Ledger
plain-language theorem explainer
A Ledger packages a finite list of recognition events, each carrying a positive ratio and its associated J-cost, together with a real balance that is required to equal the sum of the logarithms of those ratios. Researchers formalizing the emergence of quantum mechanics from recognition events would reference this structure when constructing superpositions of ledger configurations. The definition is a plain record whose single field constraint directly encodes conservation of the logarithmic measure.
Claim. A ledger consists of a list of entries, each an object carrying a positive real ratio $r_i$ together with its J-cost, and a real number $b$ satisfying $b = sum_i log r_i$.
background
The QuantumLedger module formalizes the link between recognition events and quantum states by treating quantum states as superpositions over ledger configurations, with the Born rule emerging from J-cost minimization. A LedgerEntry records one recognition event via its identifier, positive ratio, J-cost, and phase in the eight-tick cycle. The module states that measurement collapses to the minimum J-cost configuration while ledger balance remains conserved under evolution.
proof idea
The declaration is a direct structure definition. Its balance field is accompanied by an explicit equality constraint that forces the balance to equal the sum of logarithms of the entry ratios; no lemmas or tactics are applied.
why it matters
This structure supplies the basic object on which the quantum ledger theorems of the module rest, including ledger_conservation and born_rule_from_jcost. It realizes the Recognition Science claim that quantum states arise as superpositions of recognition events whose probabilities derive from J-cost. The construction follows the definition of J in the forcing chain and precedes the derivation of the Born rule from cost minimization.
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