RESEARCH

M4 Test Analysis

Complete breakdown of what's proven and what's not

3
Tests Passed
2
Tests Failed
5
Total Tests
✓ Test 1: Balance Law Validation PASSED
1000
Iterations
0
Failures
1.42e-14
Max Deviation

The Balance Law (τ₁ + τ₂ + τ₃ + τ₄ = 0) was tested with 1000 random input values. In every single case, the sum of torsions was essentially zero - the maximum deviation was 1.42e-14, which is floating-point precision noise, not actual imbalance.

Implication

The Balance Law is a validated geometric principle. This is mathematical fact, not speculation.

✓ Test 2: Transform Sum Identity PASSED
100
Iterations
0
Failures

T₁ + T₂ + T₃ + T₄ = (0, 0) always holds. The four transforms (facing, mirror, recursive, inverted) positioned at the diagonal nodes of the dipyramid sum to zero.

Implication

This is geometric necessity, not assumption. The transform identity is proven.

✗ Test 3: Energy Decay FAILED
4.85%
Expected
3.64%
Actual Average
25%
Deviation

The energy decay in the simulator doesn't exactly match (59/60)^180. After 180 steps, we expected 4.85% energy remaining but measured 3.64% on average.

Implication

This is likely an implementation issue, not a fundamental flaw. The transform operations may be compounding differently than expected. Needs refinement.

✗ Test 4: Resolution vs Iteration CRITICAL - NOT PROVEN
50
Problems Tested
0%
Zero-Step Resolutions
138.1
Avg Steps Needed
180
Max Steps

This is the critical test. The claim was that the geometry allows "resolution without iteration" - finding solutions in one step. Our tests show 0% zero-step resolutions. Problems still need to step through the tetrahelix to find clean solutions, averaging 138.1 steps.

Core Hypothesis Unproven

The claim that "the geometry resolves without iteration" is NOT demonstrated in this implementation. This doesn't mean it's wrong - it may mean the resolution algorithm needs redesign.

✓ Test 5: Base-60 vs Base-10 PASSED (No Advantage)
1.2e-16
Avg Difference
12
Values Tested

Base-60 and base-10 produce mathematically identical results. The average difference is 1.2e-16 - essentially zero (floating-point noise). The choice of base is computational convenience, not fundamental difference.

Implication

This debunks the claim that base-60 is computationally special. There's no "magic" in base-60 vs base-10.

Honest Assessment

✓ What IS Validated

  • ✓
    Balance Law works - The four torsions sum to zero. This is mathematical fact.
  • ✓
    Transform identity works - T₁+T₂+T₃+T₄ = (0,0). Geometric fact.
  • ✓
    The geometry is self-consistent - No contradictions found.

✗ What is NOT Validated

  • ✗
    "Resolution without iteration" - Still requires iteration. No advantage over conventional approaches demonstrated.
  • ✗
    "One move is checkmate" - Not demonstrated. Problems still need many steps (avg 138).
  • ✗
    "Base-60 computational advantage" - Not demonstrated. Same results as base-10.
  • ✗
    "^32 information density" - Not testable in current implementation.

What Needs to Happen Next

Option 1: Refine the Model

The current implementation may not correctly capture the "resolution" concept. The crossroads reading logic may need redesign based on methodology documents.

Option 2: Accept Iterative Approach

Perhaps the geometry helps WITH iteration, not replaces it. The 4 transforms may reduce search space or guide convergence.

Option 3: Identify Problem Class

The geometry may work for specific problem types we haven't tested - constraint satisfaction where τ₁+τ₂+τ₃+τ₄=0 IS the solution.

Recommendation for M4 Hardware

Before investing $12,600 in Mac hardware: The simulator should demonstrate SOME advantage first. "Resolution without iteration" is not proven. Continue software simulation until we can demonstrate measurable advantage.

Test Date: January 1, 2026 | Timestamp: 22:20:34

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