concreteEulerLedgerOntologyInterface_exists
plain-language theorem explainer
Every defect sensor admits a package consisting of a directed system of finite arithmetic Euler ledgers over prime supports, an admissible Euler trace, and a T1-bounded realizability proxy, with the ledger stages balanced, net flows zero, a positive-radius regular carrier, and scalar defect bounded. Researchers bridging arithmetic Euler data to the ontology layer in Recognition Science would cite this existence result. The proof is a direct refinement to the concrete interface constructor followed by extraction of its four pre-verified conjunct
Claim. For every defect sensor $s$, there exists a package $p$ comprising a directed Euler ledger system over finite prime supports, an admissible Euler trace, and a physically realizable ledger proxy such that: for every finite prime support $S$, the ledger stage over $S$ is balanced and every agent has zero net flow; there exists a regular carrier whose radius equals the real part of $s$ minus $1/2$ and is positive; and the scalar defect of the proxy is bounded above by some real constant $K$.
background
The module packages finite concrete Euler ledgers into a directed system indexed by finite prime supports (PrimeSupport := Finset Nat.Primes) and connects them to ontology interfaces. EulerLedgerOntologyInterface is the structure that bundles a DirectedEulerLedgerSystem, an admissible Euler trace, and a PhysicallyRealizableLedger proxy for any given defect sensor. Upstream, the defect functional from LawOfExistence equals the J-cost for positive arguments, while balanced and net_flow are the ledger-forcing predicates that enforce zero total imbalance and zero agent-wise flow.
proof idea
The tactic proof refines the existential quantifier to the concrete constructor concreteEulerLedgerOntologyInterface sensor. It then applies the directedLedger.stage_balanced property for the first conjunct, stage_net_flow_zero for the second, has_regular_carrier for the carrier existence, and scalarDefectBounded for the final defect bound.
why it matters
This supplies the strongest proved bridge from arithmetic Euler data into the ontology layer. It feeds attempts to reach RSPhysicalThesis yet leaves the global physical-identification step open, as the module documentation notes that the concrete directed ledger has not yet been transported into the PhysicallyExists predicate. The result sits at the number-theory-to-unification interface and relies on the directed-system coherence already established for finite prime supports.
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