ledger_conservative
plain-language theorem explainer
Ledger conservative asserts existence of a unique positive real where the defect vanishes. Black hole information researchers cite it as the structural basis for conservation in RS ledger theories. The definition encodes that information entries transform but do not vanish, drawn directly from the Law of Existence defect property.
Claim. There exists a unique positive real number $x$ such that the defect functional $J(x)$ equals zero.
background
The module addresses BH-002, the black hole information paradox resolution in Recognition Science. It posits that the ledger substrate conserves total information content, with entries able to move or transform but not disappear. The defect functional is defined as defect(x) := J(x) for positive x, and upstream results establish its zero at the unity state along with completeness predicates from backpropagation and simplicial ledger bridges.
proof idea
The declaration is a direct definition stating the unique existence of a positive real with zero defect. It applies the defect definition from LawOfExistence without further reduction steps.
why it matters
This definition supports the parent theorems information_conserved and no_information_sink in the same module. It fills the BH-002 structural claim that the ledger is complete with no information sink. It relates to the J-uniqueness in the forcing chain (T5) and the absence of sinks in the framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.