Statistical Rigor
Comprehensive documentation of statistical methodology, limitations, and proper interpretation of findings.
Statistical Rigor
Purpose
This section provides detailed documentation of the statistical methodology employed in this research, including explicit discussion of assumptions, limitations, and proper interpretation guidelines.
Confidence Tier System
All claims in this documentation are classified according to the following tier system:
Tier Definitions
| Tier | Label | Criteria | Example |
|---|---|---|---|
| Tier 1 | Verified | Directly computable, deterministic | 1221069728 % 121 = 43 |
| Tier 2 | Supported | Statistical test p < 0.01 | Chi-squared rejection of uniform distribution |
| Tier 3 | Plausible | Consistent with hypothesis, p < 0.05 | Code style pattern matching |
| Tier 4 | Speculative | Logical inference, not statistically tested | Common authorship claims |
Application Guidelines
- Tier 1 claims can be independently verified with a calculator
- Tier 2 claims require statistical computation but produce reproducible results
- Tier 3 claims involve interpretation and should be treated as suggestive
- Tier 4 claims are hypotheses for further investigation, not conclusions
Independence Assumptions
The Critical Caveat
Combined probability calculations rely on the assumption that individual findings are statistically independent and specified in advance. For the findings earlier versions combined, this assumption was not met.
Sources of Potential Correlation
| Finding Pair | Potential Correlation Source |
|---|---|
| Timestamp mod 121 ↔ Cluster gap | Both involve same blockchain |
| Matrix cell values ↔ 27-div sums | Both derived from Anna Matrix |
| Dead key positions ↔ Block heights | Dead keys are a subset of blocks |
Impact on Combined Probability
Earlier versions of this page gave combined p-values between 10⁻¹⁴ and 10⁻⁴. They are retired: the findings were not independent and were selected after looking at the data.
Multiple Testing Correction
The Problem
When testing many hypotheses, some will appear significant by chance alone. With 100 tests at α = 0.05, we expect ~5 false positives.
Corrections Applied
| Method | Formula | Application |
|---|---|---|
| Bonferroni | α_adjusted = α / n | Conservative, used for primary claims |
| Benjamini-Hochberg | FDR control | Used for exploratory analysis |
Adjusted Thresholds
For n = 20 primary tests at α = 0.05:
α_adjusted = 0.05 / 20 = 0.0025
Findings must achieve p < 0.0025 to be considered significant after correction.
Current Findings After Correction
Earlier versions listed four findings as significant after correction, among them the 27-divisible sum. That table is retired. The moduli and cells behind it were chosen after looking at the data, so no fixed number of tests existed to correct for.
Alternative Explanations
Null Hypothesis Alternatives
For each finding, we consider alternative explanations:
Finding: Timestamp mod 121 = 43
| Explanation | Probability Assessment |
|---|---|
| Random coincidence | 1/121 = 0.83% |
| Intentional design | Unknown prior |
| Post-hoc selection | If 121 was chosen because it worked, p increases |
Mitigating Factor: 121 = 11² has independent significance in Qubic architecture.
Finding: Dead Key Non-Uniform Distribution
| Explanation | Probability Assessment |
|---|---|
| Mining difficulty changes | Would not explain clustering |
| Hardware availability | Possible but doesn't match pattern |
| Intentional placement | Not supported; the original distribution test was not independently reproduced |
Selection Bias Considerations
| Potential Bias | Mitigation |
|---|---|
| Choosing "significant" moduli | Not mitigated: moduli such as 121, 43 and 27 were picked after looking at the data |
| Selecting favorable block ranges | Using complete early blockchain (0-50,000) |
| Cherry-picking matrix cells | Not mitigated: cell mappings were chosen after looking at the data |
Sample Size Considerations
Current Limitations
| Dataset | Sample Size | Statistical Power |
|---|---|---|
| Dead Key blocks | n = 53 | Moderate |
| Cluster gaps | n = 6 | Low |
| 27-divisible blocks | n = 4 | Very low |
Implications
- Small sample sizes increase uncertainty
- Effect sizes may be overestimated
- Results should be replicated with larger datasets where possible
Effect Size Analysis
Beyond P-Values
Statistical significance alone does not indicate practical importance. We also report effect sizes:
| Finding | Effect Size | Interpretation |
|---|---|---|
| Dead key clustering | Cramer's V = 0.49 (reported, not independently reproduced) | - |
| Timestamp alignment | Not applicable (exact match) | - |
| Matrix correlation | r = 0.23 | Small-medium effect |
Falsifiability
What Would Falsify the Design Hypothesis?
| Observation | Impact |
|---|---|
| Alternative explanation for mod 121 = 43 | Weakens Tier 1 finding |
| Dead keys follow mining difficulty curve | Explains non-uniformity naturally |
| Matrix values are randomly generated | Undermines correlation claims |
| No additional correlations in extended analysis | Suggests cherry-picking |
Pre-Registered Predictions
For future validation:
- Prediction 1 (not confirmed): Earlier versions predicted that March 12, 2026 would show mathematical significance (17.5 years from Pre-Genesis). The date passed without an event.
- Prediction 2: Additional hash bytes will correlate with matrix structures. Since the matrix is a hand-compiled table of bot replies to
x+y=?, there is no mechanism for such a correlation. - Prediction 3: Extended block analysis (50,000-100,000) will show continued patterns. Not tested.
Interpretation Guidelines
What the Evidence Supports
- Several arithmetic relations between Bitcoin values and numbers such as 121 or 43 are true as arithmetic
- After the September 2026 re-check, none of them is shown to be unlikely by chance, because the relations were selected after looking at the data
- The Anna Matrix itself is a hand-compiled table of bot replies, so correlations between it and Bitcoin data have no known mechanism
What the Evidence Does Not Prove
- Identity of any individual
- Causal relationship between projects
- Future behavior of any system
Recommended Citation Language
Accurate: "Some arithmetic relations hold, but they were found after looking at the data and are not evidence of design."
Avoid: "This proves that..." or "It is certain that..."
Peer Review Status
| Component | Status | Reviewer |
|---|---|---|
| Statistical calculations | Internal review | Complete |
| Methodology | Internal review | Complete |
| External peer review | Pending | Invited |
Conclusion
This page sets out the statistical standards we aim for. Measured against them, the Bitcoin-matrix findings of earlier versions do not support intentional design. Readers should:
- Evaluate individual findings independently
- Consider alternative explanations
- Await external peer review
- Apply appropriate skepticism to combined probability claims
The goal of this documentation is transparent presentation of evidence for independent evaluation, not advocacy for a predetermined conclusion.