dynamic-route-reasoning.ts

import type { OpenAIResponsesProviderOptions } from "@ai-sdk/openai";
import { generateText } from "ai";
import { createAiGateway } from "ai-gateway-provider";
import { createOpenAI } from "ai-gateway-provider/providers/openai";
import { createUnified } from "ai-gateway-provider/providers/unified";
import { env } from "cloudflare:workers";

export default defineEventHandler(async (event) => {
  const aigateway = createAiGateway({
    binding: env.AI.gateway(env.NUXT_CLOUDFLARE_AI_GATEWAY_ID),
  });

  // Normal provider, reasoning works
  const provider = createOpenAI()
  const model = aigateway(provider("gpt-5.2"));

  const req1 = generateText({
    model: model,
    prompt: "what is the most unknown mathematical equation right now? try to solve it in a paragraph.",
    providerOptions: {
      openai: {
        reasoningEffort: "medium",
        reasoningSummary: "detailed",
      } satisfies OpenAIResponsesProviderOptions,
    },
  });

  // Dynamic route provider with unified, reasoning does NOT work
  const unified = createUnified();
  const model2 = aigateway(unified("dynamic/chat"));
  const req2 = generateText({
    model: model2,
    prompt: "what is the most unknown mathematical equation right now? try to solve it in a paragraph.",
    providerOptions: {
      openai: {
        reasoningEffort: "medium",
        reasoningSummary: "detailed",
      } satisfies OpenAIResponsesProviderOptions,
    },
  });


  const [response1, response2] = await Promise.all([req1, req2]);

  return {
    normal: {
      answer: response1.text,
      reasoning: response1.steps?.map(s => s.content.map(c => c.type === 'reasoning' ? c.text : null)).filter(Boolean).join('\n'),
      sentBody: response1.request.body
    },
    dynamic: {
      answer: response2.text,
      reasoning: response2.steps?.map(s => s.content.map(c => c.type === 'reasoning' ? c.text : null)).filter(Boolean).join('\n'),
      sentBody: response2.request.body,
    },
   
  };
});

This is the response:

{
  "normal": {
    "answer": "There isn’t a single “most unknown” mathematical equation—“unknown” could mean *obscure* (few people have heard of it) or *unsolved* (the best experts don’t know the answer). If you mean *unsolved*, a strong candidate is the **Navier–Stokes existence and smoothness problem**, governed by the Navier–Stokes PDE for fluid velocity \\(u(x,t)\\) and pressure \\(p(x,t)\\): \\(\\partial_t u + (u\\!\\cdot\\!\\nabla)u = -\\nabla p + \\nu \\Delta u\\), with \\(\\nabla\\!\\cdot\\!u=0\\). “Solving it” would mean proving that for all smooth initial data in 3D, a unique smooth solution exists for all time (or exhibiting a finite-time singularity). A plausible route to a proof would be to show that the nonlinear “vortex stretching” mechanism can always be controlled by viscosity by deriving an a priori bound that prevents norms like \\(\\|\\nabla u\\|_{L^\\infty}\\) from blowing up—e.g., prove an inequality that forces the enstrophy \\(\\int |\\nabla \\times u|^2\\) to stay finite for all time, perhaps by exploiting cancellations from incompressibility and a refined estimate linking \\((u\\!\\cdot\\!\\nabla)u\\) to \\(\\Delta u\\). But no one has found the missing global bound (or a counterexample), which is exactly why it remains a Millennium Prize Problem and why I can’t honestly “solve it” in a paragraph.",
    "reasoning": "**Explaining unknown equations**\n\nI'm thinking about the idea of the \"most unknown equation,\" which seems vague. I could interpret this as referring to open problems or unsolved equations, like the Navier-Stokes equation or the Riemann hypothesis. I need to choose one and express that I can't solve it, providing a brief one-paragraph summary or intuition instead of an actual proof. It's also important to clarify what \"unknown\" means—whether it's about being unsolved or just obscured. I'll be honest in my approach!,",
    "sentBody": {
      "model": "gpt-5.2",
      "input": [
        {
          "role": "user",
          "content": [
            {
              "type": "input_text",
              "text": "what is the most unknown mathematical equation right now? try to solve it in a paragraph."
            }
          ]
        }
      ],
      "reasoning": {
        "effort": "medium",
        "summary": "detailed"
      }
    }
  },
  "dynamic": {
    "answer": "There isn’t a single “most unknown equation” in math, because what’s “unknown” is usually a *problem* (prove/disprove, compute, classify), not a specific mysterious formula. A good candidate for “most famously unknown” is the **Navier–Stokes existence and smoothness** problem (a Clay Millennium Prize): in 3D, for reasonable initial fluid velocity \\(u(x,0)=u_0(x)\\), does the incompressible Navier–Stokes equation\n\\[\n\\partial_t u + (u\\cdot\\nabla)u = -\\nabla p + \\nu \\Delta u,\\qquad \\nabla\\cdot u=0\n\\]\nalways have a globally smooth solution, or can it “blow up” (develop a singularity) in finite time? A one-paragraph “try” at solving it would go like this: you attempt to prove global smoothness by deriving an a priori bound on a norm that controls all derivatives (for instance an \\(H^1\\) or \\(H^2\\) Sobolev norm) using energy methods—start from the basic energy identity \\(\\frac12\\frac{d}{dt}\\|u\\|_{L^2}^2+\\nu\\|\\nabla u\\|_{L^2}^2=0\\), then try to bootstrap to higher norms by differentiating the equation and estimating the nonlinear term \\((u\\cdot\\nabla)u\\) via inequalities like Sobolev embedding and Gagliardo–Nirenberg so that viscosity \\(\\nu\\Delta u\\) dominates and prevents growth; the obstruction is that in 3D the available estimates are “critical,” and the nonlinear vortex-stretching can in principle transfer energy to ever smaller scales faster than dissipation controls it, so no known inequality closes the argument (and no explicit blow-up example is known either).  \n\nIf you tell me what area you mean by “unknown” (unsolved, recently discovered, obscure/rarely studied), I can give a better-matching example.",
    "reasoning": "",
    "sentBody": "{\"model\":\"dynamic/chat\",\"messages\":[{\"role\":\"user\",\"content\":\"what is the most unknown mathematical equation right now? try to solve it in a paragraph.\"}]}"
  }
}