{
  "schema_version": 1,
  "concept": "4I.4",
  "title": "P.2040-4 material and slab applicability contract",
  "artifact": "material-applicability",
  "model_id": "p2040_material_slab_reference_v1",
  "model_version": "v1",
  "recommendation": "ITU-R P.2040-4",
  "revision": "2025-09",
  "reference_url": "https://www.itu.int/rec/R-REC-P.2040-4-202509-I/en",
  "pdf_url": "https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.2040-4-202509-I!!PDF-E.pdf",
  "range_note": "P.2040-4 covers 1 MHz–450 GHz, but each Table 3 row has its own enforced range. The evaluator does not extrapolate a row.",
  "audited_sections_and_equations": {
    "property_contract": ["Annex 1 §2.1.2 equations (9)–(16)", "Annex 1 §2.1.4 equations (28)–(29)", "§3 equations (57)–(59)"],
    "interface_contract": ["Annex 1 §2.2.1 equations (30)–(38)"],
    "slab_contract": ["Annex 1 §2.2.2.1 equations (39)–(42)", "§2.2.2.2 equations (43a)–(44)"],
    "convention": "εrc = εr′ − jεr″ under exp(−jωt); εr″ = 17.98 σ/fGHz; tanδ = εr″/εr′."
  },
  "required_inputs": {
    "frequency_ghz": "finite positive frequency within the selected row",
    "material": "one P.2040 Table 3 row or one user-defined electrical-property form",
    "thickness_m": "required, finite, non-negative; no universal default",
    "incidence_angle_deg": "0° normal; [0°, 90°) only",
    "polarization": ["TE", "TM"],
    "incident_medium": "explicit relative permittivity, conductivity, and property provenance",
    "exit_medium": "explicit relative permittivity, conductivity, and property provenance"
  },
  "property_derivation": {
    "table_3": "εr′ = a fGHz^b; σ = c fGHz^d; εr″ = 17.98 σ/fGHz",
    "user_conductivity": "εr″ = 17.98 σ/fGHz; tanδ = εr″/εr′",
    "user_loss_tangent": "εr″ = εr′ tanδ; σ = 0.05563 εr′ tanδ fGHz",
    "user_complex": "complex relative permittivity is supplied as real εr′ and positive imaginary-loss magnitude εr″; the evaluator stores εr′ − jεr″",
    "redundancy_rule": "exactly one user electrical-property form is accepted"
  },
  "supported_table_3_rows": [
    {"material_id": "concrete_1_100", "name": "Concrete", "frequency_range_ghz": [1, 100], "a": 5.24, "b": 0, "c": 0.0462, "d": 0.7822},
    {"material_id": "concrete_110_330", "name": "Concrete", "frequency_range_ghz": [110, 330], "a": 5.17, "b": 0, "c": 0.0145, "d": 1.09},
    {"material_id": "brick_1_40", "name": "Brick", "frequency_range_ghz": [1, 40], "a": 3.91, "b": 0, "c": 0.0238, "d": 0.16},
    {"material_id": "brick_110_330", "name": "Brick", "frequency_range_ghz": [110, 330], "a": 4.15, "b": 0, "c": 0.0006, "d": 1.5712},
    {"material_id": "plasterboard_1_100", "name": "Plasterboard", "frequency_range_ghz": [1, 100], "a": 2.73, "b": 0, "c": 0.0085, "d": 0.9395},
    {"material_id": "plasterboard_110_330", "name": "Plasterboard", "frequency_range_ghz": [110, 330], "a": 2.56, "b": 0, "c": 0.0001, "d": 1.7799},
    {"material_id": "plasterboard_100_400", "name": "Plasterboard", "frequency_range_ghz": [100, 400], "a": 2.65, "b": 0, "c": 0.0002, "d": 1.598},
    {"material_id": "wood_0p001_100", "name": "Wood", "frequency_range_ghz": [0.001, 100], "a": 1.99, "b": 0, "c": 0.0047, "d": 1.0718},
    {"material_id": "wood_110_330", "name": "Wood", "frequency_range_ghz": [110, 330], "a": 1.82, "b": 0, "c": 0.004, "d": 1.0761},
    {"material_id": "wood_100_400", "name": "Wood", "frequency_range_ghz": [100, 400], "a": 2.1183, "b": 0, "c": 0.0055, "d": 1.1113},
    {"material_id": "glass_0p1_100", "name": "Glass", "frequency_range_ghz": [0.1, 100], "a": 6.31, "b": 0, "c": 0.0036, "d": 1.3394},
    {"material_id": "glass_220_450", "name": "Glass", "frequency_range_ghz": [220, 450], "a": 5.79, "b": 0, "c": 0.0004, "d": 1.658},
    {"material_id": "glass_100_400", "name": "Glass", "frequency_range_ghz": [100, 400], "a": 6.5767, "b": 0, "c": 0.0012, "d": 1.4697},
    {"material_id": "clear_acrylic_110_330", "name": "Clear acrylic", "frequency_range_ghz": [110, 330], "a": 2.58, "b": 0, "c": 0.0001, "d": 1.6524},
    {"material_id": "ceiling_board_1_100", "name": "Ceiling board", "frequency_range_ghz": [1, 100], "a": 1.48, "b": 0, "c": 0.0011, "d": 1.075},
    {"material_id": "ceiling_board_220_450", "name": "Ceiling board", "frequency_range_ghz": [220, 450], "a": 1.52, "b": 0, "c": 0.0029, "d": 1.029},
    {"material_id": "ceiling_board_100_400", "name": "Ceiling board", "frequency_range_ghz": [100, 400], "a": 1.2567, "b": 0, "c": 0.00013, "d": 1.454},
    {"material_id": "chipboard_1_100", "name": "Chipboard", "frequency_range_ghz": [1, 100], "a": 2.58, "b": 0, "c": 0.0217, "d": 0.78},
    {"material_id": "chipboard_100_200", "name": "Chipboard", "frequency_range_ghz": [100, 200], "a": 2.16, "b": 0, "c": 0.0023, "d": 1.359},
    {"material_id": "plywood_1_40", "name": "Plywood", "frequency_range_ghz": [1, 40], "a": 2.71, "b": 0, "c": 0.33, "d": 0},
    {"material_id": "plywood_110_330", "name": "Plywood", "frequency_range_ghz": [110, 330], "a": 1.94, "b": 0, "c": 0.0067, "d": 0.9982},
    {"material_id": "plywood_100_400", "name": "Plywood", "frequency_range_ghz": [100, 400], "a": 2.17, "b": 0, "c": 0.0063, "d": 1.045}
  ],
  "user_defined_policy": {
    "classification": "user_assumption",
    "accepted_property_sources": ["measured", "manufacturer", "user_declared", "inferred", "unknown"],
    "frequency_range": "optional but enforced when supplied",
    "osm_material_mapping": "disabled"
  },
  "excluded_or_deferred": [
    {"item": "metal", "status": "material_frequency_out_of_range", "reason": "No selected Table 3 row is allowed without explicit 140 GHz coverage in this implementation."},
    {"item": "multilayer construction", "status": "deferred", "reason": "Single homogeneous slab is the smallest auditable scope."},
    {"item": "roughness, diffuse scattering, air gaps, frames, coatings, moisture", "status": "deferred", "reason": "No site or material evidence contract exists yet."},
    {"item": "whole-building entry and P.2109 extrapolation", "status": "not_claimed", "reason": "This endpoint is a material/interface reference only."}
  ],
  "readiness": "reference_only",
  "promotion": false
}