Fix #95: Add BinPacking model

.gitignore

@@ -84,3 +84,4 @@ claude-output.log
 .worktrees/
 .worktree/
 *.json
+.claude/worktrees/

Makefile

@@ -189,12 +189,13 @@ PLAN_FILE ?= $(shell ls -t docs/plans/*.md 2>/dev/null | head -1)
 run-plan:
 	@NL=$$'\n'; \
 	BRANCH=$$(git branch --show-current); \
+	PLAN_FILE="$(PLAN_FILE)"; \
 	if [ "$(AGENT_TYPE)" = "claude" ]; then \
-		PROCESS="1. Read the plan file$${NL}2. Use /subagent-driven-development to execute tasks$${NL}3. Push: git push origin $$BRANCH$${NL}4. Create a pull request"; \
+		PROCESS="1. Read the plan file$${NL}2. Choose the right skill to execute: use /add-model for new problem models, /add-rule for new reduction rules, or /subagent-driven-development for other tasks$${NL}3. Push: git push origin $$BRANCH$${NL}4. Create a pull request"; \
 	else \
 		PROCESS="1. Read the plan file$${NL}2. Execute the tasks step by step. For each task, implement and test before moving on.$${NL}3. Push: git push origin $$BRANCH$${NL}4. Create a pull request"; \
 	fi; \
-	PROMPT="Execute the plan in '$${PLAN_FILE}'."; \
+	PROMPT="Execute the plan in '$$PLAN_FILE'."; \
 	if [ -n "$(INSTRUCTIONS)" ]; then \
 		PROMPT="$${PROMPT}$${NL}$${NL}## Additional Instructions$${NL}$(INSTRUCTIONS)"; \
 	fi; \

docs/paper/reductions.typ

@@ -49,6 +49,7 @@
   "BMF": [Boolean Matrix Factorization],
   "PaintShop": [Paint Shop],
   "BicliqueCover": [Biclique Cover],
+  "BinPacking": [Bin Packing],
 )
 
 // Definition label: "def:<ProblemName>" — each definition block must have a matching label
@@ -801,6 +802,46 @@ Biclique Cover is equivalent to factoring the biadjacency matrix $M$ of the bipa
 ) <fig:biclique-cover>
 ]
 
+#problem-def("BinPacking")[
+  Given $n$ items with sizes $s_1, dots, s_n in RR^+$ and bin capacity $C > 0$, find an assignment $x: {1, dots, n} -> NN$ minimizing $|{x(i) : i = 1, dots, n}|$ (the number of distinct bins used) subject to $forall j: sum_(i: x(i) = j) s_i lt.eq C$.
+][
+  Bin Packing is one of the classical NP-hard optimization problems @garey1979, with applications in logistics, cutting stock, and cloud resource allocation. The best known exact algorithm runs in $O^*(2^n)$ time via inclusion-exclusion over set partitions @bjorklund2009.
+
+  *Example.* Consider $n = 6$ items with sizes $(6, 6, 5, 5, 4, 4)$ and capacity $C = 10$. The lower bound is $ceil(30 slash 10) = 3$ bins. An optimal packing uses exactly 3 bins: $B_1 = {6, 4}$, $B_2 = {6, 4}$, $B_3 = {5, 5}$, each with total load $10 = C$.
+
+  #figure({
+    canvas(length: 1cm, {
+      let s = 0.28
+      let w = 1.0
+      let gap = 0.6
+      let bins = ((6, 4), (6, 4), (5, 5))
+      let fills = (
+        (graph-colors.at(0), graph-colors.at(1)),
+        (graph-colors.at(0), graph-colors.at(1)),
+        (graph-colors.at(2), graph-colors.at(2)),
+      )
+      for i in range(3) {
+        let x = i * (w + gap)
+        draw.rect((x, 0), (x + w, 10 * s), stroke: 0.8pt + black)
+        let y = 0
+        for j in range(bins.at(i).len()) {
+          let sz = bins.at(i).at(j)
+          let c = fills.at(i).at(j)
+          draw.rect((x, y), (x + w, y + sz * s), stroke: 0.4pt, fill: c)
+          draw.content((x + w / 2, y + sz * s / 2), text(8pt, fill: white)[#sz])
+          y += sz * s
+        }
+        draw.content((x + w / 2, -0.3), text(8pt)[$B_#(i + 1)$])
+      }
+      draw.line((-0.15, 10 * s), (2 * (w + gap) + w + 0.15, 10 * s),
+        stroke: (dash: "dashed", paint: luma(150), thickness: 0.5pt))
+      draw.content((-0.5, 10 * s), text(7pt)[$C$])
+    })
+  },
+  caption: [Optimal packing of items with sizes $(6, 6, 5, 5, 4, 4)$ into 3 bins of capacity $C = 10$. Numbers indicate item sizes; all bins are fully utilized.],
+  ) <fig:binpacking-example>
+]
+
 // Completeness check: warn about problem types in JSON but missing from paper
 #{
   let json-models = {

docs/src/reductions/problem_schemas.json

@@ -51,6 +51,22 @@
       }
     ]
   },
+  {
+    "name": "BinPacking",
+    "description": "Assign items to bins minimizing number of bins used, subject to capacity",
+    "fields": [
+      {
+        "name": "sizes",
+        "type_name": "Vec<W>",
+        "description": "Item sizes s_i for each item"
+      },
+      {
+        "name": "capacity",
+        "type_name": "W",
+        "description": "Bin capacity C"
+      }
+    ]
+  },
   {
     "name": "CircuitSAT",
     "description": "Find satisfying input to a boolean circuit",