docs: verify reduction #973 — SubsetSum → Partition

[zazabap]

Summary

• Typst proof of SubsetSum → Partition reduction with 3-case construction (Σ=2T, Σ>2T, Σ<2T), bidirectional correctness proofs, solution extraction, overhead, YES example (n=5), NO example (n=3)
• Constructor verification: 47,233 checks, 0 failures, all 7 mandatory sections, exhaustive n ≤ 5
• Adversary verification: 236,283 checks, 0 failures, independent implementation with 4 hypothesis strategies
• Cross-comparison: 690 instances compared, 0 disagreements, 0 feasibility mismatches

Verification Report

=== Verification Report: SubsetSum → Partition (#973) ===

Typst proof: docs/paper/verify-reductions/subsetsum_partition.typ
  - Construction: ✓ (3 steps, 3 cases)
  - Correctness: ✓ (⟹ + ⟸ for each case + infeasible case)
  - Extraction: ✓ (same/opposite side from padding)
  - Overhead: ✓ (num_elements = n+1 worst case)
  - YES example: ✓ (5 elements, S={3,5,7,1,4}, T=8)
  - NO example: ✓ (3 elements, S={3,7,11}, T=5)

Constructor: verify_subsetsum_partition.py
  - Checks: 47,233 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_subsetsum_partition.py
  - Checks: 236,283 passed, 0 failed
  - Property-based: 4 hypothesis strategies, 3500 examples
  - Forward: exhaustive n ≤ 5
  - Backward: exhaustive n ≤ 5
  - Bugs found: none

Cross-comparison:
  - Instances compared: 690
  - Structural agreement: 690/690
  - Feasibility agreement: 690/690

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

Verdict: VERIFIED

Closes #973

🤖 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 (d4abdb9).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #981   +/-   ##
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  Coverage   98.03%   98.03%           
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  Files         784      784           
  Lines       82310    82310           
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  Hits        80695    80695           
  Misses       1615     1615           

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