solutionDecidable
plain-language theorem explainer
The declaration supplies classical decidability for the predicate that a finite subset meets the target weight sum, residue neutrality modulo 8, and J-cost bound inside an 8-balanced J-subset-sum instance. Researchers formalizing Recognition Science structures inside cryptographic search problems would cite it to confirm the predicate remains decidable over finite data. The implementation is a one-line wrapper that invokes classical logic and the built-in decidability of finite predicates.
Claim. Let $I$ be a finite instance consisting of $n$ integer weights, residues in $Z/8Z$, rungs, an integer target, and a real cost bound. For any subset $S$ of the indices, the predicate that the weights in $S$ sum to the target, the residues in $S$ sum to zero modulo 8, and the total J-cost of $S$ lies at most at the bound is decidable.
background
The module defines the first RS-native cryptography candidate in deliberately elementary form with no security claim. An instance collects a finite collection of integer weights, residues in ZMod 8, phi-rungs, an integer target, and a real J-cost bound; a witness is simply the selected Finset support. The solution predicate requires the subset to meet the weight target, residue neutrality in ZMod 8, and the J-cost bound; the latter draws on the cost functions defined in MultiplicativeRecognizerL4 and ObserverForcing.
proof idea
The definition is a one-line wrapper that applies the classical tactic and then invokes inferInstance to obtain the Decidable instance for the finite predicate.
why it matters
This definition supplies the decidability infrastructure for the core solution predicate inside the 8-Balanced J-Subset Sum module. It directly supports the eight-tick octave structure (ZMod 8) from the forcing chain T7 while keeping all invariants dependent only on the public instance fields. No downstream uses appear yet, leaving open its integration into larger Recognition Science cryptography constructions.
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