eulerPhysicallyRealizableLedger
plain-language theorem explainer
The declaration supplies a definition showing that the Euler carrier satisfies the physically realizable ledger interface for any defect sensor, using the Euler trace admissibility predicate for the admissible field and the Euler scalar proxy for the state. Recognition Science researchers working on T1-bounded unification would cite it to confirm the Euler trace remains realizable without violating defect bounds. The construction is a direct definition that assembles the four required fields from prior Euler proxy lemmas.
Claim. For any defect sensor $s$, the Euler carrier defines a physically realizable ledger in which the admissible trace is the Euler trace admissibility predicate at $s$, the scalar state is the Euler scalar proxy at $s$, the state remains positive, and the T1 defect of the state is uniformly bounded.
background
PhysicallyRealizableLedger is the class interface requiring an admissible Euler trace, a positive scalar proxy state $x_N$ indexed by refinement depth $N$, and a uniform bound on the T1 defect of that state. The module replaces the earlier OntologicalPrimeLedger (contradicted by unbounded annular cost) with a three-component architecture: cost divergence under nonzero charge, Euler trace admissibility, and this realizable ledger instance for the Euler carrier. Upstream results include the Euler instantiation data establishing convergence and bounded logarithmic derivative, plus the J-cost structure from PhiForcingDerived and the ledger factorization from DAlembert.
proof idea
The definition directly constructs the instance by assigning admissible to the Euler trace admissibility predicate at the sensor, scalarState to the Euler scalar proxy, scalarStatePos to the positivity lemma for that proxy, and scalarDefectBounded to the defect boundedness lemma for the proxy. No tactics or reductions are needed beyond field assignment from the referenced Euler proxy results.
why it matters
This definition completes the proved segment of the Unified RH proof chain, placing the Euler carrier inside the PhysicallyRealizableLedger interface and thereby enabling the subsequent boundary transport hypothesis. It fills the T1-bounded realizability step in the module architecture, linking Euler instantiation to the broader Recognition Science forcing chain (T5 J-uniqueness through T8 three-dimensional emergence) without invoking total annular cost bounds. The open question it leaves is the external bridge hypothesis that would force boundary approach under cost divergence.
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