scale_free_causal_closure
plain-language theorem explainer
The theorem states that scale-free causal closure parameters remain fixed at β = 1 and γ = 1 under the assumption of dimensional forcing. Researchers packaging Gap 3 results in Recognition Science papers would cite it to anchor scaling arguments. The proof is a direct one-line return of the input hypothesis without reduction or external lemmas.
Claim. Assume the dimensional forcing condition holds, so that the scaling exponents satisfy $β = 1$ and $γ = 1$. Then the scale-free causal closure is satisfied by the same equality $β = 1 ∧ γ = 1$.
background
Recognition Science places physical quantities on discrete φ-tiers whose densities and fluxes are calibrated by the J-cost function. Upstream structures include nuclear densities ρ_nuc ~ φ^{n_nuclear} × ρ_Planck from NucleosynthesisTiers and the initial release rate r_0 from MarsAtmosphereJCostSchedule. The module packages Gap 3 results on causal closure, drawing on LedgerFactorization for (ℝ₊, ×) calibration of J and PhiForcingDerived for J-cost structure.
proof idea
The proof is a one-line wrapper that directly returns the hypothesis h_dim.
why it matters
The declaration packages the Gap 3 claim that dimensional forcing fixes closure scaling. It supplies a machine-checked anchor for the DIF paper's causal closure arguments and connects to the forcing chain step T8 that forces D = 3 spatial dimensions. No downstream uses are recorded yet, leaving open how the bound integrates with solar-system scaling estimates.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.