This research release develops bilateral deficiency, a residual satisfiability parameter motivated by an earlier Evidence Press candidate counterexample to the T-X Graffiti Conjecture fifteen slash three. That parent release exhibited a connected cubic graph on fifty vertices whose independent domination number is sixteen, while its minimum maximal matching number is fifteen.

Bilateral deficiency is defined through partial assignments of Boolean formulas. A variable may remain undecided only when both its positive and negative forms still appear in the surviving clauses. The parameter minimizes the difference between surviving clauses and undecided variables. The manuscript gives it an intrinsic residual interpretation and proves a size-preserving correspondence with independent dominating sets in a formula graph. It also develops algebraic operations, a solution-polynomial identity, connections with MaxSAT, and a clause-width-sensitive complexity boundary.

The main graph-theoretic result applies to finite simple regular graphs equipped with a dominating induced matching, abbreviated D-I-M. In that class, bilateral deficiency exactly measures the difference between the independent domination number and the minimum maximal matching number. The candidate gives a constructive upper bound and builds connected cubic D-I-M families whose gap grows linearly. The resulting density of one part in seventy-two is sharp only for this amplifier construction.

The minimum-order statement has the same essential qualification. The candidate proves that fifty vertices is minimum among cubic graphs admitting a dominating induced matching for which independent domination exceeds minimum maximal matching. It does not claim minimum order among all cubic graphs. Exact extremal constants, counterexamples outside the D-I-M class, and the classification of all order-fifty extremisers remain open.

The evidence package contains a twenty-two-page manuscript, an eight-page reproducibility supplement, exact Python and C-plus-plus implementations, ordinary and optimized test runs, native and Lean checks of three named finite certificate claims, and a Lean proof of the finite terminal signature over all six thousand five hundred and sixty-one partial assignments. It also includes producer-side clean-room encoding validation, hashes, replay records, and an optional extended proof object.

These checks support the identified finite propositions and implementation interfaces. They do not fully formalize the universal theory, imported theorems, compiler, or every bridge from files to propositions. The clean-room validator was produced within the same workflow and is not independent reproduction.

This remains an anonymous, unrefereed candidate. No journal submission, external specialist review, unaffiliated rerun, independent reimplementation, or editorial peer review has occurred. The parent release remains unchanged, and any later correction, review, formalization, or reproduction should appear as a separately identified record.

This is an Evidence Press audio briefing, released on the ninth of August, twenty twenty-six. The manuscript, reproducibility package, certificates, and open follow-up problems are linked on this page. The audio uses an AI-generated voice and is not additional mathematical evidence.