger consisting of recognition events $e_i$. The total J-cost of $L$ is $C(L) = sum_i c(e_i)$, where $c(e)$ denotes the J-cost of each entry $e$.
background
A ledger is a structure holding a list of entries together with a balance required to equal the sum of the logarithms of the entry ratios. Each entry represents a recognition event whose J-cost is supplied by the upstream cost definition on recognition events. The module treats quantum states as superpositions over ledger configurations, with the Born rule obtained from J-cost minimization rather than postulated separately.
proof idea
This is a one-line definition that maps the entry list to the per-entry cost function and sums the resulting real numbers.
why it matters
The definition supplies the aggregate cost used in cost density and balance predicates for spacetime regions in dark energy models. It is invoked inside the SMLagrangianCert to establish vacuum vanishing of total cost. In the Recognition framework it operationalizes the total J-cost for ledger-based quantum mechanics, feeding derivations that connect to the phi-ladder and eight-tick octave.
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