balance_from_conservation
plain-language theorem explainer
The declaration shows that the dual-balance dimension equals one whenever the ledger satisfies the global conservation constraint that the balance function vanishes identically. Physicists deriving the curvature correction in the fine-structure constant would cite it to justify the five-dimensional phase space. The proof is a direct term-mode construction that exhibits the zero function as the constraint and closes by reflexivity.
Claim. There exists a function $c : ℝ → ℝ$ such that if $c(s) = 0$ for every real $s$, then the dual-balance dimension forced by conservation equals one.
background
In Recognition Science the ledger configuration space comprises three spatial dimensions (forced by T8), one temporal dimension from the eight-tick cycle, and one dual-balance dimension. The latter is defined to be one precisely when the conservation law T3 imposes the constraint surface σ = Σ debits − Σ credits = 0. Upstream results supply the tick as the fundamental time quantum and the explicit definition balance_dim_forced := 1 whose doc-comment states that the balance dimension arises from the conservation law T3.
proof idea
The proof is a one-line term-mode wrapper. It constructs the constant-zero function as the constraint, introduces the hypothesis that the constraint vanishes everywhere, and closes the equality by reflexivity.
why it matters
This result supplies the fifth dimension required for the phase-space integral that produces the π^5 factor in the curvature correction δ_κ = −103/(102π^5) inside the fine-structure formula. It directly implements the T3 conservation law within the module that derives why the denominator contains π^5 rather than π^3 or π^6. The declaration is a proved terminal step with no open scaffolding.
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