[sharareh-y]

Summary

This PR changes SCORE_POWER in src/score.py from 0.5 (square root) to
1.0 (linear). SCORE_SPEEDUP_THRESHOLD stays at 1.05. The formula, the
zero-score rules (compile/correctness failure, invalid or non-comparable
speedup, speedup at or below the threshold) and the aggregation rules do not
change.

score = max(0, 1 - 1.05 / speedup) ** p        p: 0.5 -> 1.0

Speedup	Score, p = 0.5 (before)	Score, p = 1 (after)
<= 1.05x	0	0
1.1x	0.2132	0.0455
1.2x	0.3536	0.1250
1.5x	0.5477	0.3000
2x	0.6892	0.4750

Why

The figure plots score against task speedup (log scale, 1x to 1000x) at
t = 1.05 for p = 0.25, 0.5, 1, 2. All curves are zero up to 1.05x. The
p < 1 curves rise almost vertically just after the threshold and then flatten
early: under p = 0.5 a 2x kernel already gets 0.689. The p = 1 curve leaves
the threshold with a finite slope and keeps more room between 10x and 100x.

1. The square root has an infinite slope at the threshold

With t = SCORE_SPEEDUP_THRESHOLD and speedup x > t:

d score / d x = p * (1 - t/x)^(p-1) * t / x^2

For p < 1 the factor (1 - t/x)^(p-1) diverges as x -> t+, so the slope is
infinite at the threshold. For p = 1 the slope is t / x^2, which is finite
(at most 1 / t ~ 0.95 per unit of speedup at the threshold). So under
p = 0.5, a kernel just above 1.05x gets a score that swings strongly with
ordinary timing noise; under p = 1 it does not.

Monte Carlo with lognormal noise on the measured speedup (50,000 draws per
point, t = 1.05), peak score standard deviation:

Noise on speedup	p = 0.5	p = 1
2%	0.074 (at 1.06x)	0.019 (at 1.10x)
5%	0.116 (at 1.08x)	0.044 (at 1.16x)

On a real 32-task hip2hip run (all correct), one task sat 0.2% above the
threshold (1.0517x). Under p = 0.5 that single task carried 59% of the
run's sensitivity to small speedup changes (its share of d(mean score)/d ln x).
Under p = 1 it carries 10%.

2. The square root saturates early

p	2x	10x	100x
0.5 (before)	0.689	0.946	0.995
1 (after)	0.475	0.895	0.990

Under p = 0.5, going from 10x to 100x adds 0.049. Under p = 1 it adds
0.095, about twice the headroom, so large wins remain distinguishable.

3. The linear score has a plain meaning

With p = 1, score = 1 - candidate_time / (baseline_time / 1.05): the
fraction of runtime saved beyond the threshold. Over a set of tasks that all
score above zero, the mean score is 1 - 1.05 / H, where H is the
harmonic-mean speedup of those tasks.

Trade-off

Modest wins earn less. A 1.5x kernel goes from 0.548 to 0.300, and a 1.1x
kernel from 0.213 to 0.045. If the project wants to reward breadth of small
wins strongly, p = 0.5 does that, but at the cost of the near-threshold
noise described above.

Changes

• src/score.py: SCORE_POWER = 1.0; docstring describes the linear default.
• README.md ("Reward and Scoring Signals"): p = 1 (linear), recomputed
  example table (1.1x 0.0455, 1.2x 0.1250, 2x 0.4750), and a description of the
  linear score and its mean.
• docs/reference/api-reference.md (Scoring): default curve, constants table
  (SCORE_POWER default 1.0), slope note, and the 1.25x worked example
  (default 0.16; 0.4 with p = 0.5).
• tests/test_score.py: new test pinning the defaults (power 1.0, threshold
  1.05); default-curve test now checks linear values at 1.0x, 1.05x, 1.1x, 1.2x,
  1.25x and 2x; configurable-power test covers 0.5, 1.0 and 2.0; the
  task_result_scoring 1.5x case expects 0.3.
• tests/test_task_run_v2.py, tests/test_candidate_verification.py,
  tests/test_held_out_v2.py: synthetic 2x fixtures expect 0.475 (was 0.6892).
• tests/test_postprocessing_outcomes_v2.py: the 1.1x reporting fixture
  expects 1/22 (0.0455 in four-decimal reports; was 0.2132).
• tests/test_score.py (threshold test): with the threshold set to 1.2, a 1.25x
  speedup expects 0.04 (was sqrt(0.04) = 0.2).
• docs/reference/release-notes.md: "Unreleased" entry for the curve change.

Testing

CPU-only tests, run on an MI355X node (no GPU validation is claimed):

python3 -m pytest -q tests/test_score.py tests/test_task_run_v2.py tests/test_candidate_verification.py tests/test_held_out_v2.py tests/test_postprocessing_outcomes_v2.py tests/test_held_out.py tests/test_task_boundary_failures_v2.py

Result: 139 passed.