Fix #491: Add ExactCoverBy3Sets model (#603)

* Add plan for #491: ExactCoverBy3Sets model

* Implement #491: Add ExactCoverBy3Sets model

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* chore: remove plan file after implementation

* Fix Copilot review: validate distinct elements and sort triples in X3C

- Sort each triple on construction to enforce the "sorted triple" invariant
- Validate that each subset contains 3 distinct elements
- Add CLI validation before calling new() to avoid panics

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* docs: add ExactCoverBy3Sets to CLAUDE.md architecture section

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

* fix(x3c): close review gaps

* fix: remove duplicate display-name entries and add missing coverage test

Remove 3 duplicate display-name entries (OptimalLinearArrangement, RuralPostman,
LongestCommonSubsequence) introduced by merge conflict in reductions.typ. Add
missing should_panic test for duplicate-element validation in X3C constructor.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* docs: load X3C paper example from models.json, add load-model-example helper

Add load-model-example() Typst function (mirrors load-example() for rules)
that loads canonical model examples from generated models.json. Rewrite the
ExactCoverBy3Sets problem-def example to derive all concrete values from JSON
instead of hand-writing them.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* docs: migrate all paper examples to load from JSON, add CLI X3C example

- Migrate 28 problem-def example sections in reductions.typ to use
  load-model-example() instead of hand-written data. All concrete values
  now derived from models.json via Typst expressions.
- Add load-model-example() helper (mirrors load-example() for rules)
- Add concrete X3C example to CLI help text and docs/src/cli.md
- 10 problems without models.json entries remain hand-written:
  GraphPartitioning, OptimalLinearArrangement, BinPacking, Knapsack,
  RuralPostman, SubgraphIsomorphism, LongestCommonSubsequence, SubsetSum,
  MinimumFeedbackArcSet, FlowShopScheduling

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
Co-authored-by: GiggleLiu <cacate0129@gmail.com>

Author: 3 people

docs/paper/reductions.typ

@@ -274,6 +274,7 @@ pred create SpinGlass --graph 0-1,1-2 -o sg.json
 pred create MaxCut --graph 0-1,1-2,2-0 -o maxcut.json
 pred create Factoring --target 15 --bits-m 4 --bits-n 4 -o factoring.json
 pred create Factoring --target 21 --bits-m 3 --bits-n 3 -o factoring2.json
+pred create X3C --universe 9 --sets "0,1,2;0,2,4;3,4,5;3,5,7;6,7,8;1,4,6;2,5,8" -o x3c.json
 ```
 
 Canonical examples are useful when you want a known-good instance from the paper/example database.

docs/src/cli.md

@@ -89,6 +89,22 @@
       }
     ]
   },
+  {
+    "name": "ExactCoverBy3Sets",
+    "description": "Determine if a collection of 3-element subsets contains an exact cover",
+    "fields": [
+      {
+        "name": "universe_size",
+        "type_name": "usize",
+        "description": "Size of universe X (must be divisible by 3)"
+      },
+      {
+        "name": "subsets",
+        "type_name": "Vec<[usize; 3]>",
+        "description": "Collection C of 3-element subsets of X"
+      }
+    ]
+  },
   {
     "name": "Factoring",
     "description": "Factor a composite integer into two factors",