Canonical +1 and -1 · genuine signed products · constructive solutions · Constructive arithmetic

Actual signed units and affine equations

SignedUnit(u) ⇒ ∃a b. SignedMul(a,u,b) ∧ SignedAdd(r,b,e)

Classify every actual signed product equal to one and solve the affine equation needed for finite inversion.

Open the definition-aware map Read the final theorem See campaign milestone G009

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 certificate

Fully expanded arithmetic

Inspect all 401 native tactic lines and 36 actual proof prerequisites with every definition fully expanded.

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Focused route

Final dependency cone

Start at theorem ZU0009 and follow only the lemmas and conservative definitions supporting dirichlet_signed_unit_affine_unique.

Trace prerequisites →
Zoom between mathematical scales: complete research atlas → research domain → proof family → G009 milestone → theorem and definition dependencies.
Major independently established statements: ZU0002 dirichlet_signed_unit_product_classification · ZU0008 dirichlet_signed_unit_affine_solve · ZU0009 dirichlet_signed_unit_affine_unique.
Independently verified Alpha v34 checked-use theorem family: 9 dependency-curried kernel-checked theorem bodies · 36 proof prerequisites · 4 linked definitions · 2 definition-dependency arrows · 401 exact tactic lines · first admitted v31 · not Stable. The unchanged intuitionistic kernel and separately compiled Lean verifier independently accept all 71 bundle nodes; SHA-256 5045f1feb2f21a79ecb3cb03f95aaefeb8f01e616a4aa8640cbada3da62ae47b.
Exact mathematical boundary: Canonical signed +1 is code 2 and -1 is code 1. The two-case unit graph does not assume an inverse or cancellation law: its actual product characterization and affine existence and uniqueness are proved. These scalar lemmas support the separately checked finite inverse criterion; full G009 remains broader.