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Decision continuations and exact word movement

Abstract

Decision continuations and exact word movement.

Both Boolean halts of a test dispatch to their respective continuation, counting the terminal jump. Word movement clears its destination and performs two reversals, so it preserves bit order and empties scratch. Fixed fallback words are installed by literal one-bit pushes. Disjoint finite control labels support branches with unrelated programs.

Theorem 1.1 (exec_choose).

Lean statement: D5/S0/Computability/BinaryMachine/StackControl.exec_choose

Proof. Machine-checked in Lean as D5/S0/Computability/BinaryMachine/StackControl.exec_choose (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. RBarish-UTokyo (2026). NPCompleteness-Lean4 finite binary machine and composition source. URL: https://github.com/RBarish-UTokyo/NPCompleteness-Lean4/tree/3e603e795b44fedcf7d6dd65b7d1e30547ead925.

Commentary.

Both Boolean halts of a test dispatch to their respective continuation, counting the terminal jump. Word movement clears its destination and performs two reversals, so it preserves bit order and empties scratch. Fixed fallback words are installed by literal one-bit pushes. Disjoint finite control labels support branches with unrelated programs.

Theorem 1.2 (exec_moveWord).

Lean statement: D5/S0/Computability/BinaryMachine/StackControl.exec_moveWord

Proof. Machine-checked in Lean as D5/S0/Computability/BinaryMachine/StackControl.exec_moveWord (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. RBarish-UTokyo (2026). NPCompleteness-Lean4 finite binary machine and composition source. URL: https://github.com/RBarish-UTokyo/NPCompleteness-Lean4/tree/3e603e795b44fedcf7d6dd65b7d1e30547ead925.

Commentary.

Both Boolean halts of a test dispatch to their respective continuation, counting the terminal jump. Word movement clears its destination and performs two reversals, so it preserves bit order and empties scratch. Fixed fallback words are installed by literal one-bit pushes. Disjoint finite control labels support branches with unrelated programs.

Theorem 1.3 (exec_write).

Lean statement: D5/S0/Computability/BinaryMachine/StackControl.exec_write

Proof. Machine-checked in Lean as D5/S0/Computability/BinaryMachine/StackControl.exec_write (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. RBarish-UTokyo (2026). NPCompleteness-Lean4 finite binary machine and composition source. URL: https://github.com/RBarish-UTokyo/NPCompleteness-Lean4/tree/3e603e795b44fedcf7d6dd65b7d1e30547ead925.

Commentary.

Both Boolean halts of a test dispatch to their respective continuation, counting the terminal jump. Word movement clears its destination and performs two reversals, so it preserves bit order and empties scratch. Fixed fallback words are installed by literal one-bit pushes. Disjoint finite control labels support branches with unrelated programs.

Theorem 1.4 (exec_widenLeft).

Lean statement: D5/S0/Computability/BinaryMachine/StackControl.exec_widenLeft

Proof. Machine-checked in Lean as D5/S0/Computability/BinaryMachine/StackControl.exec_widenLeft (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. RBarish-UTokyo (2026). NPCompleteness-Lean4 finite binary machine and composition source. URL: https://github.com/RBarish-UTokyo/NPCompleteness-Lean4/tree/3e603e795b44fedcf7d6dd65b7d1e30547ead925.

Commentary.

Both Boolean halts of a test dispatch to their respective continuation, counting the terminal jump. Word movement clears its destination and performs two reversals, so it preserves bit order and empties scratch. Fixed fallback words are installed by literal one-bit pushes. Disjoint finite control labels support branches with unrelated programs.

Theorem 1.5 (exec_widenRight).

Lean statement: D5/S0/Computability/BinaryMachine/StackControl.exec_widenRight

Proof. Machine-checked in Lean as D5/S0/Computability/BinaryMachine/StackControl.exec_widenRight (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. RBarish-UTokyo (2026). NPCompleteness-Lean4 finite binary machine and composition source. URL: https://github.com/RBarish-UTokyo/NPCompleteness-Lean4/tree/3e603e795b44fedcf7d6dd65b7d1e30547ead925.

Commentary.

Both Boolean halts of a test dispatch to their respective continuation, counting the terminal jump. Word movement clears its destination and performs two reversals, so it preserves bit order and empties scratch. Fixed fallback words are installed by literal one-bit pushes. Disjoint finite control labels support branches with unrelated programs.

References