LedgerTransition
plain-language theorem explainer
LedgerTransition denotes the type of maps from one discrete ledger state to another within the 8-phase finite space. Physicists deriving the physical Church-Turing thesis from Recognition Science use it to bound all dynamics to table-lookup computable functions. The definition is a direct alias to the arrow type over DiscreteLedgerState, which itself is Fin 8 to Bool.
Claim. A ledger transition is any function $f : (Fin 8 → Bool) → (Fin 8 → Bool)$, where each state records which phases of the 8-tick cycle are active.
background
The module IC-003 derives the physical Church-Turing thesis from the discrete ledger structure of Recognition Science. DiscreteLedgerState is the sibling definition Fin 8 → Bool, with each entry a Boolean flag for phase activity. LedgerTransition then supplies the arrow type over these states so that every physical update remains a map on a finite set of size 256.
proof idea
The declaration is a one-line type alias that directly identifies LedgerTransition with the function space DiscreteLedgerState → DiscreteLedgerState.
why it matters
LedgerTransition supplies the domain for the downstream theorem discrete_ledger_computable, which proves every such map admits a finite lookup table. It fills the IC-003.3 step linking the eight-tick octave to Turing-computable physics and appears in the L3_scope semantic core of the claim boundaries paper.
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