{
  "checks": {
    "max_reliability_identity_error": 2.225997164373439e-14,
    "max_rental_benchmark_identity_error": 4.440892098500626e-16,
    "max_rental_schedule_identity_error": 2.842170943040401e-14
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  "hardware_cost_bridge": [
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      "annualized_capex_rental_floor_usd_per_accelerator_hour": 2.952339967709119,
      "annualized_capex_rental_floor_usd_per_rack_hour": 212.56847767505658,
      "capacity_gw": 10.0,
      "capex_per_kw_usd": 50000.0,
      "capex_per_mw_usd": 50000000.0,
      "effective_capacity_kw_per_rack": 120.0,
      "gb200_nvl72_gpus_per_rack": 72,
      "gb200_nvl72_rack_kw": 120.0,
      "if_all_capacity_were_gb200_nvl72": {
        "accelerator_hours_per_year_at_utilization": 44676000000.0,
        "implied_accelerators": 6000000.0,
        "implied_racks": 83333.33333333333
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      "implied_total_infrastructure_capex_per_accelerator_usd": 83333.33333333333,
      "implied_total_infrastructure_capex_per_gb200_rack_usd": 6000000.0,
      "investment_usd": 500000000000.0,
      "label": "openai_stargate_full_commitment",
      "power_boundary_factor_phi": 1.0,
      "rental_schedule": [
        {
          "model_multiplier_1_over_1_minus_share": 1.0,
          "rental_usd_per_accelerator_hour": 2.952339967709119,
          "rental_usd_per_rack_hour": 212.56847767505658,
          "training_share_T_over_Qbar": 0.0
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        {
          "model_multiplier_1_over_1_minus_share": 1.3333333333333333,
          "rental_usd_per_accelerator_hour": 3.936453290278825,
          "rental_usd_per_rack_hour": 283.4246369000754,
          "training_share_T_over_Qbar": 0.25
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        {
          "model_multiplier_1_over_1_minus_share": 2.0,
          "rental_usd_per_accelerator_hour": 5.904679935418238,
          "rental_usd_per_rack_hour": 425.13695535011317,
          "training_share_T_over_Qbar": 0.5
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          "model_multiplier_1_over_1_minus_share": 4.0,
          "rental_usd_per_accelerator_hour": 11.809359870836476,
          "rental_usd_per_rack_hour": 850.2739107002263,
          "training_share_T_over_Qbar": 0.75
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        {
          "model_multiplier_1_over_1_minus_share": 10.000000000000002,
          "rental_usd_per_accelerator_hour": 29.523399677091195,
          "rental_usd_per_rack_hour": 2125.6847767505665,
          "training_share_T_over_Qbar": 0.9
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      ],
      "source_key": "openai_stargate_capacity"
    },
    {
      "annualized_capex_rental_floor_usd_per_accelerator_hour": 0.7380849919272797,
      "annualized_capex_rental_floor_usd_per_rack_hour": 53.142119418764146,
      "capacity_gw": 1.2,
      "capex_per_kw_usd": 12500.0,
      "capex_per_mw_usd": 12500000.0,
      "effective_capacity_kw_per_rack": 120.0,
      "gb200_nvl72_gpus_per_rack": 72,
      "gb200_nvl72_rack_kw": 120.0,
      "if_all_capacity_were_gb200_nvl72": {
        "accelerator_hours_per_year_at_utilization": 5361120000.0,
        "implied_accelerators": 720000.0,
        "implied_racks": 10000.0
      },
      "implied_total_infrastructure_capex_per_accelerator_usd": 20833.333333333332,
      "implied_total_infrastructure_capex_per_gb200_rack_usd": 1500000.0,
      "investment_usd": 15000000000.0,
      "label": "crusoe_abilene_joint_venture",
      "power_boundary_factor_phi": 1.0,
      "rental_schedule": [
        {
          "model_multiplier_1_over_1_minus_share": 1.0,
          "rental_usd_per_accelerator_hour": 0.7380849919272797,
          "rental_usd_per_rack_hour": 53.142119418764146,
          "training_share_T_over_Qbar": 0.0
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          "model_multiplier_1_over_1_minus_share": 1.3333333333333333,
          "rental_usd_per_accelerator_hour": 0.9841133225697063,
          "rental_usd_per_rack_hour": 70.85615922501886,
          "training_share_T_over_Qbar": 0.25
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        {
          "model_multiplier_1_over_1_minus_share": 2.0,
          "rental_usd_per_accelerator_hour": 1.4761699838545594,
          "rental_usd_per_rack_hour": 106.28423883752829,
          "training_share_T_over_Qbar": 0.5
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        {
          "model_multiplier_1_over_1_minus_share": 4.0,
          "rental_usd_per_accelerator_hour": 2.952339967709119,
          "rental_usd_per_rack_hour": 212.56847767505658,
          "training_share_T_over_Qbar": 0.75
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        {
          "model_multiplier_1_over_1_minus_share": 10.000000000000002,
          "rental_usd_per_accelerator_hour": 7.380849919272799,
          "rental_usd_per_rack_hour": 531.4211941876416,
          "training_share_T_over_Qbar": 0.9
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      ],
      "source_key": "crusoe_abilene_financing"
    }
  ],
  "notes": [
    "This is a calibration bridge, not a new equilibrium theorem.",
    "The common 1-q_r^n failure form is written here as 1-p^n to avoid conflicting with the paper's capability variable q.",
    "Observed success S_n maps to p=S_n^(1/n), lambda=-log(p), and q_model=-log(lambda) because the paper uses lambda(q)=exp(-q).",
    "Hardware scenarios derive effective all-in infrastructure capex per MW and per accelerator from public aggregate commitments; they are not observed GPU transaction prices.",
    "The baseline power-boundary factor phi=1 treats public capacity and rack power as already measured on the same boundary; if public MW is facility power and rack kW is IT load, phi is the PUE-style facility-power-to-IT-load factor.",
    "Published cloud rental benchmarks can be mapped into the model as tau_hat=1-r0/R_market only if hardware, region, service bundle, utilization, and contract terms are comparable."
  ],
  "parameters": {
    "annuity_factor": 0.26379748079474524,
    "asset_life_years": 5,
    "baseline_task_length_units": 137.0,
    "discount_rate": 0.1,
    "gb200_nvl72_gpus": 72,
    "gb200_nvl72_rack_kw": 120.0,
    "h100_sxm_tdp_kw": 0.7,
    "power_boundary_factor_phi": 1.0,
    "success_probability_at_horizon": 0.5,
    "task_length_unit": "minutes",
    "utilization": 0.85
  },
  "published_rental_benchmarks": [
    {
      "hardware": "NVIDIA H100 80GB HGX",
      "label": "crusoe_h100_hgx_on_demand",
      "note": "Directly listed by Crusoe as dollars per GPU-hour.",
      "pricing_type": "on_demand",
      "provider": "Crusoe Cloud",
      "source_key": "crusoe_cloud_pricing",
      "usd_per_accelerator_hour": 3.9
    },
    {
      "hardware": "NVIDIA H200 141GB HGX",
      "label": "crusoe_h200_hgx_on_demand",
      "note": "Directly listed by Crusoe as dollars per GPU-hour.",
      "pricing_type": "on_demand",
      "provider": "Crusoe Cloud",
      "source_key": "crusoe_cloud_pricing",
      "usd_per_accelerator_hour": 4.29
    },
    {
      "accelerators_per_instance": 4,
      "hardware": "NVIDIA GB200 NVL72",
      "label": "coreweave_gb200_nvl72_on_demand",
      "note": "Converted from a listed 4-GPU instance price to per-GPU equivalent.",
      "pricing_type": "on_demand_instance_equivalent",
      "provider": "CoreWeave",
      "source_key": "coreweave_cloud_pricing",
      "usd_per_accelerator_hour": 10.5,
      "usd_per_instance_hour": 42.0
    },
    {
      "accelerators_per_instance": 8,
      "hardware": "NVIDIA HGX H100",
      "label": "coreweave_h100_hgx_on_demand",
      "note": "Converted from a listed 8-GPU instance price to per-GPU equivalent.",
      "pricing_type": "on_demand_instance_equivalent",
      "provider": "CoreWeave",
      "source_key": "coreweave_cloud_pricing",
      "usd_per_accelerator_hour": 6.155,
      "usd_per_instance_hour": 49.24
    }
  ],
  "rental_benchmark_comparison": [
    {
      "benchmark_label": "crusoe_h100_hgx_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 2.952339967709119,
      "hardware": "NVIDIA H100 80GB HGX",
      "identity_check_rental_times_residual_share": 2.952339967709119,
      "implied_training_share_if_comparable": 0.2429897518694567,
      "market_to_floor_multiplier": 1.3209860797387172,
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      "published_rental_usd_per_accelerator_hour": 3.9,
      "scenario_label": "openai_stargate_full_commitment",
      "source_key": "crusoe_cloud_pricing"
    },
    {
      "benchmark_label": "crusoe_h200_hgx_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 2.952339967709119,
      "hardware": "NVIDIA H200 141GB HGX",
      "identity_check_rental_times_residual_share": 2.952339967709119,
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      "scenario_label": "openai_stargate_full_commitment",
      "source_key": "crusoe_cloud_pricing"
    },
    {
      "benchmark_label": "coreweave_gb200_nvl72_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 2.952339967709119,
      "hardware": "NVIDIA GB200 NVL72",
      "identity_check_rental_times_residual_share": 2.9523399677091193,
      "implied_training_share_if_comparable": 0.7188247649800839,
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    {
      "benchmark_label": "coreweave_h100_hgx_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 2.952339967709119,
      "hardware": "NVIDIA HGX H100",
      "identity_check_rental_times_residual_share": 2.9523399677091184,
      "implied_training_share_if_comparable": 0.5203346924924259,
      "market_to_floor_multiplier": 2.084787005331232,
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      "published_rental_usd_per_accelerator_hour": 6.155,
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      "source_key": "coreweave_cloud_pricing"
    },
    {
      "benchmark_label": "crusoe_h100_hgx_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 0.7380849919272797,
      "hardware": "NVIDIA H100 80GB HGX",
      "identity_check_rental_times_residual_share": 0.7380849919272798,
      "implied_training_share_if_comparable": 0.8107474379673641,
      "market_to_floor_multiplier": 5.283944318954869,
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      "published_rental_usd_per_accelerator_hour": 3.9,
      "scenario_label": "crusoe_abilene_joint_venture",
      "source_key": "crusoe_cloud_pricing"
    },
    {
      "benchmark_label": "crusoe_h200_hgx_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 0.7380849919272797,
      "hardware": "NVIDIA H200 141GB HGX",
      "identity_check_rental_times_residual_share": 0.7380849919272797,
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      "published_rental_usd_per_accelerator_hour": 4.29,
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      "source_key": "crusoe_cloud_pricing"
    },
    {
      "benchmark_label": "coreweave_gb200_nvl72_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 0.7380849919272797,
      "hardware": "NVIDIA GB200 NVL72",
      "identity_check_rental_times_residual_share": 0.7380849919272798,
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      "published_rental_usd_per_accelerator_hour": 10.5,
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      "source_key": "coreweave_cloud_pricing"
    },
    {
      "benchmark_label": "coreweave_h100_hgx_on_demand",
      "caveat": "This maps a published rental benchmark into the model only if the hardware class, service bundle, region, utilization, power-boundary convention, and contract terms are comparable to the capex scenario.",
      "cold_floor_usd_per_accelerator_hour": 0.7380849919272797,
      "hardware": "NVIDIA HGX H100",
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      "published_rental_usd_per_accelerator_hour": 6.155,
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      "source_key": "coreweave_cloud_pricing"
    }
  ],
  "source_anchors": {
    "coreweave_cloud_pricing": {
      "claim_used": "CoreWeave lists NVIDIA GB200 NVL72 at $42.00/hour for a 4-GPU instance and NVIDIA HGX H100 at $49.24/hour for an 8-GPU instance.",
      "url": "https://www.coreweave.com/pricing"
    },
    "crusoe_abilene_financing": {
      "claim_used": "Crusoe, Blue Owl, and Primary Digital Infrastructure announced a $15 billion joint venture to fund a 1.2 GW AI data center in Abilene, Texas.",
      "url": "https://www.crusoe.ai/resources/newsroom/crusoe-blue-owl-capital-and-primary-digital-infrastructure-enter-joint-venture"
    },
    "crusoe_cloud_pricing": {
      "claim_used": "Crusoe Cloud lists on-demand H100 80GB HGX pricing at $3.90/GPU-hr and H200 141GB HGX pricing at $4.29/GPU-hr.",
      "url": "https://www.crusoe.ai/cloud/pricing"
    },
    "metr_time_horizons": {
      "claim_used": "Task-completion horizons provide an observed task-length scale; the public page reports an example GPT-5 agent horizon of about 2 hours 17 minutes for tasks in the 90-minute to 3-hour band.",
      "url": "https://metr.org/time-horizons/"
    },
    "nvidia_gb200_nvl72": {
      "claim_used": "An NVL72 rack has a 72-GPU NVLink domain; rack power consumption is approximately 120 kW.",
      "url": "https://docs.nvidia.com/dgx/dgxgb200-user-guide/hardware.html"
    },
    "nvidia_h100": {
      "claim_used": "H100 SXM max thermal design power is up to 700 W.",
      "url": "https://www.nvidia.com/en-us/data-center/h100/"
    },
    "openai_stargate_announcement": {
      "claim_used": "The Stargate announcement states a $500 billion four-year AI infrastructure plan and $100 billion of immediate deployment.",
      "url": "https://openai.com/index/announcing-the-stargate-project/"
    },
    "openai_stargate_capacity": {
      "claim_used": "OpenAI describes the full Stargate commitment as $500 billion and 10 GW, with nearly 7 GW and over $400 billion planned in the announced sites.",
      "url": "https://openai.com/index/five-new-stargate-sites/"
    }
  },
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      "capability_gap_vs_baseline": -1.518783544165979,
      "failure_check_one_minus_p_to_n": 0.5000000000000007,
      "failure_probability": 0.5,
      "frontier_value_ratio_vs_baseline_a1": 0.21897810218977895,
      "horizon_ratio_vs_baseline": 0.21897810218978103,
      "lambda_q": 0.023104906018664894,
      "model_capability_q": 3.7677103022438176,
      "per_step_failure_probability": 0.022840031565754093,
      "per_step_reliability_p": 0.9771599684342459,
      "success_check_p_to_n": 0.4999999999999993,
      "success_probability": 0.5,
      "task_length": 30.0
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      "capability_gap_vs_baseline": 0.0,
      "failure_check_one_minus_p_to_n": 0.49999999999999745,
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      "frontier_value_ratio_vs_baseline_a1": 1.0,
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}