Rewrite getting-started with Factoring→SpinGlass and path overhead API

[GiggleLiu]

Summary

• Rewrite getting-started.md Example 2 from ksat→MIS to Factoring→SpinGlass with jupyter notebook style (code input followed by text output)
• Add path_overheads() as single source of truth for per-edge overhead lookup; refactor compose_path_overhead() to build on it (DRY)
• Remove evaluate_path_overhead() in favor of symbolic per-edge polynomial checks in tests
• Add 7 rich paper examples recovered from stash (SAT→KColoring, SAT→DominatingSet, SAT→KSatisfiability, CircuitSAT→SpinGlass, Factoring→CircuitSAT, MaxCut→SpinGlass, SpinGlass→MaxCut)
• Fix rustdoc unresolved link to ProblemSize
• Add force-push prohibition to CLAUDE.md

Test plan

• make test passes (all 47 doctests + unit/integration tests)
• Example runs correctly: cargo run --features ilp --example chained_reduction_factoring_to_spinglass
• make doc builds mdBook with updated getting-started page
• Verify paper compiles with make paper

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 93.42105% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.13%. Comparing base (5be5149) to head (3313354).
⚠️ Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
src/rules/graph.rs	88.37%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #78      +/-   ##
==========================================
+ Coverage   96.10%   96.13%   +0.02%     
==========================================
  Files         193      193              
  Lines       26567    26585      +18     
==========================================
+ Hits        25532    25557      +25     
+ Misses       1035     1028       -7     

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[Copilot]

Pull request overview

This PR refactors the reduction graph overhead API and updates documentation with richer examples. The main changes include adding path_overheads() as a new API for per-edge overhead inspection, removing the old evaluate_path_overhead() function in favor of symbolic polynomial checks, and rewriting the getting-started guide's Example 2 to demonstrate the Factoring→SpinGlass reduction path.

Changes:

• Adds path_overheads() API returning per-edge overhead polynomials, refactors compose_path_overhead() to build on it (DRY principle)
• Replaces numeric overhead evaluation with symbolic polynomial checks in tests for better clarity
• Rewrites getting-started Example 2 from KSat→MIS to Factoring→SpinGlass with Jupyter-style code/output blocks
• Adds Display implementations for ReductionPath and ReductionStep with arrow notation (→)
• Fixes rustdoc link, corrects JSON field names (num_elements→universe_size), and adds 7 paper reduction examples

Reviewed changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
src/rules/graph.rs	Added path_overheads() for per-edge polynomials, refactored compose_path_overhead(), added Display impls for ReductionPath/Step
src/unit_tests/reduction_graph.rs	Replaced evaluate_path_overhead() numeric checks with symbolic polynomial assertions
src/traits.rs	Fixed rustdoc link to use full path crate::types::ProblemSize
src/rules/mod.rs	Minor formatting change (line wrapping)
examples/chained_reduction_factoring_to_spinglass.rs	Added anchors and overhead inspection code demonstrating path_overheads() and compose_path_overhead()
docs/src/getting-started.md	Rewrote Example 2 to use Factoring→SpinGlass path with step-by-step walkthrough
docs/src/reductions/reduction_graph.json	Corrected field names (num_elements→universe_size, added num_literals fields, fixed num_gates→num_variables+num_assignments)
docs/paper/reductions.typ	Added 7 paper examples with real test data (SAT→KColoring, SAT→DominatingSet, SAT→KSat, CircuitSAT→SpinGlass, Factoring→CircuitSAT, MaxCut→SpinGlass, SpinGlass→MaxCut)
.claude/CLAUDE.md	Added force-push prohibition guideline

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