fix(skill+cli): correct pred direction in find-solver/find-problem, fix KColoring/KN serialization

find-solver Step 3 used `pred to` (incoming) when it should use `pred from`
(outgoing) to find solver-ready targets. find-problem Step 2 had the mirror
bug: `pred from` (outgoing) instead of `pred to` (incoming) for discovering
problems that reduce to the user's model.

Also fix KColoring/KN schema-driven creation: inject `num_colors` from --k
into JSON so the value round-trips correctly. Without this, KN instances
deserialized with num_colors=0, causing all solvers to return no solution.

Found via agentic skill tests with simulated expert users.

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

Author: GiggleLiu

.claude/skills/find-problem/SKILL.md

@@ -37,7 +37,7 @@ Step 4: Generate Solution Doc (docs/solutions/<name>.md)
 
 Bash tool results are hidden from the user in the Claude Code UI. **After every `pred` command, you MUST copy-paste the full stdout/stderr into your response as text.** The pattern for every command is:
 
-1. Announce the command and why: "Let me run `pred from MIS --hops 3` to discover all problems that can reduce to MIS:"
+1. Announce the command and why: "Let me run `pred to MIS --hops 3` to discover all problems that can reduce to MIS:"
 2. Run the command via the Bash tool
 3. Copy the COMPLETE output into your text response inside a fenced code block
 4. Then add your brief explanation
@@ -69,7 +69,7 @@ Never skip step 1 or 3.
 
 **Actions:**
 
-1. **Run `pred from <model> --hops 3`** to find all problems that can reduce to the user's model within 3 hops. Copy-paste the full output.
+1. **Run `pred to <model> --hops 3`** to find all problems that can reduce to the user's model within 3 hops (incoming direction). Copy-paste the full output.
 
 2. **For each discovered problem**, run:
    - `pred path <source> <model>` — get the cheapest witness-capable reduction path
@@ -181,6 +181,6 @@ pred solve bundle.json --solver ilp --timeout 60
 - **Compact formatting.** Write explanations as plain paragraphs. Do not use blockquote `>` syntax for explanations. Keep tight: command announcement, code block output, 1-3 sentence explanation.
 - **Conversational tone.** Guided consultation, not a lecture.
 - **Live execution.** Every `pred` command runs for real. No fake output.
-- **Graceful fallbacks.** If `pred from` returns no results, suggest trying with more hops or a different model. If `pred path` fails for a specific source, skip it and note it in the table.
+- **Graceful fallbacks.** If `pred to` returns no results (no incoming reductions), suggest trying with more hops or a different model. If `pred path` fails for a specific source, skip it and note it in the table.
 - **Help with complexity notation.** If the user gives informal complexity, show `pred show <model>` size fields and help them write a formal expression.
 - **Cap results at 10.** If discovery returns many problems, show top 10 by effective complexity and offer to show more.

.claude/skills/find-solver/SKILL.md

@@ -34,7 +34,7 @@ Adapt the flow: if the user provides a formal problem name, validate it with `pr
 ```
 Step 1: Clarify Problem (skip if user knows the formal name)
 Step 2: Match to Library Models (web search + pred list)
-Step 3: Explore Reduction Paths (auto-explore via pred to --hops 3)
+Step 3: Explore Reduction Paths (auto-explore via pred from --hops 3)
 Step 4: Recommend Solvers (web search + pred solve options)
 Step 5: Generate Solution Doc (docs/solutions/<name>.md)
 ```
@@ -110,7 +110,7 @@ Use `AskUserQuestion` for each question. Format options as **(a)**/**(b)**/**(c)
 
 **Actions:**
 
-1. **Run `pred to <model> --hops 3`** to find all problems reachable within 3 hops. Copy-paste the full output.
+1. **Run `pred from <model> --hops 3`** to find all problems reachable via outgoing reductions within 3 hops. Copy-paste the full output.
 
 2. **For each reachable problem**, gather info:
    - Run `pred path <model> <target>` to get the cheapest witness-capable reduction path and composed overhead
@@ -127,7 +127,7 @@ Use `AskUserQuestion` for each question. Format options as **(a)**/**(b)**/**(c)
 
 4. **Ask the user** using `AskUserQuestion`: "Which reduction path would you like to use? Pick a number."
 
-**If `--hops 3` returns more than 15 results:** present only the top 10 by overhead and mention the rest are available.
+**If `pred from --hops 3` returns more than 15 results:** present only the top 10 by overhead and mention the rest are available.
 
 **Proceed to Step 4 with the chosen path.**
 

problemreductions-cli/src/commands/create/schema_support.rs

@@ -178,6 +178,16 @@ pub(super) fn create_schema_driven(
         json_map.insert(field.name.clone(), value);
     }
 
+    // KColoring/KN stores the number of colors at runtime in `num_colors`.
+    // The schema only declares `graph`, so inject `num_colors` from --k for KN.
+    if canonical == "KColoring"
+        && resolved_variant.get("k").map(|s| s.as_str()) == Some("KN")
+    {
+        if let Some(k) = args.k {
+            json_map.insert("num_colors".to_string(), serde_json::json!(k));
+        }
+    }
+
     // Decision<P> types serialize as {inner: {graph, weights, ...}, bound} but schema
     // fields are flat (graph, weights, bound).  Restructure when the canonical name
     // indicates a Decision wrapper.