{
  "schema_version": "fasttool-flagship-input-output-oracle/v1",
  "canonical_url": "https://fasttool.app/proof/flagship-input-output-oracle/",
  "created_at": "2026-06-25T03:02:59.459Z",
  "run_date": "2026-06-25",
  "summary": {
    "total_cases": 35,
    "failed_cases": 0,
    "formula_oracle_cases": 34,
    "exact_output_cases": 1,
    "artifact_gate_count": 4
  },
  "constants": {
    "speed_of_sound_mps_at_20c": 343.42,
    "canonical_domain": "https://fasttool.app"
  },
  "cases": [
    {
      "id": "audio-speed-of-sound-20c",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-mode-3d-acoustic-studio",
      "tool_name": "Room Mode 3D Acoustic Studio",
      "input": {
        "temperature_c": 20
      },
      "actual": 343.42,
      "expected": 343.42,
      "tolerance": 0.000001,
      "unit": "m/s",
      "delta": 0,
      "passed": true,
      "formula": "c = 331.3 + 0.606 * T(celsius)",
      "comparison_basis": "The public tool must disclose the speed-of-sound constant used for all room-mode, SBIR and phase calculations.",
      "source_refs": [
        "temperature-adjusted speed of sound model"
      ],
      "notes": ""
    },
    {
      "id": "room-mode-100",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-mode-3d-acoustic-studio",
      "tool_name": "Room Mode 3D Acoustic Studio",
      "input": {
        "length_m": 4.6,
        "width_m": 3.5,
        "height_m": 2.55,
        "temperature_c": 20,
        "max_frequency_hz": 300,
        "mode": [
          1,
          0,
          0
        ]
      },
      "actual": 37.328261,
      "expected": 37.328261,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f = c/2 * sqrt((nx/L)^2 + (ny/W)^2 + (nz/H)^2)",
      "comparison_basis": "Axial length mode for the FastTool sample room.",
      "source_refs": [
        "rectangular room mode equation",
        "Hunecke/Bob Golds/Sengpiel calculator family",
        "FastTool room-mode-3d-acoustic-studio renderer"
      ],
      "notes": ""
    },
    {
      "id": "room-mode-010",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-mode-3d-acoustic-studio",
      "tool_name": "Room Mode 3D Acoustic Studio",
      "input": {
        "length_m": 4.6,
        "width_m": 3.5,
        "height_m": 2.55,
        "temperature_c": 20,
        "max_frequency_hz": 300,
        "mode": [
          0,
          1,
          0
        ]
      },
      "actual": 49.06,
      "expected": 49.06,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f = c/2 * sqrt((nx/L)^2 + (ny/W)^2 + (nz/H)^2)",
      "comparison_basis": "Axial width mode for the FastTool sample room.",
      "source_refs": [
        "rectangular room mode equation",
        "Hunecke/Bob Golds/Sengpiel calculator family",
        "FastTool room-mode-3d-acoustic-studio renderer"
      ],
      "notes": ""
    },
    {
      "id": "room-mode-110",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-mode-3d-acoustic-studio",
      "tool_name": "Room Mode 3D Acoustic Studio",
      "input": {
        "length_m": 4.6,
        "width_m": 3.5,
        "height_m": 2.55,
        "temperature_c": 20,
        "max_frequency_hz": 300,
        "mode": [
          1,
          1,
          0
        ]
      },
      "actual": 61.646433,
      "expected": 61.646433,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f = c/2 * sqrt((nx/L)^2 + (ny/W)^2 + (nz/H)^2)",
      "comparison_basis": "Tangential length-width mode for the FastTool sample room.",
      "source_refs": [
        "rectangular room mode equation",
        "Hunecke/Bob Golds/Sengpiel calculator family",
        "FastTool room-mode-3d-acoustic-studio renderer"
      ],
      "notes": ""
    },
    {
      "id": "room-mode-001",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-mode-3d-acoustic-studio",
      "tool_name": "Room Mode 3D Acoustic Studio",
      "input": {
        "length_m": 4.6,
        "width_m": 3.5,
        "height_m": 2.55,
        "temperature_c": 20,
        "max_frequency_hz": 300,
        "mode": [
          0,
          0,
          1
        ]
      },
      "actual": 67.337255,
      "expected": 67.337255,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f = c/2 * sqrt((nx/L)^2 + (ny/W)^2 + (nz/H)^2)",
      "comparison_basis": "Axial height mode for the FastTool sample room.",
      "source_refs": [
        "rectangular room mode equation",
        "Hunecke/Bob Golds/Sengpiel calculator family",
        "FastTool room-mode-3d-acoustic-studio renderer"
      ],
      "notes": ""
    },
    {
      "id": "room-mode-counts-300hz",
      "category": "Audio science",
      "proof_level": "exact_output",
      "tool_slug": "room-mode-3d-acoustic-studio",
      "tool_name": "Room Mode 3D Acoustic Studio",
      "input": {
        "length_m": 4.6,
        "width_m": 3.5,
        "height_m": 2.55,
        "temperature_c": 20,
        "max_frequency_hz": 300
      },
      "actual": {
        "total": 163,
        "axial": 18,
        "tangential": 70,
        "oblique": 75
      },
      "expected": {
        "total": 163,
        "axial": 18,
        "tangential": 70,
        "oblique": 75
      },
      "tolerance": 0,
      "unit": "",
      "delta": 0,
      "passed": true,
      "formula": "count all nx,ny,nz > 0 combinations with f <= max_frequency_hz, then classify by active axes",
      "comparison_basis": "Mode-count parity for a 300 Hz room-mode limit; 200 Hz intentionally produces fewer rows.",
      "source_refs": [
        "rectangular room mode equation",
        "Hunecke/Bob Golds/Sengpiel calculator family",
        "FastTool room-mode-3d-acoustic-studio renderer"
      ],
      "notes": "This is the comparison that prevents hidden mismatch between calculator sites that use different max-frequency limits."
    },
    {
      "id": "sbir-front-wall-095",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "studio-monitor-sbir-3d-planner",
      "tool_name": "Studio Monitor SBIR 3D Planner",
      "input": {
        "boundary_distance_m": 0.95,
        "order": 1,
        "temperature_c": 20
      },
      "actual": 90.373684,
      "expected": 90.373684,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f = (2n - 1) * c / (4d)",
      "comparison_basis": "Front-wall quarter-wave cancellation estimate.",
      "source_refs": [
        "quarter-wave SBIR boundary model",
        "FastTool studio-monitor-sbir-3d-planner renderer"
      ],
      "notes": ""
    },
    {
      "id": "sbir-rear-wall-115",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "studio-monitor-sbir-3d-planner",
      "tool_name": "Studio Monitor SBIR 3D Planner",
      "input": {
        "boundary_distance_m": 1.15,
        "order": 1,
        "temperature_c": 20
      },
      "actual": 74.656522,
      "expected": 74.656522,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f = (2n - 1) * c / (4d)",
      "comparison_basis": "Rear-wall quarter-wave cancellation estimate.",
      "source_refs": [
        "quarter-wave SBIR boundary model",
        "FastTool studio-monitor-sbir-3d-planner renderer"
      ],
      "notes": ""
    },
    {
      "id": "helmholtz-reference",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "helmholtz-bass-trap-tuner",
      "tool_name": "Helmholtz Bass Trap Tuner",
      "input": {
        "port_radius_m": 0.05,
        "port_area_m2": 0.007853982,
        "cavity_volume_m3": 0.05,
        "neck_length_m": 0.1,
        "end_correction_radius_multiplier": 1.7,
        "temperature_c": 20
      },
      "actual": 50.363951,
      "expected": 50.363951,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f = c/(2*pi) * sqrt(A/(V*(L + 1.7r)))",
      "comparison_basis": "Helmholtz bass trap tuning with explicit end-correction assumption.",
      "source_refs": [
        "Helmholtz resonator equation",
        "acoustic modelling Helmholtz calculator family"
      ],
      "notes": ""
    },
    {
      "id": "qrd-n7-depth-0",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "qrd-diffuser-design-studio",
      "tool_name": "QRD Diffuser Design Studio",
      "input": {
        "index": 0,
        "prime": 7,
        "well_depth_m": 0.18
      },
      "actual": 0,
      "expected": 0,
      "tolerance": 0.000001,
      "unit": "m",
      "delta": 0,
      "passed": true,
      "formula": "depth(n) = ((n*n) mod (2*prime)) * well_depth",
      "comparison_basis": "Quadratic residue depth sequence sanity check.",
      "source_refs": [
        "quadratic residue diffuser sequence"
      ],
      "notes": ""
    },
    {
      "id": "qrd-n7-depth-1",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "qrd-diffuser-design-studio",
      "tool_name": "QRD Diffuser Design Studio",
      "input": {
        "index": 1,
        "prime": 7,
        "well_depth_m": 0.18
      },
      "actual": 0.18,
      "expected": 0.18,
      "tolerance": 0.000001,
      "unit": "m",
      "delta": 0,
      "passed": true,
      "formula": "depth(n) = ((n*n) mod (2*prime)) * well_depth",
      "comparison_basis": "Quadratic residue depth sequence sanity check.",
      "source_refs": [
        "quadratic residue diffuser sequence"
      ],
      "notes": ""
    },
    {
      "id": "qrd-n7-depth-2",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "qrd-diffuser-design-studio",
      "tool_name": "QRD Diffuser Design Studio",
      "input": {
        "index": 2,
        "prime": 7,
        "well_depth_m": 0.18
      },
      "actual": 0.72,
      "expected": 0.72,
      "tolerance": 0.000001,
      "unit": "m",
      "delta": 0,
      "passed": true,
      "formula": "depth(n) = ((n*n) mod (2*prime)) * well_depth",
      "comparison_basis": "Quadratic residue depth sequence sanity check.",
      "source_refs": [
        "quadratic residue diffuser sequence"
      ],
      "notes": ""
    },
    {
      "id": "qrd-n7-depth-3",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "qrd-diffuser-design-studio",
      "tool_name": "QRD Diffuser Design Studio",
      "input": {
        "index": 3,
        "prime": 7,
        "well_depth_m": 0.18
      },
      "actual": 1.62,
      "expected": 1.62,
      "tolerance": 0.000001,
      "unit": "m",
      "delta": 0,
      "passed": true,
      "formula": "depth(n) = ((n*n) mod (2*prime)) * well_depth",
      "comparison_basis": "Quadratic residue depth sequence sanity check.",
      "source_refs": [
        "quadratic residue diffuser sequence"
      ],
      "notes": ""
    },
    {
      "id": "rbj-peaking-b0",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-eq-target-curve-filter-planner",
      "tool_name": "Room EQ Target Curve and Filter Planner",
      "input": {
        "frequency_hz": 100,
        "q": 2,
        "gain_db": -6,
        "sample_rate_hz": 48000,
        "coefficient": "b0"
      },
      "actual": 0.997705,
      "expected": 0.997705,
      "tolerance": 0.000001,
      "unit": "",
      "delta": 0,
      "passed": true,
      "formula": "RBJ Audio EQ Cookbook peaking EQ coefficient equations, normalized by a0",
      "comparison_basis": "Known-value EQ coefficient regression for exported filter plans.",
      "source_refs": [
        "RBJ Audio EQ Cookbook peaking EQ"
      ],
      "notes": ""
    },
    {
      "id": "rbj-peaking-b1",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-eq-target-curve-filter-planner",
      "tool_name": "Room EQ Target Curve and Filter Planner",
      "input": {
        "frequency_hz": 100,
        "q": 2,
        "gain_db": -6,
        "sample_rate_hz": 48000,
        "coefficient": "b1"
      },
      "actual": -1.990627,
      "expected": -1.990627,
      "tolerance": 0.000001,
      "unit": "",
      "delta": 0,
      "passed": true,
      "formula": "RBJ Audio EQ Cookbook peaking EQ coefficient equations, normalized by a0",
      "comparison_basis": "Known-value EQ coefficient regression for exported filter plans.",
      "source_refs": [
        "RBJ Audio EQ Cookbook peaking EQ"
      ],
      "notes": ""
    },
    {
      "id": "rbj-peaking-b2",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-eq-target-curve-filter-planner",
      "tool_name": "Room EQ Target Curve and Filter Planner",
      "input": {
        "frequency_hz": 100,
        "q": 2,
        "gain_db": -6,
        "sample_rate_hz": 48000,
        "coefficient": "b2"
      },
      "actual": 0.993093,
      "expected": 0.993093,
      "tolerance": 0.000001,
      "unit": "",
      "delta": 0,
      "passed": true,
      "formula": "RBJ Audio EQ Cookbook peaking EQ coefficient equations, normalized by a0",
      "comparison_basis": "Known-value EQ coefficient regression for exported filter plans.",
      "source_refs": [
        "RBJ Audio EQ Cookbook peaking EQ"
      ],
      "notes": ""
    },
    {
      "id": "rbj-peaking-a1",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-eq-target-curve-filter-planner",
      "tool_name": "Room EQ Target Curve and Filter Planner",
      "input": {
        "frequency_hz": 100,
        "q": 2,
        "gain_db": -6,
        "sample_rate_hz": 48000,
        "coefficient": "a1"
      },
      "actual": -1.990627,
      "expected": -1.990627,
      "tolerance": 0.000001,
      "unit": "",
      "delta": 0,
      "passed": true,
      "formula": "RBJ Audio EQ Cookbook peaking EQ coefficient equations, normalized by a0",
      "comparison_basis": "Known-value EQ coefficient regression for exported filter plans.",
      "source_refs": [
        "RBJ Audio EQ Cookbook peaking EQ"
      ],
      "notes": ""
    },
    {
      "id": "rbj-peaking-a2",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-eq-target-curve-filter-planner",
      "tool_name": "Room EQ Target Curve and Filter Planner",
      "input": {
        "frequency_hz": 100,
        "q": 2,
        "gain_db": -6,
        "sample_rate_hz": 48000,
        "coefficient": "a2"
      },
      "actual": 0.990798,
      "expected": 0.990798,
      "tolerance": 0.000001,
      "unit": "",
      "delta": 0,
      "passed": true,
      "formula": "RBJ Audio EQ Cookbook peaking EQ coefficient equations, normalized by a0",
      "comparison_basis": "Known-value EQ coefficient regression for exported filter plans.",
      "source_refs": [
        "RBJ Audio EQ Cookbook peaking EQ"
      ],
      "notes": ""
    },
    {
      "id": "sub-phase-delta-80hz",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "subwoofer-crossover-phase-aligner",
      "tool_name": "Subwoofer Crossover Phase Alignment Lab",
      "input": {
        "crossover_hz": 80,
        "path_delta_m": 0.4,
        "temperature_c": 20
      },
      "actual": 33.54493,
      "expected": 33.54493,
      "tolerance": 0.0008,
      "unit": "deg",
      "delta": 0,
      "passed": true,
      "formula": "phase = 360 * f * path_delta / c, wrapped to -180..180",
      "comparison_basis": "Crossover phase estimate from path-length mismatch.",
      "source_refs": [
        "phase from acoustic path delay",
        "FastTool subwoofer-crossover-phase-aligner renderer"
      ],
      "notes": ""
    },
    {
      "id": "sub-vector-loss-80hz",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "subwoofer-crossover-phase-aligner",
      "tool_name": "Subwoofer Crossover Phase Alignment Lab",
      "input": {
        "crossover_hz": 80,
        "path_delta_m": 0.4,
        "phase_deg": 33.54493
      },
      "actual": -0.377603,
      "expected": -0.377603,
      "tolerance": 0.0008,
      "unit": "dB",
      "delta": 0,
      "passed": true,
      "formula": "loss_db = 20 * log10(abs(cos(phase/2)))",
      "comparison_basis": "Vector-sum loss from phase mismatch at crossover.",
      "source_refs": [
        "two-source vector sum model"
      ],
      "notes": ""
    },
    {
      "id": "rt60-sabine-sample",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-treatment-rt60-planner",
      "tool_name": "Room Treatment RT60 Planner",
      "input": {
        "volume_m3": 41.055,
        "absorption_sabins": 20
      },
      "actual": 0.330493,
      "expected": 0.330493,
      "tolerance": 0.0008,
      "unit": "s",
      "delta": 0,
      "passed": true,
      "formula": "RT60 = 0.161 * V / A",
      "comparison_basis": "Sabine RT60 known-value check for treatment planning.",
      "source_refs": [
        "Sabine reverberation equation"
      ],
      "notes": ""
    },
    {
      "id": "rt60-eyring-sample",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-treatment-rt60-planner",
      "tool_name": "Room Treatment RT60 Planner",
      "input": {
        "volume_m3": 41.055,
        "surface_area_m2": 73.51,
        "average_absorption": 0.272072
      },
      "actual": 0.283158,
      "expected": 0.283158,
      "tolerance": 0.0008,
      "unit": "s",
      "delta": 0,
      "passed": true,
      "formula": "RT60 = 0.161 * V / (-S * ln(1 - alpha))",
      "comparison_basis": "Eyring RT60 known-value check for higher absorption rooms.",
      "source_refs": [
        "Eyring reverberation equation"
      ],
      "notes": ""
    },
    {
      "id": "schroeder-frequency-sample",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "room-treatment-rt60-planner",
      "tool_name": "Room Treatment RT60 Planner",
      "input": {
        "rt60_s": 0.32,
        "volume_m3": 41.055
      },
      "actual": 176.572049,
      "expected": 176.572049,
      "tolerance": 0.0008,
      "unit": "Hz",
      "delta": 0,
      "passed": true,
      "formula": "f_s = 2000 * sqrt(RT60 / V)",
      "comparison_basis": "Schroeder transition frequency shown in acoustic treatment outputs.",
      "source_refs": [
        "Schroeder frequency estimate"
      ],
      "notes": ""
    },
    {
      "id": "mirror-reflection-y",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "acoustic-panel-reflection-mapper",
      "tool_name": "Acoustic Panel First Reflection Mapper",
      "input": {
        "source": {
          "x": -1.1,
          "y": 0.48,
          "z": 1.1
        },
        "listener": {
          "x": 1.75,
          "y": 1.75,
          "z": 1.18
        },
        "wall": "left x=0",
        "coordinate": "y"
      },
      "actual": 0.970175,
      "expected": 0.970175,
      "tolerance": 0.0008,
      "unit": "m",
      "delta": 0,
      "passed": true,
      "formula": "linear interpolation from source to listener at reflected wall crossing",
      "comparison_basis": "Mirror-method panel center coordinate sanity check.",
      "source_refs": [
        "mirror-method first reflection geometry"
      ],
      "notes": ""
    },
    {
      "id": "mirror-reflection-z",
      "category": "Audio science",
      "proof_level": "formula_oracle",
      "tool_slug": "acoustic-panel-reflection-mapper",
      "tool_name": "Acoustic Panel First Reflection Mapper",
      "input": {
        "source": {
          "x": -1.1,
          "y": 0.48,
          "z": 1.1
        },
        "listener": {
          "x": 1.75,
          "y": 1.75,
          "z": 1.18
        },
        "wall": "left x=0",
        "coordinate": "z"
      },
      "actual": 1.130877,
      "expected": 1.130877,
      "tolerance": 0.0008,
      "unit": "m",
      "delta": 0,
      "passed": true,
      "formula": "linear interpolation from source to listener at reflected wall crossing",
      "comparison_basis": "Mirror-method panel center coordinate sanity check.",
      "source_refs": [
        "mirror-method first reflection geometry"
      ],
      "notes": ""
    },
    {
      "id": "revenue-conservative-gross",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "conservative",
        "monthlyPageviews": 640,
        "pageviewsPerVisitor": 1.35,
        "botShare": 18,
        "adSlots": 2.2,
        "viewability": 68,
        "fillRate": 82,
        "adRpm": 4.8,
        "monthlyCosts": 38,
        "organicImpressions": 12000,
        "currentCtr": 1.2,
        "targetCtr": 3.4
      },
      "actual": 1.774368,
      "expected": 1.774368,
      "tolerance": 0.00001,
      "unit": "USD/month",
      "delta": 0,
      "passed": true,
      "formula": "((human_pageviews * ad_slots * viewability * fill_rate) / 1000) * rpm * scenario_rpm",
      "comparison_basis": "Revenue model parity for the default FastTool evidence sample.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer",
        "ad revenue arithmetic gate"
      ],
      "notes": ""
    },
    {
      "id": "revenue-conservative-net",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "conservative",
        "monthly_costs_usd": 38
      },
      "actual": -36.225632,
      "expected": -36.225632,
      "tolerance": 0.00001,
      "unit": "USD/month",
      "delta": 0,
      "passed": true,
      "formula": "net = gross_revenue - monthly_costs",
      "comparison_basis": "Net-revenue proof must stay negative for the default low-traffic evidence sample.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer"
      ],
      "notes": ""
    },
    {
      "id": "revenue-conservative-human-visitors",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "conservative",
        "pageviews_per_visitor": 1.35,
        "bot_share_percent": 18
      },
      "actual": 310.020741,
      "expected": 310.020741,
      "tolerance": 0.00001,
      "unit": "visitors/month",
      "delta": 0,
      "passed": true,
      "formula": "human_visitors = monthly_pageviews * (1 - bot_share) / pageviews_per_visitor",
      "comparison_basis": "Human traffic floor is separated from raw pageviews before monetization.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer"
      ],
      "notes": ""
    },
    {
      "id": "revenue-base-gross",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "base",
        "monthlyPageviews": 640,
        "pageviewsPerVisitor": 1.35,
        "botShare": 18,
        "adSlots": 2.2,
        "viewability": 68,
        "fillRate": 82,
        "adRpm": 4.8,
        "monthlyCosts": 38,
        "organicImpressions": 12000,
        "currentCtr": 1.2,
        "targetCtr": 3.4
      },
      "actual": 4.364846,
      "expected": 4.364846,
      "tolerance": 0.00001,
      "unit": "USD/month",
      "delta": 0,
      "passed": true,
      "formula": "((human_pageviews * ad_slots * viewability * fill_rate) / 1000) * rpm * scenario_rpm",
      "comparison_basis": "Revenue model parity for the default FastTool evidence sample.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer",
        "ad revenue arithmetic gate"
      ],
      "notes": ""
    },
    {
      "id": "revenue-base-net",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "base",
        "monthly_costs_usd": 38
      },
      "actual": -33.635154,
      "expected": -33.635154,
      "tolerance": 0.00001,
      "unit": "USD/month",
      "delta": 0,
      "passed": true,
      "formula": "net = gross_revenue - monthly_costs",
      "comparison_basis": "Net-revenue proof must stay negative for the default low-traffic evidence sample.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer"
      ],
      "notes": ""
    },
    {
      "id": "revenue-base-human-visitors",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "base",
        "pageviews_per_visitor": 1.35,
        "bot_share_percent": 18
      },
      "actual": 549.096296,
      "expected": 549.096296,
      "tolerance": 0.00001,
      "unit": "visitors/month",
      "delta": 0,
      "passed": true,
      "formula": "human_visitors = monthly_pageviews * (1 - bot_share) / pageviews_per_visitor",
      "comparison_basis": "Human traffic floor is separated from raw pageviews before monetization.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer"
      ],
      "notes": ""
    },
    {
      "id": "revenue-upside-gross",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "upside",
        "monthlyPageviews": 640,
        "pageviewsPerVisitor": 1.35,
        "botShare": 18,
        "adSlots": 2.2,
        "viewability": 68,
        "fillRate": 82,
        "adRpm": 4.8,
        "monthlyCosts": 38,
        "organicImpressions": 12000,
        "currentCtr": 1.2,
        "targetCtr": 3.4
      },
      "actual": 7.751948,
      "expected": 7.751948,
      "tolerance": 0.00001,
      "unit": "USD/month",
      "delta": 0,
      "passed": true,
      "formula": "((human_pageviews * ad_slots * viewability * fill_rate) / 1000) * rpm * scenario_rpm",
      "comparison_basis": "Revenue model parity for the default FastTool evidence sample.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer",
        "ad revenue arithmetic gate"
      ],
      "notes": ""
    },
    {
      "id": "revenue-upside-net",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "upside",
        "monthly_costs_usd": 38
      },
      "actual": -30.248052,
      "expected": -30.248052,
      "tolerance": 0.00001,
      "unit": "USD/month",
      "delta": 0,
      "passed": true,
      "formula": "net = gross_revenue - monthly_costs",
      "comparison_basis": "Net-revenue proof must stay negative for the default low-traffic evidence sample.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer"
      ],
      "notes": ""
    },
    {
      "id": "revenue-upside-human-visitors",
      "category": "Traffic and revenue",
      "proof_level": "formula_oracle",
      "tool_slug": "website-ad-revenue-calculator",
      "tool_name": "Website Revenue Reality Forecaster",
      "input": {
        "scenario": "upside",
        "pageviews_per_visitor": 1.35,
        "bot_share_percent": 18
      },
      "actual": 780.154074,
      "expected": 780.154074,
      "tolerance": 0.00001,
      "unit": "visitors/month",
      "delta": 0,
      "passed": true,
      "formula": "human_visitors = monthly_pageviews * (1 - bot_share) / pageviews_per_visitor",
      "comparison_basis": "Human traffic floor is separated from raw pageviews before monetization.",
      "source_refs": [
        "FastTool website-ad-revenue-calculator renderer"
      ],
      "notes": ""
    },
    {
      "id": "contrast-teal-white-ratio",
      "category": "UX accessibility",
      "proof_level": "formula_oracle",
      "tool_slug": "color-contrast-checker",
      "tool_name": "Color Contrast Checker",
      "input": {
        "foreground": "#0A8D83",
        "background": "#FFFFFF"
      },
      "actual": 4.077199,
      "expected": 4.077199,
      "tolerance": 0.00001,
      "unit": ":1",
      "delta": 0,
      "passed": true,
      "formula": "WCAG relative luminance contrast ratio = (L1 + 0.05) / (L2 + 0.05)",
      "comparison_basis": "Known color-pair check used by the contrast proof pack smoke test.",
      "source_refs": [
        "WCAG relative luminance formula",
        "FastTool color-contrast-checker renderer"
      ],
      "notes": ""
    }
  ],
  "failed_cases": [],
  "artifact_gates": [
    {
      "name": "Traffic + revenue browser artifact smoke",
      "command": "node scripts/revenue_traffic_artifact_smoke_20260625.mjs {base_url}",
      "verifies": "GSC/Cloudflare reconciler and revenue forecaster render visible results, emit conversion events, copy receipts and download artifacts on desktop, 390px and 320px."
    },
    {
      "name": "Readability + contrast browser artifact smoke",
      "command": "node scripts/readability_contrast_artifact_smoke_20260625.mjs {base_url}",
      "verifies": "Readability and contrast tools produce proof packs, JSON receipts, CSV/CSS artifacts and no mobile overflow."
    },
    {
      "name": "Studio monitor SBIR 3D browser smoke",
      "command": "FASTTOOL_BASE_URL={base_url} node scripts/studio_monitor_sbir_3d_planner_smoke_20260622.js",
      "verifies": "SBIR 3D planner renders nonblank canvas output, 12 SBIR rows, formulas, artifact hashes, copy/download parity and audio discovery links."
    },
    {
      "name": "Scientific oracle release gate",
      "command": "node scripts/scientific_oracle_gate_20260624.mjs",
      "verifies": "Original deterministic acoustic/math oracle remains green alongside this public proof table."
    }
  ],
  "boundaries": [
    "This proves deterministic known-value cases and artifact behavior, not every possible room shape, material, browser or analytics dataset.",
    "Different room-mode calculators can legitimately differ when they use another speed of sound, room rounding, max-frequency limit or inclusive/exclusive frequency cutoff.",
    "Traffic and revenue arithmetic proof is not a promise of traffic, AdSense approval, ranking or earnings."
  ]
}