diff --git a/README.md b/README.md
index 04de02c42..8c2cb4ca4 100755
--- a/README.md
+++ b/README.md
@@ -364,7 +364,7 @@ tasks:
 
 Every normal optimization task produces `task_result.yaml` with compilation and correctness status, baseline and optimized times, speedup, timing-method metadata, and the final score.
 
-The score uses the power family with **`p = 0.5`** (square root):
+The score uses the power family with **`p = 1`** (linear):
 
 ```text
 score = max(0, 1 - speedup_threshold / speedup_ratio) ** p
@@ -378,13 +378,17 @@ must be more than 5% faster to earn a positive score:
 | Speedup | Score |
 | --- | ---: |
 | At or below 1.05× | 0 |
-| 1.1× | 0.2132 |
-| 1.2× | 0.3536 |
-| 2× | 0.6892 |
-
-Scores are bounded between `0` and `1`. The concave curve gives modest qualifying
-improvements more credit than a linear curve. A zero score does not imply a
-correctness failure; compilation, correctness, and acceptance have separate fields.
+| 1.1× | 0.0455 |
+| 1.2× | 0.1250 |
+| 2× | 0.4750 |
+
+Scores are bounded between `0` and `1`. With the linear curve, the score is the
+fraction of runtime saved beyond the threshold, `1 - candidate_time /
+(baseline_time / 1.05)`, and its slope stays finite just above the cutoff, so
+timing noise moves near-threshold scores only slightly. Over a set of tasks that
+all score above zero, the mean score is `1 - 1.05 / H`, where `H` is their
+harmonic-mean speedup. A zero score does not imply a correctness failure;
+compilation, correctness, and acceptance have separate fields.
 
 To adjust the curve, edit `SCORE_POWER` in [`src/score.py`](src/score.py): `0.5`
 is concave, `1.0` is linear, and `2.0` is convex. Edit
diff --git a/docs/reference/api-reference.md b/docs/reference/api-reference.md
index 6dde3a946..b4bd3fa62 100644
--- a/docs/reference/api-reference.md
+++ b/docs/reference/api-reference.md
@@ -342,7 +342,7 @@ the ordinary correctness run.
 ## Scoring
 
 The existing `score` field uses a bounded power-family reward. The default is
-the concave square-root curve (`p = 0.5`) with a `1.05×` speedup cutoff:
+the linear curve (`p = 1`) with a `1.05×` speedup cutoff:
 
 ```text
 s = speedup_ratio
@@ -375,19 +375,23 @@ run-configuration section:
 
 | Constant | Default | Effect |
 | --- | ---: | --- |
-| `SCORE_POWER` | `0.5` | Exponent `p`: `0.5` is concave, `1.0` linear, `2.0` convex |
+| `SCORE_POWER` | `1.0` | Exponent `p`: `1.0` linear, `0.5` concave, `2.0` convex |
 | `SCORE_SPEEDUP_THRESHOLD` | `1.05` | Speedup at or below which the score is zero |
 
-Both constants must be finite and positive. `p = 0.5` raises scores for modest
-qualifying improvements; `p = 2.0` emphasizes large improvements. All choices
-preserve the ranking above the cutoff. Changing `p` does not provide a signal
+Both constants must be finite and positive. With the default `p = 1`, the score
+is the fraction of runtime saved beyond the threshold, and its slope
+`d score / d s = speedup_threshold / s**2` stays finite at the cutoff. Any
+`p < 1` has an unbounded slope as `s` approaches the cutoff from above, so
+scores of candidates just above `1.05×` swing with timing noise. `p = 0.5`
+raises scores for modest qualifying improvements; `p = 2.0` emphasizes large
+improvements. All choices preserve the ranking above the cutoff. Changing `p` does not provide a signal
 below the cutoff. Setting the threshold to `1.0` removes the 5% margin but still
 gives zero to baseline-equivalent and slower candidates.
 
 **Example**: For a correct candidate taking 80 microseconds against a
 100-microsecond baseline, `s = 1.25`. The default score is
-`sqrt(1 - 1.05 / 1.25) = 0.4`. The same measurement scores `0.16` with `p = 1`
-and `0.0256` with `p = 2`.
+`1 - 1.05 / 1.25 = 0.16`. The same measurement scores `0.4` with `p = 0.5`
+(`sqrt(0.16)`) and `0.0256` with `p = 2`.
 
 #### Result interpretation and historical reports
 
diff --git a/docs/reference/release-notes.md b/docs/reference/release-notes.md
index 84d3075d0..3963e6449 100644
--- a/docs/reference/release-notes.md
+++ b/docs/reference/release-notes.md
@@ -11,6 +11,12 @@ This topic summarizes the features available in each AgentKernelArena release. F
 
 ## Unreleased
 
+- Changed the default per-task score curve from square root to linear
+  (`SCORE_POWER` 0.5 → 1.0); the 1.05× threshold is unchanged. The linear
+  curve has a finite slope at the threshold, so scores just above it no longer
+  swing with timing noise. Positive scores decrease (for example, 2× now scores
+  0.475 instead of 0.689), so scores from earlier revisions are not directly
+  comparable. See [Scoring](api-reference.md#scoring).
 - Added the opt-in `deepseek_harness` agent with a pinned headless CLI,
   API-key authentication, isolated per-task sessions, and Docker/Slurm
   quickstarts. See the [integration guide](../../agents/deepseek_harness/README.md)
diff --git a/src/score.py b/src/score.py
index eedbdfb6f..053f9a215 100755
--- a/src/score.py
+++ b/src/score.py
@@ -5,7 +5,7 @@
 
 
 # Power-family scoring; see docs/reference/api-reference.md#scoring.
-SCORE_POWER = 0.5
+SCORE_POWER = 1.0
 SCORE_SPEEDUP_THRESHOLD = 1.05
 
 
@@ -56,8 +56,9 @@ def score(
     Calculate a bounded power-family score for a correct, comparable candidate.
 
     The score is ``max(0, 1 - SCORE_SPEEDUP_THRESHOLD / speedup) ** SCORE_POWER``.
-    Defaults use the concave square-root curve and require more than 1.05x
-    speedup for a positive score. Compilation/correctness failures and invalid
+    Defaults use the linear curve (power 1), which scores the fraction of
+    runtime saved beyond the threshold, and require more than 1.05x speedup
+    for a positive score. Compilation/correctness failures and invalid
     performance comparisons receive zero, with no partial-credit bonuses.
 
     Args:
diff --git a/tests/test_candidate_verification.py b/tests/test_candidate_verification.py
index 90b0b2847..f6f596318 100644
--- a/tests/test_candidate_verification.py
+++ b/tests/test_candidate_verification.py
@@ -139,7 +139,7 @@ def test_review_gate_controls_final_acceptance_and_exports(tmp_path, monkeypatch
     assert saved['candidate_accepted'] is accepted
     assert bool(saved['exports']) is accepted
     assert saved['speedup_ratio'] == (2 if accepted else 0)
-    assert saved['score'] == (pytest.approx(0.689202437604511) if accepted else 0)
+    assert saved['score'] == (pytest.approx(0.475) if accepted else 0)
 
 
 def test_backend_uses_read_only_tools_and_never_exposes_shell(monkeypatch, tmp_path):
diff --git a/tests/test_held_out_v2.py b/tests/test_held_out_v2.py
index a77109467..eb480318b 100644
--- a/tests/test_held_out_v2.py
+++ b/tests/test_held_out_v2.py
@@ -69,7 +69,7 @@ def test_uses_saved_baseline_and_shared_actions_instead_of_current_task_checkout
     result = evaluate(workspace, task_dir)
     assert result["generalization_status"] == "both_pass", result
     assert result["speedup_ratio"] == 2.0
-    assert result["score"] == pytest.approx(0.689202437604511)
+    assert result["score"] == pytest.approx(0.475)
     orig = tmp_path / "heldout" / "orig" / "kernel.py"
     assert "return 3" in orig.read_text()
     assert "return 1 + 2" in (workspace / "kernel.py").read_text()
diff --git a/tests/test_postprocessing_outcomes_v2.py b/tests/test_postprocessing_outcomes_v2.py
index e73b783a4..4e43462c0 100644
--- a/tests/test_postprocessing_outcomes_v2.py
+++ b/tests/test_postprocessing_outcomes_v2.py
@@ -15,7 +15,7 @@ def test_final_outcomes_survive_all_report_formats_without_changing_scores(
     tmp_path, monkeypatch, recover_from_text,
 ):
     # A positive score exercises the four-decimal report and dashboard formats.
-    speedup, expected_score = 1.1, 0.21320071635561044
+    speedup, expected_score = 1.1, 1 / 22  # 1 - 1.05/1.1, reported as 0.0455
     run = tmp_path / "workspace_MI355X_codex" / "run_20260916_120000"
     # Legacy results have numerical evidence, but no evidence of final acceptance.
     fixtures = [
diff --git a/tests/test_score.py b/tests/test_score.py
index 340b31465..87b72fdf9 100644
--- a/tests/test_score.py
+++ b/tests/test_score.py
@@ -3,6 +3,7 @@
 import pytest
 import yaml
 
+import src.score as score_module
 from src.score import resolve_speedup_ratio, score, task_result_scoring
 
 
@@ -67,10 +68,16 @@ def test_explicit_speedup_without_method_metadata_gets_no_performance_points():
     ) == 0.0
 
 
+def test_default_scoring_constants_are_linear_with_5_percent_cutoff():
+    assert score_module.SCORE_POWER == 1.0
+    assert score_module.SCORE_SPEEDUP_THRESHOLD == 1.05
+
+
 @pytest.mark.parametrize("speedup,expected", [
-    (1.0, 0.0), (1.05, 0.0), (1.25, 0.4), (2.0, 0.689202437604511),
+    (1.0, 0.0), (1.05, 0.0), (1.1, 1 / 22), (1.2, 0.125), (1.25, 0.16), (2.0, 0.475),
 ])
-def test_default_square_root_score(speedup, expected):
+def test_default_linear_score(speedup, expected):
+    # 1 - 1.05/1.1 = 1/22 ~ 0.0455; 1 - 1.05/1.2 = 0.125; 1 - 1.05/2 = 0.475.
     assert score(True, True, 100.0, 100.0 / speedup, speedup, True) == pytest.approx(expected)
 
 
@@ -89,7 +96,7 @@ def test_score_requires_boolean_method_consistency(consistent):
     assert score(True, True, 100.0, 50.0, 2.0, consistent) == 0.0
 
 
-@pytest.mark.parametrize("power,expected", [(1.0, 0.16), (2.0, 0.0256)])
+@pytest.mark.parametrize("power,expected", [(0.5, 0.4), (1.0, 0.16), (2.0, 0.0256)])
 def test_power_constant_selects_curve(monkeypatch, power, expected):
     monkeypatch.setattr("src.score.SCORE_POWER", power)
     assert score(True, True, 100.0, 80.0, 1.25, True) == pytest.approx(expected)
@@ -99,7 +106,7 @@ def test_speedup_threshold_constant_changes_cutoff(monkeypatch):
     monkeypatch.setattr("src.score.SCORE_SPEEDUP_THRESHOLD", 1.2)
     assert score(True, True, 100.0, 90.0, 1.1, True) == 0.0
     assert score(True, True, 100.0, 100.0 / 1.2, 1.2, True) == 0.0
-    assert score(True, True, 100.0, 80.0, 1.25, True) == pytest.approx(0.2)
+    assert score(True, True, 100.0, 80.0, 1.25, True) == pytest.approx(0.04)
 
 
 @pytest.mark.parametrize("name", ["SCORE_POWER", "SCORE_SPEEDUP_THRESHOLD"])
@@ -132,5 +139,5 @@ def test_task_result_scores_explicit_mean_speedup_and_preserves_measurements(tmp
 
     calculated = task_result_scoring(str(tmp_path))
 
-    assert calculated == pytest.approx(0.5477225575051661)
+    assert calculated == pytest.approx(0.3)
     assert yaml.safe_load(result_file.read_text()) == {**result, "score": calculated}
diff --git a/tests/test_task_run_v2.py b/tests/test_task_run_v2.py
index 35275dc03..e3184cdd9 100644
--- a/tests/test_task_run_v2.py
+++ b/tests/test_task_run_v2.py
@@ -84,7 +84,7 @@ def observe(self, action, *args, **kwargs):
     assert report["candidate_accepted"] is not blocked
     assert ("performance" in actions) is not blocked
     assert report["speedup_ratio"] == (0 if blocked else 2)
-    assert report["score"] == (0 if blocked else pytest.approx(0.689202437604511))
+    assert report["score"] == (0 if blocked else pytest.approx(0.475))
     assert report["benchmark_method_consistent"] is not blocked
     if blocked:
         assert "Process sweep" in report["speedup_calculation_error_message"]
@@ -93,7 +93,7 @@ def observe(self, action, *args, **kwargs):
     summary = json.loads((workspace.parent / "reports/task_type_breakdown.json").read_text())["overall"]
     assert summary["valid_speedup_count"] == (0 if blocked else 1)
     assert summary["speedup_gt_1_count"] == (0 if blocked else 1)
-    assert read_report(workspace)["score"] == (0 if blocked else pytest.approx(0.689202437604511))
+    assert read_report(workspace)["score"] == (0 if blocked else pytest.approx(0.475))
 
 
 def test_complete_pipeline_keeps_baseline_and_evaluates_after_agent_error(tmp_path):