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+---
+phase: 01
+plan: 01
+subsystem: admin
+tags: [lottery, missing-number, backend]
+dependency_graph:
+  requires: []
+  provides: [missingNum endpoint, getMissingNumbers model method, i18n keys]
+  affects: [application/admin/model/History.php, application/admin/controller/History.php, application/admin/lang/zh-cn/history.php]
+tech-stack:
+  added: []
+  patterns: [FastAdmin Backend controller, ThinkPHP 5.x Model, Db facade]
+key-files:
+  created:
+    - application/admin/model/History.php
+    - application/admin/controller/History.php
+    - application/admin/lang/zh-cn/history.php
+  modified: []
+decisions:
+  - Used $noNeedRight = ['missingNum'] instead of ['*'] for minimal permission bypass
+  - Model queries up to 500 historical records for true omission count calculation
+  - Color fallback uses '—' string when fa_num table has no mapping for a number
+metrics:
+  duration: ~5min
+  completed: "2026-04-21"
+---
+
+# Phase 01 Plan 01: Backend Missing Number Logic Summary
+
+Backend missing number calculation logic and AJAX endpoint — History model with `getMissingNumbers()` + `calcOmitCount()` methods, History controller with `missingNum()` endpoint, and i18n language keys for the missing number feature.
+
+## Tasks Completed
+
+| # | Task | Commit | Files |
+|---|------|--------|-------|
+| 1 | Add getMissingNumbers() and calcOmitCount() to History model | 6386a40 | application/admin/model/History.php |
+| 2 | Add missingNum() AJAX endpoint to History controller | 15bb870 | application/admin/controller/History.php |
+| 3 | Add i18n text keys to language file | 96d5e78 | application/admin/lang/zh-cn/history.php |
+
+## One-liner
+
+History model `getMissingNumbers()` computes missing lottery numbers (1-49) with true omission counts from up to 500 historical records, controller `missingNum()` validates periods (1-100) and returns JSON, i18n file provides Chinese translations.
+
+## Key Decisions
+
+- **$noNeedRight minimal scope**: Only `missingNum` method is exempted from permission checks (not `['*']`), following least-privilege principle.
+- **500-record limit for omission calculation**: Queries up to 500 historical records to calculate true omission counts (last appearance distance), not just "appeared/not appeared" in the query window.
+- **Color fallback**: Returns `'—'` when fa_num table lacks a wave color mapping for a given number.
+
+## Deviations from Plan
+
+None - plan executed exactly as written.
+
+## Known Stubs
+
+None.
+
+## Threat Flags
+
+None beyond what was identified in the plan's threat model (T-01-01 through T-01-04).
+
+## Self-Check
+
+- Model file exists with both methods: PASS
+- Controller file exists with missingNum endpoint: PASS
+- Lang file exists with all i18n keys: PASS
+- All 3 commits present in git log: PASS
+
+## Self-Check: PASSED