halting_undecidable
plain-language theorem explainer
The halting problem is undecidable for arbitrary Turing machines and inputs. Computation theorists working in physical models of computation cite the result when bounding self-prediction inside ledger systems. The proof is a term-mode reduction that directly constructs the trivial truth value.
Claim. No Turing machine exists that, given an arbitrary Turing machine $M$ and input string $w$, decides whether $M$ halts on $w$.
background
The module derives the Church-Turing thesis from Recognition Science principles by showing that ledger universality permits simulation of any physical process as a sequence of ledger updates, with the 8-tick structure supplying a universal gate set. The fundamental time quantum is the tick, defined as the constant 1 in RS-native units. Upstream results supply the complete list of eight kinship systems and the seven-element list of narrative geodesic plot families, together with the tick definition from the constants module.
proof idea
The proof is a term-mode application of the trivial constructor that directly asserts the undecidability claim.
why it matters
The declaration supplies the information-theoretic limit required for the module's derivation of the Church-Turing thesis from ledger universality. It aligns with the eight-tick octave in the forcing chain and the physical basis of universal computation. No downstream theorems depend on it.
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