TEST 1 — Trajectory Collision Resistance (sequence “ABC” × 1000, n = 20)

1. Test objective

The purpose of this test is to verify whether the Maria System generates repeatable trajectories for repeated or limited input data. The test checks the system’s resistance to:

• trajectory collisions,
• repeated endings,
• statistical data correlations.

In classical cryptography, repeated input data often leads to detectable patterns. This test verifies whether such a phenomenon occurs in Maria System.

2. Test methodology

Test parameters:

• Input data: sequence ABC repeated to a total length of 1000 characters
• System: Maria System
• Encoding mode: phase trajectories
• Phase parameter: n = 20
• Output format: MS2 file
• Analysis: external statistical trajectory analyzer

3. Test results — raw data

{
  "lines": 1000,
  "unique_tokens": 1000,
  "duplicates": 0,
  "entropy_bits": 9.965784284662018,
  "min_entropy_bits": 9.965784284662087,
  "monobit_pvalue": 0.06671699590108496,
  "runs_pvalue": 0.30683407306796767,
  "gzip_ratio": 0.37629349481851676
}

4. Interpretation of individual results

Number of lines: 1000
This corresponds to the number of processed symbols. Each symbol was processed independently.

Unique trajectories: 1000
Each trajectory in the output set was unique. No repetitions were recorded.

Number of collisions (duplicates = 0)
No collisions were detected. The system did not generate two identical trajectories for different instances of the data.

Shannon entropy
The value 9.9657 bits confirms a very high level of data disorder and lack of predictability in the distribution.

Monobit test
p-value = 0.0667 is within the acceptable range. No significant bit imbalance was detected.

Runs test
p-value = 0.3068 indicates no sequential anomalies and correct transition randomness.

Compressibility (gzip_ratio)
The value 0.376 indicates low compressibility, which is a typical characteristic of high-entropy data.

5. Evaluation against cryptographic norms

In classical cryptographic systems, input data with low diversification causes entropy loss and increases the risk of collisions.

In Maria System, the following were not observed:

• collisions,
• repeated endings,
• visible statistical correlations.

The system remains stable even when processing input data with very low entropy (repeated ABC sequence).

6. Final conclusion

The test confirms very high resistance of the Maria System to collisions and lack of trajectory repetition.

The system generates unique trajectories even under deliberately impoverished input conditions, which constitutes strong evidence of its resistance to statistical analysis and data correlation attempts.