docs: verify reduction #841 — NAESatisfiability → SetSplitting

[zazabap]

Summary

• Typst proof of NAESatisfiability → SetSplitting reduction with construction, correctness (⟹ + ⟸), solution extraction, overhead table, YES example (n=4), and NO example (n=3)
• Constructor verification script: 32,513 checks, 0 failures, all 7 mandatory sections, exhaustive n ≤ 5
• Adversary verification script: 46,774 checks, 0 failures, independent implementation with hypothesis property-based testing
• Cross-comparison: 615 instances compared, 0 disagreements, 0 feasibility mismatches

Verification Report

=== Verification Report: NAESatisfiability → SetSplitting (#841) ===

Typst proof: docs/paper/verify-reductions/naesat_setsplitting.typ
  - Construction: ✓ (3 steps)
  - Correctness: ✓ (⟹ + ⟸)
  - Extraction: ✓
  - Overhead: ✓ (universe_size = 2n, num_subsets = n + m)
  - YES example: ✓ (4 variables)
  - NO example: ✓ (3 variables, all 8 assignments shown to fail)

Constructor: verify_naesat_setsplitting.py
  - Checks: 32,513 passed, 0 failed
  - Sections: 1(sympy) 2(exhaustive) 3(extraction) 4(overhead) 5(structural) 6(YES) 7(NO)
  - Forward: exhaustive n ≤ 5
  - Backward: exhaustive n ≤ 5
  - Gap analysis: all claims covered

Adversary: adversary_naesat_setsplitting.py
  - Checks: 46,774 passed, 0 failed
  - Property-based: 3 hypothesis strategies, 500 examples each
  - Forward: exhaustive n ≤ 5
  - Backward: exhaustive n ≤ 5
  - Bugs found: none

Cross-comparison:
  - Instances compared: 615
  - Structural agreement: 615/615
  - Feasibility agreement: 615/615

Bugs found: none
Iterations: 1 round (first-pass clean)

Verdict: VERIFIED

Closes #841

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.03%. Comparing base (423506c) to head (168f6be).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #980   +/-   ##
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  Coverage   98.03%   98.03%           
=======================================
  Files         784      784           
  Lines       82310    82310           
=======================================
  Hits        80695    80695           
  Misses       1615     1615           

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