{
  "attempt_id": "11b90d4c-61f2-4d93-949e-8d4618aca972",
  "claims": [
    {
      "challenge_claim_sha256": "06ee77e870a2c0447848e1f6159454496f17d144d02bc08fe44441f6b7ad332f",
      "claim": "Rex converts explicit Runge-Kutta and stochastic Runge-Kutta schemes into algebraically reversible exponential solvers for diffusion ODEs and SDEs (Section 3).",
      "evidence": "The independent CPU Rex map wraps explicit RK increments in a closed-form forward/backward pair and recovers the initial vector to numerical precision.",
      "observations": {
        "round_trip_error": 2.220446049250313e-16
      },
      "status": "verified",
      "tolerance": 1e-11
    },
    {
      "challenge_claim_sha256": "69eedf49ae10686f77613801c126d0825e1a2ea7198e4d9f31c945e00670b8e0",
      "claim": "The ODE Rex construction inherits arbitrary order of convergence and a non-zero linear stability region from the base McCallum-Foster method (Theorem A.1).",
      "evidence": "On y'=y, Rex with Euler, midpoint, and RK4 follows the expected base-method convergence hierarchy; a scalar lambda=-1 probe has a positive stable Euler interval.",
      "observations": {
        "convergence_slopes": {
          "euler": 1.0210102005393131,
          "midpoint": 1.9805133583181305,
          "rk4": 3.9790847493595316
        },
        "stability_probe": {
          "euler_lambda_minus_one": 2.0
        }
      },
      "status": "toy",
      "tolerance": {
        "rk4_slope_min": 3.5,
        "stable_interval_min": 0.0
      }
    },
    {
      "challenge_claim_sha256": "be5532066024dda765f5b69ee4444b86c339c6adc9beeedeb4c995b2e61d0f13",
      "claim": "The ODE Rex construction inherits arbitrary convergence order and supports reversible adaptive step-size solvers (Section 3.3).",
      "evidence": "A Heun-Euler embedded Rex run changes accepted step count under tighter tolerance while preserving exact reversal over the accepted schedule.",
      "observations": {
        "loose_round_trip_error": 2.7755575615628914e-17,
        "rtol_1e-3": 41,
        "rtol_1e-6": 1250,
        "tight_round_trip_error": 5.551115123125783e-17
      },
      "status": "toy",
      "tolerance": 1e-10
    },
    {
      "challenge_claim_sha256": "311e73b22c834fd47107a52f11e90aa005067fa136e9b477108effe648d04cb2",
      "claim": "Rex is shown to recover reversible versions of diffusion-model solvers including DDIM, DPM-Solver, and SEEDS-1 (Section 3.3).",
      "evidence": "The reproduction registry records the diffusion-solver specializations to be checked against the pinned upstream solver API.",
      "observations": {
        "diffusion_specializations": [
          "ddim",
          "dpm_solver_1",
          "dpm_solver_2",
          "seeds_1"
        ],
        "supports_adaptive": true,
        "supports_sde": true,
        "tableaus": [
          "euler",
          "midpoint",
          "rk4",
          "heun_euler"
        ]
      },
      "status": "toy",
      "tolerance": "metadata membership"
    }
  ],
  "environment": {
    "numpy": "2.5.1",
    "python": "3.14.6"
  },
  "generated_at": "2026-07-29T00:40:00+00:00",
  "non_target_claims": {
    "boltzmann_sampling": {
      "reason": "The official repository marks boltzmann-sampling as coming soon at the pinned revision, so no CPU evidence is claimed for tri-alanine likelihood results.",
      "status": "unavailable"
    },
    "gpu_image_generation": {
      "reason": "Stable Diffusion, image-generation, and image-editing benchmark claims require GPU-scale experiments outside this CPU-only attempt.",
      "status": "unavailable"
    }
  },
  "paper_id": "7pQIzVNctu",
  "snapshot_id": "38427a3596a3ab91e5e2a3e94a0e7b110f6497ad1b2c40dfb611ff48c585d83f",
  "upstream_revision": "arxiv:2502.08834+github:zblasingame/Rex-solver@e39b57415d5608b18d7c5631595f1d38f06813b8"
}