{
  "article_slug": "weighted-terrain-pathfinding-in-godot",
  "artifact": "Standalone Godot weighted-terrain pathfinding correctness proof",
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  "counterexample": {
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    "discounted_row_weight": 0.25,
    "goal": "(4, 0)",
    "region": "5x2",
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    "patch": 0,
    "status": "stable",
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  "measurement_scope": "Deterministic correctness verification only. No search-time, throughput, allocation, or memory claim.",
  "passed": true,
  "passed_count": 17,
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    "cost_semantics": "Each step charges compute_cost(from, destination) multiplied by the destination cell weight; the starting cell is not charged.",
    "diagonals": "Diagonal modes inspect adjacent solid cells; adjacent expensive-but-walkable cells are not charged unless entered.",
    "discounts": "Weights below 1.0 require an admissible scaled estimate or a zero estimate for Dijkstra-style search.",
    "profiles": "AStarGrid2D has one native point-weight layer per grid; stable profiles use separate prepared grids in this proof.",
    "safe_baseline": "Four-way Manhattan movement, jumping disabled, cheapest authored terrain weight 1.0, expensive terrain above 1.0."
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  "proof_boundary": {
    "not_verified": "TileSet authoring UX, influence-map generation, tactical AP transactions, multi-cell footprint transitions, and production performance.",
    "product_scope": "The standalone source demonstrates public Godot behavior. Private PathForge tests are supporting product evidence, not part of this package.",
    "verified_here": "Built-in AStarGrid2D weight semantics, exact route-cost reconstruction, JPS interaction, GDScript cost/estimate overrides, one discounted-road counterexample, diagonal point-agent corner policy, and stable profile-specific grids."
  },
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    "report": {
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      "diagonal_always_cuts_corner": true,
      "diagonal_strict_blocks_corner": true,
      "discount_counterexample_visible": true,
      "safe_route_avoids_expensive_cell": true,
      "safe_route_cost": 6.0
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  },
  "verified_at": "2026-07-14T07:57:47",
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