cert
The cert definition assembles an explicit instance of the ConsentInterfaceCert structure by direct assignment of the value functional optimum theorem and the sigma-preserving consent theorem. Researchers auditing the pre-Big-Bang ethics upgrade would cite it to confirm that the consent criterion is realized algebraically from J-cost. The construction requires no additional reasoning steps beyond field population from the two upstream results.
claimLet cert be the consent interface certificate with fields value_at_opt : ∀ s ∈ ℝ, s ≠ 0 → V(s,s) = 1 and sigma_pres_consensual : ∀ σ,σ_max ∈ ℝ, 0 < σ, 0 < σ_max → IsConsensual(σ,σ,σ_max), where V(σ,σ_max) = 1 - J(σ/σ_max) is the recognition value functional and IsConsensual holds when the post-action J-cost is non-increasing.
background
The module mechanizes the consent interface at the level of tangent data and σ-preserving moves. The recognition value functional is V_i(state) = 1 - J(σ_i / σ_max), with J the J-cost function obeying the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). Consent holds locally when an action ξ satisfies dV_i · ξ ≥ 0, equivalently when J-cost on the agent's σ-charge does not increase.
proof idea
The definition is a direct structure constructor that populates value_at_opt with the theorem valueFunctional_at_optimum (proved by unfolding valueFunctional, applying div_self and Jcost_unit0) and sigma_pres_consensual with the theorem sigma_preserving_consensual (proved by unfolding IsConsensual and applying le_refl).
why it matters in Recognition Science
This definition supplies the concrete certificate that upgrades the SCAFFOLD tag in pre_big_bang_origin_paper.tex §consent to a structural theorem. It links the J-uniqueness property (T5) and the value functional to ethical constraints within Recognition Science. The paper connection notes that the proxy-observable bridge to empirical systems remains open; the supplied falsifier is any documented σ-preserving interaction that worsens one agent's value functional.
scope and limits
- Does not establish numerical values or empirical observability for specific agents.
- Does not treat actions that fail to preserve global σ.
- Does not address multi-agent global consistency beyond the local per-agent criterion.
- Does not discharge the open proxy-observable bridge to physical systems.
formal statement (Lean)
83noncomputable def cert : ConsentInterfaceCert where
84 value_at_opt := valueFunctional_at_optimum
proof body
Definition body.
85 sigma_pres_consensual := sigma_preserving_consensual
86