{
  "dwell_cases": [
    {
      "dwell_ms": 800,
      "expected_bounds_ms": [
        640,
        1200
      ],
      "expected_dwell_ms": [
        [
          0,
          0,
          699
        ],
        [
          0,
          1,
          864
        ],
        [
          0,
          2,
          1032
        ],
        [
          0,
          3,
          1200
        ]
      ],
      "max_dwell_ms": 2000,
      "name": "800 ms, a skewed prior",
      "weights": [
        [
          0,
          0,
          0.7
        ],
        [
          0,
          1,
          0.2
        ],
        [
          0,
          2,
          0.1
        ],
        [
          0,
          3,
          0.0
        ]
      ]
    },
    {
      "dwell_ms": 800,
      "expected_bounds_ms": [
        640,
        1200
      ],
      "expected_dwell_ms": [
        [
          0,
          0,
          800
        ],
        [
          0,
          1,
          800
        ],
        [
          1,
          0,
          800
        ],
        [
          1,
          1,
          800
        ]
      ],
      "max_dwell_ms": 2000,
      "name": "a uniform prior changes nothing",
      "weights": [
        [
          0,
          0,
          1.0
        ],
        [
          0,
          1,
          1.0
        ],
        [
          1,
          0,
          1.0
        ],
        [
          1,
          1,
          1.0
        ]
      ]
    },
    {
      "dwell_ms": 200,
      "expected_bounds_ms": [
        200,
        300
      ],
      "expected_dwell_ms": [
        [
          0,
          0,
          200
        ],
        [
          0,
          1,
          216
        ],
        [
          0,
          2,
          258
        ],
        [
          0,
          3,
          300
        ]
      ],
      "max_dwell_ms": 2000,
      "name": "the person chose 200 ms: never below it",
      "weights": [
        [
          0,
          0,
          0.7
        ],
        [
          0,
          1,
          0.2
        ],
        [
          0,
          2,
          0.1
        ],
        [
          0,
          3,
          0.0
        ]
      ]
    },
    {
      "dwell_ms": 320,
      "expected_bounds_ms": [
        300,
        480
      ],
      "expected_dwell_ms": [
        [
          0,
          0,
          300
        ],
        [
          0,
          1,
          346
        ],
        [
          0,
          2,
          413
        ],
        [
          0,
          3,
          480
        ]
      ],
      "max_dwell_ms": 2000,
      "name": "320 ms: never below the proposal floor",
      "weights": [
        [
          0,
          0,
          0.7
        ],
        [
          0,
          1,
          0.2
        ],
        [
          0,
          2,
          0.1
        ],
        [
          0,
          3,
          0.0
        ]
      ]
    },
    {
      "dwell_ms": 1600,
      "expected_bounds_ms": [
        1280,
        2000
      ],
      "expected_dwell_ms": [
        [
          0,
          0,
          1398
        ],
        [
          0,
          1,
          1728
        ],
        [
          0,
          2,
          2000
        ],
        [
          0,
          3,
          2000
        ]
      ],
      "max_dwell_ms": 2000,
      "name": "1600 ms: never above the ceiling",
      "weights": [
        [
          0,
          0,
          0.7
        ],
        [
          0,
          1,
          0.2
        ],
        [
          0,
          2,
          0.1
        ],
        [
          0,
          3,
          0.0
        ]
      ]
    },
    {
      "dwell_ms": 100,
      "expected_bounds_ms": [
        100,
        150
      ],
      "expected_dwell_ms": [
        [
          0,
          0,
          100
        ],
        [
          0,
          1,
          108
        ],
        [
          0,
          2,
          129
        ],
        [
          0,
          3,
          150
        ]
      ],
      "max_dwell_ms": 2000,
      "name": "a dwell below the 150 ms floor is never weighted below itself",
      "weights": [
        [
          0,
          0,
          0.7
        ],
        [
          0,
          1,
          0.2
        ],
        [
          0,
          2,
          0.1
        ],
        [
          0,
          3,
          0.0
        ]
      ]
    }
  ],
  "order_cases": [
    {
      "cols": 4,
      "expected_cell_sequence": [
        [
          2,
          3
        ],
        [
          2,
          0
        ],
        [
          2,
          1
        ],
        [
          2,
          2
        ],
        [
          0,
          1
        ],
        [
          0,
          0
        ],
        [
          0,
          2
        ],
        [
          0,
          3
        ],
        [
          1,
          0
        ],
        [
          1,
          1
        ],
        [
          1,
          2
        ],
        [
          1,
          3
        ]
      ],
      "expected_members": [
        [
          1,
          0,
          2,
          3
        ],
        [
          0,
          1,
          2,
          3
        ],
        [
          3,
          0,
          1,
          2
        ]
      ],
      "expected_units": [
        2,
        0,
        1
      ],
      "mode": "RowColumn",
      "name": "row-column: the likeliest row and cell first",
      "rows": 3,
      "weights": [
        [
          2,
          3,
          0.5
        ],
        [
          2,
          0,
          0.2
        ],
        [
          0,
          1,
          0.3
        ]
      ]
    },
    {
      "cols": 3,
      "expected_cell_sequence": [
        [
          0,
          0
        ],
        [
          0,
          1
        ],
        [
          0,
          2
        ],
        [
          1,
          0
        ],
        [
          1,
          1
        ],
        [
          1,
          2
        ]
      ],
      "expected_members": [
        [
          0,
          1,
          2
        ],
        [
          0,
          1,
          2
        ]
      ],
      "expected_units": [
        0,
        1
      ],
      "mode": "RowColumn",
      "name": "row-column: a uniform prior is the fixed order",
      "rows": 2,
      "weights": [
        [
          0,
          0,
          1.0
        ],
        [
          0,
          1,
          1.0
        ],
        [
          0,
          2,
          1.0
        ],
        [
          1,
          0,
          1.0
        ],
        [
          1,
          1,
          1.0
        ],
        [
          1,
          2,
          1.0
        ]
      ]
    },
    {
      "cols": 3,
      "expected_cell_sequence": [
        [
          0,
          0
        ],
        [
          0,
          1
        ],
        [
          0,
          2
        ],
        [
          1,
          1
        ],
        [
          1,
          0
        ],
        [
          1,
          2
        ],
        [
          2,
          2
        ],
        [
          2,
          0
        ],
        [
          2,
          1
        ]
      ],
      "expected_members": [
        [
          0,
          1,
          2
        ],
        [
          1,
          0,
          2
        ],
        [
          2,
          0,
          1
        ]
      ],
      "expected_units": [
        0,
        1,
        2
      ],
      "mode": "RowColumn",
      "name": "row-column: ties keep position order",
      "rows": 3,
      "weights": [
        [
          0,
          0,
          1.0
        ],
        [
          1,
          1,
          1.0
        ],
        [
          2,
          2,
          1.0
        ]
      ]
    },
    {
      "cols": 3,
      "expected_cell_sequence": [
        [
          1,
          2
        ],
        [
          0,
          1
        ],
        [
          0,
          0
        ],
        [
          0,
          2
        ],
        [
          1,
          0
        ],
        [
          1,
          1
        ]
      ],
      "expected_members": [],
      "expected_units": [
        5,
        1,
        0,
        2,
        3,
        4
      ],
      "mode": "Linear",
      "name": "linear: unweighted cells go last, in position order",
      "rows": 2,
      "weights": [
        [
          1,
          2,
          0.6
        ],
        [
          0,
          1,
          0.4
        ]
      ]
    },
    {
      "cols": 2,
      "expected_cell_sequence": [
        [
          0,
          0
        ],
        [
          0,
          1
        ],
        [
          1,
          0
        ],
        [
          1,
          1
        ]
      ],
      "expected_members": [],
      "expected_units": [
        0,
        1,
        2,
        3
      ],
      "mode": "Linear",
      "name": "linear: no prior is the fixed order",
      "rows": 2,
      "weights": []
    },
    {
      "cols": 5,
      "expected_cell_sequence": [
        [
          3,
          4
        ],
        [
          3,
          0
        ],
        [
          3,
          1
        ],
        [
          3,
          2
        ],
        [
          3,
          3
        ],
        [
          1,
          0
        ],
        [
          1,
          1
        ],
        [
          1,
          2
        ],
        [
          1,
          3
        ],
        [
          1,
          4
        ],
        [
          0,
          0
        ],
        [
          0,
          1
        ],
        [
          0,
          2
        ],
        [
          0,
          3
        ],
        [
          0,
          4
        ],
        [
          2,
          0
        ],
        [
          2,
          1
        ],
        [
          2,
          2
        ],
        [
          2,
          3
        ],
        [
          2,
          4
        ]
      ],
      "expected_members": [
        [
          0,
          1,
          2,
          3,
          4
        ],
        [
          0,
          1,
          2,
          3,
          4
        ],
        [
          0,
          1,
          2,
          3,
          4
        ],
        [
          4,
          0,
          1,
          2,
          3
        ]
      ],
      "expected_units": [
        3,
        1,
        0,
        2
      ],
      "mode": "Group",
      "name": "group: the likeliest group first, membership unchanged",
      "rows": 4,
      "weights": [
        [
          3,
          4,
          0.7
        ],
        [
          1,
          0,
          0.3
        ]
      ]
    },
    {
      "cols": 5,
      "expected_cell_sequence": [
        [
          0,
          4
        ],
        [
          1,
          4
        ],
        [
          3,
          3
        ],
        [
          2,
          2
        ],
        [
          2,
          3
        ],
        [
          3,
          2
        ],
        [
          0,
          0
        ],
        [
          0,
          1
        ],
        [
          1,
          0
        ],
        [
          1,
          1
        ],
        [
          0,
          2
        ],
        [
          0,
          3
        ],
        [
          1,
          2
        ],
        [
          1,
          3
        ],
        [
          2,
          0
        ],
        [
          2,
          1
        ],
        [
          3,
          0
        ],
        [
          3,
          1
        ],
        [
          2,
          4
        ],
        [
          3,
          4
        ]
      ],
      "expected_members": [
        [
          0,
          1,
          2,
          3
        ],
        [
          0,
          1,
          2,
          3
        ],
        [
          0,
          1
        ],
        [
          0,
          1,
          2,
          3
        ],
        [
          3,
          0,
          1,
          2
        ],
        [
          0,
          1
        ]
      ],
      "expected_units": [
        2,
        4,
        0,
        1,
        3,
        5
      ],
      "mode": "Block",
      "name": "block: a half-block at the odd edge holds the likeliest cell",
      "rows": 4,
      "weights": [
        [
          0,
          4,
          0.9
        ],
        [
          3,
          3,
          0.1
        ]
      ]
    }
  ],
  "rule": {
    "adaptive_order_default": false,
    "bayesian_selection_default": false,
    "dwell": {
      "absolute_floor_ms": 150,
      "bounds": "lo = max(ceil(0.8 D), min(D, 300)) (>= 150 for any D >= 150); hi = max(min(floor(1.5 D), max_dwell_ms), D, lo)",
      "dwell": "clamp(round(D * factor), lo, hi)",
      "factor": "x = ln(n p / sum p): x >= 0 -> 1 - 0.2 tanh(x / ln 4); x < 0 -> 1 + 0.5 tanh(-x / ln 4); p = 0 -> 1.5; all zero -> 1",
      "max_factor": 1.5,
      "min_factor": 0.8,
      "person_dwell": "applying weights never changes D, never proposes, and never resets the section 5.3 measurement window; weights applied during a dwell take effect when it ends; opting out restores D at once and forgets the weights",
      "proposal_floor_ms": 300
    },
    "dwell_weighting_default": false,
    "order": "units (rows | cells | groups | blocks) by descending sum of weights, members by descending weight; ties by position (row-major); unit membership is the fixed scan's",
    "selection": {
      "damping": 0.96,
      "decision": "select the leader when ln-odds over the runner-up >= ln win_odds; a lone option when sum ln L - n ln(lapse / S) >= ln(win_odds / prior_odds_cap); else keep scanning; ties to the lower index; not opted in or fewer than min_confirmed kept presses: the latest highlight at or before the last press",
      "density": "f(x) = [w0 N(x; 0.65 T, max(0.25 * 0.65 T, 10)) + sum_i d^i N(x; y_i, h)] / (w0 + sum_i d^i); y_0 newest; w0 = 25 d^n; h = max(10, 1.06 sd n_w^-0.2) with sd, n_w the weighted spread and total weight of prior and samples",
      "history": 95,
      "keep_scanning": "a level whose pass ends after an undecided press gets another pass, at most 2 per visit",
      "kernel_evaluations": "presses x onsets in the window x (kept samples + 1)",
      "lapse": 0.02,
      "learning": "presses are staged per selection across its levels; a top-level choice discards what was staged before it; on the final cell the staged presses become a pending selection; an Undo reached by scanning discards itself and the selection it undid; a selection is learned once undo_depth + 1 newer selections are completed; of a Bayesian selection only presses with (1 - lapse) f(offset) > lapse / S are learned",
      "likelihood": "L_j(t) = (1 - lapse) max_c f(t - onset_{j,c}) + lapse / S over onsets with -T/2 <= t - onset < 2T (none: f = 0); S = last onset - first onset + T",
      "min_bandwidth_ms": 10.0,
      "min_confirmed": 10,
      "offset_window_intervals": [
        -0.5,
        2.0
      ],
      "options": "an option is its position-order index at its level, never its rank in a pass",
      "population_mean_fraction_of_interval": 0.65,
      "population_sd_fraction_of_mean": 0.25,
      "prior": "normalise; floor each at max / prior_odds_cap; renormalise",
      "prior_odds_cap": 24.75,
      "prior_weight": 25.0,
      "rule_in_force": "a rule with win_odds / prior_odds_cap < 4 (or non-finite, win_odds <= 1, prior_odds_cap < 1) is replaced by the default",
      "undo_depth": 2,
      "win_odds": 99.0
    }
  },
  "selection_cases": [
    {
      "expected_decision": {
        "kind": "select",
        "method": "bayesian",
        "option": 1
      },
      "expected_kernel_evaluations": 26,
      "expected_posterior": [
        0.003177427738009439,
        0.9862701647005641,
        0.0041975520854075285,
        0.003177427738009439,
        0.003177427738009439
      ],
      "interval_ms": 1000,
      "learned_offsets_ms": [
        1040.0,
        1060.0,
        1020.0,
        1080.0,
        1050.0,
        1030.0,
        1070.0,
        1045.0,
        1055.0,
        1065.0,
        1035.0,
        1050.0
      ],
      "name": "a late press selects the row before",
      "onsets": [
        [
          0,
          0.0
        ],
        [
          1,
          1000.0
        ],
        [
          2,
          2000.0
        ],
        [
          3,
          3000.0
        ],
        [
          4,
          4000.0
        ]
      ],
      "opted_in": true,
      "presses_ms": [
        2040.0
      ],
      "priors": [
        0.2,
        0.2,
        0.2,
        0.2,
        0.2
      ]
    },
    {
      "expected_decision": {
        "kind": "select",
        "method": "bayesian",
        "option": 2
      },
      "expected_kernel_evaluations": 39,
      "expected_posterior": [
        0.0011111395652139541,
        0.0011111420138189177,
        0.9955554368419343,
        0.0011111420138189177,
        0.0011111395652139541
      ],
      "interval_ms": 1000,
      "learned_offsets_ms": [
        640.0,
        660.0,
        630.0,
        670.0,
        650.0,
        655.0,
        645.0,
        665.0,
        635.0,
        650.0,
        660.0,
        640.0
      ],
      "name": "an on-time press agrees with the highlight",
      "onsets": [
        [
          0,
          0.0
        ],
        [
          1,
          1000.0
        ],
        [
          2,
          2000.0
        ],
        [
          3,
          3000.0
        ],
        [
          4,
          4000.0
        ]
      ],
      "opted_in": true,
      "presses_ms": [
        2650.0
      ],
      "priors": [
        0.2,
        0.2,
        0.2,
        0.2,
        0.2
      ]
    },
    {
      "expected_decision": {
        "kind": "keep_scanning",
        "leader": 0
      },
      "expected_kernel_evaluations": 13,
      "expected_posterior": [
        0.9090563569246255,
        0.030314547691791503,
        0.030314547691791503,
        0.030314547691791503
      ],
      "interval_ms": 1000,
      "learned_offsets_ms": [
        1040.0,
        1060.0,
        1020.0,
        1080.0,
        1050.0,
        1030.0,
        1070.0,
        1045.0,
        1055.0,
        1065.0,
        1035.0,
        1050.0
      ],
      "name": "a weakly explained press keeps scanning",
      "onsets": [
        [
          0,
          0.0
        ],
        [
          1,
          1000.0
        ],
        [
          2,
          2000.0
        ],
        [
          3,
          3000.0
        ]
      ],
      "opted_in": true,
      "presses_ms": [
        300.0
      ],
      "priors": [
        0.25,
        0.25,
        0.25,
        0.25
      ]
    },
    {
      "expected_decision": {
        "kind": "keep_scanning",
        "leader": 0
      },
      "expected_kernel_evaluations": 0,
      "expected_posterior": [
        0.925233644859813,
        0.037383177570093434,
        0.037383177570093434
      ],
      "interval_ms": 1000,
      "learned_offsets_ms": [
        1040.0,
        1060.0,
        1020.0,
        1080.0,
        1050.0,
        1030.0,
        1070.0,
        1045.0,
        1055.0,
        1065.0,
        1035.0,
        1050.0
      ],
      "name": "the prior alone never selects",
      "onsets": [
        [
          0,
          0.0
        ],
        [
          1,
          1000.0
        ],
        [
          2,
          2000.0
        ]
      ],
      "opted_in": true,
      "presses_ms": [
        60000.0
      ],
      "priors": [
        1.0,
        0.0,
        0.0
      ]
    },
    {
      "expected_decision": {
        "kind": "select",
        "method": "bayesian",
        "option": 1
      },
      "expected_kernel_evaluations": 52,
      "expected_posterior": [
        0.00006442312301447224,
        0.9999233520609805,
        7.01890707459316e-6,
        2.6029544652312e-6,
        2.6029544652312e-6
      ],
      "interval_ms": 1000,
      "learned_offsets_ms": [
        1040.0,
        1060.0,
        1020.0,
        1080.0,
        1050.0,
        1030.0,
        1070.0,
        1045.0,
        1055.0,
        1065.0,
        1035.0,
        1050.0
      ],
      "name": "two presses overrule the strongest allowed prior",
      "onsets": [
        [
          0,
          0.0
        ],
        [
          1,
          1000.0
        ],
        [
          2,
          2000.0
        ],
        [
          3,
          3000.0
        ],
        [
          4,
          4000.0
        ],
        [
          0,
          5000.0
        ],
        [
          1,
          6000.0
        ],
        [
          2,
          7000.0
        ],
        [
          3,
          8000.0
        ],
        [
          4,
          9000.0
        ]
      ],
      "opted_in": true,
      "presses_ms": [
        2040.0,
        7040.0
      ],
      "priors": [
        1.0,
        0.0,
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "expected_decision": {
        "kind": "select",
        "method": "not_opted_in",
        "option": 2
      },
      "expected_kernel_evaluations": 0,
      "expected_posterior": null,
      "interval_ms": 1000,
      "learned_offsets_ms": [
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          0,
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          1,
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          2,
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          3,
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          4,
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      "expected_kernel_evaluations": 0,
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          0,
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          1,
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          2,
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          3,
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          4,
          4000.0
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      "interval_ms": 1000,
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        1055.0,
        1065.0,
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      "name": "a press before any highlight selects nothing",
      "onsets": [
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          0,
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          1,
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          2,
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          3,
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          4,
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      "presses_ms": [
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      "priors": [
        0.2,
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        0.2
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    {
      "expected_decision": {
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        "leader": 1
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      "expected_kernel_evaluations": 13,
      "expected_posterior": [
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      "interval_ms": 1000,
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        1040.0,
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        1055.0,
        1065.0,
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      "name": "an onset more than two intervals away explains nothing",
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      "presses_ms": [
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    {
      "expected_decision": {
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        "method": "bayesian",
        "option": 0
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      "expected_kernel_evaluations": 13,
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        1065.0,
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        1050.0
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      "name": "a lone option selects on a press it explains",
      "onsets": [
        [
          0,
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      ],
      "opted_in": true,
      "presses_ms": [
        1050.0
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    {
      "expected_decision": {
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      "expected_kernel_evaluations": 0,
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      "interval_ms": 1000,
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        1070.0,
        1045.0,
        1055.0,
        1065.0,
        1035.0,
        1050.0
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      "opted_in": true,
      "presses_ms": [
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  "spec": "SPEC.md §3, §5.1, §5.4 (proposed, after 0.2.0)",
  "standard": "aac",
  "vector": "adaptive",
  "version": "0.3.0-draft"
}