SCALE
规模轴Scale axis
参数、数据或算力沿横轴连续增长。Parameters, data, or compute grow continuously along the x-axis.
01 · 水温连续升，警报却只响一次01 · Temperature rises smoothly, but the alarm flips once
能力每天平滑提升一点，如果考试只记“过 60 分/没过”，成绩图会不会看起来像某天突然诞生了能力？Capability improves a little each day. If the test records only pass/fail at 60, can the chart make ability look as if it appeared overnight?
02切换连续损失与通过率，并拖阈值看“涌现点”移动Switch Continuous Loss and Pass Rate, Then Move the Apparent Emergence Point
同一底层曲线 · 可拖阈值same curve · draggable threshold
状态 AMetric A
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状态 BMetric B
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状态 CMetric C
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所有概率、得分与输出均为固定种子的教学模拟，不代表真实模型。拖回主变量即可复核结论。All probabilities, scores, and outputs are fixed-seed teaching simulations, not real model output. Move the main variable back to verify the conclusion.
03把刚才的变化拆成 4 个零件Break the Change into Four Parts
Emergent CapabilitiesCAPABILITY
底层能力Underlying capability
本页固定为一条平滑改善曲线。This lesson keeps one smooth improvement curve.
METRIC
测量方式Measurement
连续损失保留细节，通过率压成过/不过。Continuous loss preserves detail; pass rate bins it into pass/fail.
THRESHOLD
通过阈值Pass threshold
阈值改变看似突然出现的位置。The threshold moves where the apparent jump occurs.
04最小机制：主交互能逐项验证Minimal Mechanism: Verify Each Link in the Interaction
MECHANISM
pass(scale) = 1[capability(scale) ≥ threshold]
底层 capability(scale) 始终不变；只有显示方式和
threshold
改变，因此跳点移动可直接复核。The underlying capability(scale) never changes. Only display mode
and threshold move, making the shifting jump point directly
verifiable.
能力平滑变化Capability changes连续改进continuous improvement
指标离散化Metric bins it过 / 不过pass / fail
看似突然出现Jump appears需检查阈值敏感性test threshold sensitivity
05把阈值抬到 82，制造更晚更陡的“涌现”Raise the Threshold to 82 and Create a Later, Sharper Emergence
主动制造失败Create a failure边界实验Boundary experiment
底层曲线完全没变，只有阈值移动；如果结论也跟着大幅移动，现象就不能只归因于模型规模。The underlying curve is unchanged; only the threshold moves. If the conclusion moves with it, scale alone cannot explain the phenomenon.
尚未执行。先在主交互中观察正常机制。Not run yet. Observe the normal mechanism in the main interaction
first.
✗ 通过率跳变证明内部机制突然诞生。A pass-rate jump proves a mechanism appeared
suddenly.→ ✓ 先检查连续指标与阈值敏感性。First inspect continuous metrics and threshold
sensitivity.
✗ 所有涌现都是测量幻觉。All emergence is a measurement illusion.→ ✓ 离散化可能解释一部分现象，不足以否定全部机制变化。Discretization can explain some cases, not disprove every
mechanism change.
✗ 阈值是客观固定的，不影响结论。Thresholds are objective and never affect
conclusions.→ ✓ 任务阈值是设计选择，应做敏感性分析。Task thresholds are design choices and need sensitivity
analysis.
06 · 一句话带走06 · One line to keep