Run gamma distribution experiment + add openrouter calibration script

Experiment 1+3 (Gamma distribution + structural ground truth):
- Pulled n=2000 active markets from gamma-api.polymarket.com (4 pages
  × 500, ~3.5s total)
- vol24hr P10/P50/P90 = $0 / $40 / $18,333
- Liquidity P10/P50/P90 = $787 / $10,138 / $221,690
- Spread P10/P50/P90 = 0.001 / 0.01 / 0.10 (present in raw Gamma —
  PR #4 spec was wrong to exclude this)
- 14-90d-to-resolution band = 693 markets (35%) — target range OK
- Derived 10,122 mutex pairs from 171 neg-risk groups → T4 $0 corpus
  validated

Implications:
- Q1 thresholds in PR #3 are way too high; data-driven values in report
- Q4 T4 corpus problem disappears (10k+ pairs from structure alone)
- PR #4 spec needs amendment for spread availability + dead-tier
  rephrasing (liquidity, not volume, as P10 boundary)

Raw NDJSON under data/experiments/ is gitignored; only script + report
committed.

Experiment 2 (OpenRouter calibration script, ~$0.001 total):
- One-shot validation that Gemini Flash V2 strict prompt actually
  produces schema-conforming JSON with verbatim grounding
- Requires OPENROUTER_API_KEY at runtime; not run yet
- Will calibrate the $0.00009/call estimate in PR #6

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: 张靖恒

reports/experiment-gamma-distribution-2026-05-12.md

@@ -0,0 +1,80 @@
+# Gamma 分布 + 结构化关系 实验报告（2026-05-12T06:16:23.751849+00:00）
+
+**来源**：`scripts/experiment_gamma_distribution.py` 一次性实验，不是 DS pkg #02 的最终实现。
+**用途**：回填 §9 Q1（长尾 tier 阈值）+ T4 $0 corpus 可行性验证 + T2 fixture 数据。
+
+---
+
+## 1. 基本统计
+
+- 拉取总市场数：2000
+- 通过过滤的活跃市场：2000
+  (active=true & enableOrderBook!=false & acceptingOrders!=false & closed!=true)
+
+## 2. 总体分布百分位（活跃市场）
+
+- **volume24hr**：P5=$0 | P10=$0 | P25=$0 | P50=$40 | P75=$1,483 | P90=$18,333 | P95=$46,489 | P99=$471,419
+- **volume1wk**：P5=$0 | P10=$0 | P25=$0 | P50=$379 | P75=$12,730 | P90=$185,724 | P95=$435,886 | P99=$1,485,768
+- **liquidity**：P5=$346 | P10=$787 | P25=$2,634 | P50=$10,138 | P75=$29,733 | P90=$221,690 | P95=$940,321 | P99=$6,003,525
+- **spread** (n=2000): P5=0.0010 | P10=0.0010 | P25=0.0010 | P50=0.0100 | P75=0.0300 | P90=0.1001 | P95=0.1900 | P99=0.7101
+
+## 3. 距 resolution 分布
+
+- `<7d`: 18 (0.9%)
+- `7-14d`: 16 (0.8%)
+- `14-30d`: 326 (16.3%)
+- `30-90d`: 367 (18.4%)
+- `90-180d`: 152 (7.6%)
+- `>180d`: 907 (45.4%)
+- `expired`: 54 (2.7%)
+- `unknown`: 160 (8.0%)
+
+## 4. Top 10 series（Gamma 无 first-class category，用 `events[0].series` 代理）
+
+- `untagged`: 1499 (75.0%)
+- `yearly-ipos`: 22 (1.1%)
+- `trump-countries-visited`: 18 (0.9%)
+- `trump-monthly-meeting`: 16 (0.8%)
+- `trump-trade-deal-countries`: 16 (0.8%)
+- `top-ai-company-style-on`: 15 (0.8%)
+- `best-ai-company`: 15 (0.8%)
+- `second-best-ai-company`: 15 (0.8%)
+- `largest-company`: 15 (0.8%)
+- `bitcoin-hit-price-monthly`: 15 (0.8%)
+
+## 5. Q1 数据驱动 tier 阈值候选
+
+**直接可填进 §9 Q1 Decision**：
+
+- `headline` tier (P90+): volume24hr ≥ $18,333, liquidity ≥ $221,690, spread ≤ 0.0010
+- `mid` tier (P50-P90):   volume24hr $40–$18,333, liquidity $10,138–$221,690, spread ≤ 0.0100
+- `longtail` tier (P10-P50): volume24hr $0–$40, liquidity $787–$10,138, spread ≤ 0.1001
+- `dead` tier (<P10):     volume24hr ≤ $0, liquidity < $787
+
+**注意**：因 P10 = $0，`longtail` 和 `dead` 的边界在 volume24hr 上重合（都从 0 起）。实务建议：用 **liquidity ≥ $791** 区分 longtail 和 dead；vol24hr=0 但 liquidity 在 $791-$10k 区间的市场是真长尾（做市商不来但有底子），vol24hr=0 且 liquidity<$791 才算 dead。
+
+**对比方案初稿**：
+
+| Tier | 方案初稿 | 数据驱动 (实测) | 差距 |
+|---|---|---|---|
+| headline (vol24h) | ≥ $50,000 | ≥ $18,333 | 初稿偏高 |
+| mid 下限 (vol24h) | ≥ $5,000  | ≥ $40 | 初稿偏高 |
+| longtail 下限 (vol24h) | ≥ $100  | ≥ $0 | 初稿偏高 |
+
+## 6. T4 $0 corpus 可行性验证
+
+- **Neg-risk 组数（≥2 市场）**：171
+- **派生 mutex pairs**：10122
+- **完全相同 question+endDate 组数**：1
+- **派生 equivalent pairs**：1
+
+✅ **T4 $0 corpus 可行**：mutex pairs (10122) ≥ 50 个，足够采样作 T4 judge 校准 ground truth。
+
+## 7. 数据质量警告
+
+- `unknown` 距 resolution 桶 = 160 个市场缺 endDate
+- 总数（2000）vs 活跃数（2000）差距 = 0 个被过滤掉
+
+---
+
+*Snapshot: 2026-05-12T06:16:23.751849+00:00, source: gamma-api.polymarket.com/markets*