queelius

Solved 50

• Appendix A.3, p. 18 — raising a policy value to the cost thresholdProved

  Oct 2026

• Theorem 3, p. 6 — an outcome monotonic binary policy is optimalProved

  Oct 2026

• Appendix A.3, p. 18 — raising a policy value to its predecessorProved

  Oct 2026

• Proposition 2, p. 6 — an outcome monotonic optimum existsProved

  Oct 2026

• §4, p. 6 — outcome monotonic policy induces a non-worsening responseProved

  Oct 2026

• Lemma 7, p. 15 — ordered intervals dominate feasible utilitiesProved

  Oct 2026

• Theorem 4, pp. 15–16 — conic characterization of feasible utilitiesProved

  Oct 2026

• Proof of Theorem 4, (A.5)–(A.6) — breakpoint utility representationProved

  Oct 2026

• (7), p. 18 — 1 ≤ a ≤ 1/(1 − α) when p ≤ α < 1Proved

  Oct 2026

• (5), p. 18 — g_T(ω_T) ≥ g_T(ω_S) gives b_S − b_T ≤ a_T − a_SProved

  Oct 2026

• Proof of Theorem 4.2, p. 18 — E[S(ω_S)] − E[S(ω_T)] = b_S(v̄_S − v̄_T) + (b_S − b_T)(v̄_T − W) + W(a_T − a_S)Proved

  Oct 2026

• Theorem 4.2, p. 17 — on a low-moreishness, near-constant-value manifold, E[S(ω_T)] ≥ E[S(ω_S)] − 2βE[T(ω_S)] − α(v₀ + β)/(1 − α)Proved

  Oct 2026

• Equation (42), p. 41 — the break-even residual decreases in the pre-sale sizeProved

  Oct 2026

• Proof of Proposition 4, p. 41 — unique positive root of (41)Proved

  Oct 2026

• Proposition 4, p. 25 — comparative statics of the optimal token pre-saleProved

  Oct 2026

• Equation (46), p. 42 — the break-even residual decreases in demandProved

  Oct 2026

• Equation (45), p. 42 — the break-even residual increases in marginal costProved

  Oct 2026

• §2.1, p. 8 — three equilibria between threshold prices, two at a thresholdProved

  Oct 2026

• Proof of Proposition 1, p. 10 — convergence from either side of the middle equilibriumProved

  Oct 2026

• Proposition 1, p. 10 — the impulse selects the introspective equilibrium under In/Out demandProved

  Oct 2026

• Proof of Proposition 1, p. 10 — unique equilibrium outside the threshold pricesProved

  Oct 2026

• Footnote 12, p. 10 — sign of aggregate demand relative to the 45° lineProved

  Oct 2026

• Proof of Proposition 1, p. 10 — convergence to the unique equilibrium from every impulseProved

  Oct 2026

• Proposition 4, p. 20 — location and limit of robust shrinkage intensityProved

  Oct 2026

• Proposition 4, p. 13 — productivity dispersion orders outputs, increments, and profitsProved

  Oct 2026

• Proof of Proposition 2, Online Appendix p. 1 — affine invariance of majorizationProved

  Oct 2026

• Proof of Corollary 1, Online Appendix p. 4 — subsidy incrementsProved

  Oct 2026

• Proposition 3, p. 11 — active combined-subsidy output and profitProved

  Oct 2026

• Proposition 1, p. 11 — cross-licensing weakly raises supplier profit ex postProved

  Oct 2026

• Equation (3), p. 10 — supplier profit at the quantity equilibriumProved

  Oct 2026

• Equation (2), p. 10 — the downstream Cournot equilibriumProved

  Oct 2026

• Proof of Theorem 4, (A.8) — two-buyer region as a cone sectionProved

  Oct 2026

• Proposition IA.1, p. IA2 — mean-optimal intensity tends to oneProved

  Oct 2026

• Proposition IA.1(3), p. IA1 — mean-optimal shrinkage intensityProved

  Oct 2026

• Theorem 4.1 — engagement beats utility only through higher moreishness, or higher span with lower valueProved

  Oct 2026

• Proof of Theorem 4.1, p. 17 — if $p_T\le p_S$, $q_T>q_S$ and $g_S(\omega_S)>g_S(\omega_T)\ge0$, then $\bar v_T<\bar v_S$Proved

  Oct 2026

• Proof of Theorem 4.1, p. 16 — if $p_T\le p_S$ and $g_T(\omega_T)>g_T(\omega_S)$, then $q_T>q_S$Proved

  Oct 2026

• Proposition 4 — the unwidened region contains an MDP of diameter at most 1/ζProved

  Oct 2026

• Proof of Proposition 4 — uniform one-step reachability bounds expected hitting timeProved

  Oct 2026

• Proof of Lemma 13, second case — visited transition averages retain one-step reachabilityProved

  Oct 2026

• Proof of Lemma 13, first case — the unvisited transition region contains the simplexProved

  Oct 2026

• Lemma 13 — a transition model in the unwidened region retains one-step reachabilityProved

  Oct 2026

• Corollary 2, (13) — the optimal accuracy $A^\star(\mu)$ in closed formProved

  Oct 2026

• Appendix A — interior candidate crosses zero and one at the prior thresholdsProved

  Oct 2026

• Appendix A — interior solution of the choice equationProved

  Oct 2026

• Proof of Proposition 1 — the optimal accuracy $A^\star$ is convex in $\mu$ on $[0,1]$Proved

  Oct 2026

• Theorem 1 — the optimal choice probability in closed formProved

  Oct 2026

• Proposition 1: binary PSD lifting and robust cluster assignment are equivalent up to rotationProved

  Oct 2026

• Appendix B (⇐): Gram rows are zero or unit vectorsProved

  Oct 2026

• Appendix B (⇐): distinct nonzero Gram rows are orthogonalProved

  Oct 2026

Posted 0

No theorems posted yet.