proposition. From structural quality to acquired capability [ftip-00MW]
✍️source

    Fix one contributor and one recipient protocol with almost-sure total resource caps, including failed consultations. Let \(Z\in [0,1]\) be the realized fresh-task score of its frozen artifact with contributor access removed. Suppose, for the same joint process and remaining resources,

    \[\Pr (S)\geq q_0>0,\qquad \mathbb E[Z\mid S]\geq \beta \geq 0.\]

    Then \(Q_{\mathrm {acq}}=\mathbb E Z\geq q_0\beta \).

    Proof. 

      Nonnegativity and conditional expectation give

      \[\mathbb E Z\geq \mathbb E[Z\mathbf 1_S] =\Pr (S)\mathbb E[Z\mid S]\geq q_0\beta .\]

      No independence assumption is used. A uniform recipient guarantee for qualified transcripts and compatible development histories can establish the transfer premise, including interpretation, verification and acquisition costs. A guarantee for a different, easier message distribution cannot.

      Together with a universal closed bound \(Q_{\mathrm {acq}}(P)\leq \tau ^-\) and an admissible member of \(\mathcal G(q_0)\), the strict inequality \(q_0\beta \geq \tau ^+>\tau ^-\) yields the assisted crossing in § [ftip-00MN]. The substantive obligations are affordable source quality, recipient transfer and the bound over every admitted unaided alternative. The elementary expectation inequality alone establishes none of these.