Explicit Universe Word Execution

Abstract

Actual scans write canonical variable names and consumer tautologies.

Theorem 1.1 (Explicit Universe Word Execution).

$$\forall w\in \mathrm{List}\left(Bool\right),\mathrm{Nonempty}\left(\mathrm{EvalsToInTime}\left(\mathrm{step}\left(reverseMachine\right),\mathrm{initList}\left(reverseMachine,w\right),\mathrm{some}\left(\mathrm{haltList}\left(reverseMachine,\mathrm{convertedWord}\left(w\right)\right)\right),\mathrm{reverseClock}\left(w\right)\right)\right)$$

Proof. Machine-checked in Lean as D5/S0/Computability/ReverseClauseMachine.reverseExecution (✓ std3). ∎

Source. Repository-derived.

Commentary.

Every raw unary source runs the fixed reverse program to a clean haltList containing convertedWord within reverseClock. The preprocessor is translated instruction by instruction. Subsequent phases scan the query coefficients, restore index counters, write canonical binary names, append one consumer tautology for each declared variable, clear scratch stacks and reverse output. Tautologies preserve unused assignments in the conventional encoding and do not modify the physical raw clauses.

References

• Truth anchor: D5/S0/Computability/ReverseClauseMachine.reverseExecution
• Dependency: D5/S0/Computability/ClausePreprocessorRefinement
• Dependency: D5/S0/Computability/ConventionalClauseWords