Parity splitting · exact square-and-multiply · canonical modular powers · Constructive arithmetic

Constructive binary modular exponentiation

e=2h+b · x′≡x²aᵇ (mod m) · 0≤r<m

Sixteen independently checked constructive theorems establish exact binary decomposition, square-and-multiply transitions, and existence and uniqueness of the bounded canonical modular power.

Open the definition-aware map Read the final theorem See campaign milestone G102

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Exact certificate

Fully expanded arithmetic

Inspect all 360 native tactic lines and 29 actual proof prerequisites with every definition fully expanded.

Open the exact edition →

Focused route

Final dependency cone

Start at theorem BX0010 and follow only the lemmas and conservative definitions supporting binary_modular_exponentiation_result_exists_unique.

Trace prerequisites →
Zoom between mathematical scales: complete research atlas → research domain → proof family → G102 milestone → theorem and definition dependencies.
Major independently established statements: BX0005 binary_exponent_split_exists · BX000D binary_modular_step_functional · BX0010 binary_modular_exponentiation_result_exists_unique.
Independently verified Alpha v34 checked-use theorem family: 16 dependency-curried kernel-checked theorem bodies · 29 proof prerequisites · 13 linked definitions · 14 definition-dependency arrows · 360 exact tactic lines · first admitted v21 · not Stable. The unchanged intuitionistic kernel and separately compiled Lean verifier independently accept all 209 bundle nodes; SHA-256 65ecae7cb6b3e102790efa281451db3da5ab83868afcf9d57e6656f7a3eafda0.
Exact mathematical boundary: G102 was OPEN when this family was first admitted in Alpha v21. It is now CLOSED in Alpha v23: every arbitrary exponent has actual canonical beta-coded digits, a complete modular execution, and exact counted bound operations≤3*BitLen(e)+2.