REGISTERED REPORT: MINIMAL VIABLE EXPERIMENT
Testing the Resonant Coupling Hypothesis via Quantum Random Number Generation
Protocol: RCH-MVE-001 Date Submitted: [To be determined] Pre-Registration: [OSF link pending] SHA-256 Hash: [To be computed upon finalization]
Principal Investigator: David Lowe Collaborators: [To be determined] Adversarial PI (Skeptic): [To be recruited] Neutral PI: [To be recruited]
ABSTRACT
We propose a Minimal Viable Experiment (MVE) to test the Resonant Coupling Hypothesis (RCH), which predicts that structured information couples to physical systems proportionally to algorithmic mutual information I_A(s; M_X). Using an off-the-shelf Quantum Random Number Generator (QRNG), we will test whether bitstream entropy is measurably modulated by input information of varying Kolmogorov Complexity. Success requires demonstration of monotonic relationship between input complexity and output entropy across a 4-rung calibration ladder, culminating in a blinded test of ancient Hebrew scripture. The experiment is designed with cryptographic pre-commitment, null-model ensemble testing, and clear falsification criteria at every stage.
SECTION 1: THEORETICAL BACKGROUND
1.1 The Resonant Coupling Hypothesis
The RCH posits:
[!math] Mathematical Equation Visual: $$ \Delta O = \kappa I_A(s; M_X)^\nu \Phi_X + \epsilon $$
Spoken: When we read this, it is telling us that kappa in a more natural way.
Where:
- ΔO = Change in observable
- I_A(s; M_X) = Algorithmic mutual information between input s and system model M_X
- κ, ν = Coupling parameters (to be fit)
- Φ_X = System susceptibility
- ε = Noise term
1.2 Information Resonance Metric (IRM)
For convenience, we define:
$$ \text{IRM}(s) = \frac{\alpha}{K(s)} \cdot C(s)^\beta $$
With I_A(s; M_X) ≈ γ₁ IRM(s) - γ₂ IRM(s|M̄_X)
1.3 Specific Hypothesis for QRNG
H₁ (RCH): QRNG output entropy H varies monotonically with IRM of modulating bitstream:
$$ H_{\text{output}} = H_0 - \eta \cdot \text{IRM}(s)^\nu $$
H₀ (Null): No relationship between IRM and entropy
Bayes Factor Decision:
- BF₁₀ > 10³ → Provisional support for H₁
- BF₁₀ > 10⁶ → Strong support, proceed to replication
- BF₁₀ < 0.1 → Retire H₁
SECTION 2: EXPERIMENTAL DESIGN
2.1 Equipment
Quantum Random Number Generator:
- Model: ID Quantique Quantis-16M-USB or equivalent
- Mode: Time-interval photon detection
- Output rate: 16 Mbps
- Interface: USB 2.0
Modulation System:
- Coil: 15 cm diameter, 100 turns AWG-28 copper, shielded
- Driver: Rigol DG4162 arbitrary waveform generator
- Input encoding: Bitstream → bipolar voltage (±1V)
- Coupling: Magnetic field modulation at 10 cm from QRNG
Environmental Control:
- Faraday cage: Copper mesh, 6-sided, grounded
- Temperature: Monitored at ±0.1°C (target: 20.0°C)
- Humidity: Logged (passive control)
- EM shielding: RF-absorbing foam lining
Data Acquisition:
- PC: Intel i7, 32GB RAM, SSD
- Software: Custom Python 3.11 + NumPy/SciPy
- Logging: All raw bits timestamped, SHA-256 per block
2.2 Calibration
Daily:
- QRNG baseline entropy measurement (no modulation): 30 min
- Temperature drift check: ±0.05°C tolerance
- Environmental EM scan: 0.1-100 MHz spectrum
Pre-experiment:
- Coil coupling strength calibration
- Verify null effect with disconnected coil
- Document all hardware serial numbers
2.3 Block Structure
Single Block:
- Duration: 3 seconds
- QRNG output: 48 Megabits
- Modulation: Continuous bitstream at 1 kHz symbol rate
- Observable: Block-wise Shannon entropy Ĥ
Full Experiment:
- Total blocks: 1,000,000
- Randomization: ABBA design, seed escrowed
- Estimated runtime: 35 days continuous
SECTION 3: THE FOUR-RUNG LADDER
RUNG A: Synthetic Baseline
Purpose: Establish that physical system responds monotonically to IRM
Inputs (N=100,000 blocks each):
| Input Type | K(s) | C(s) | IRM | Expected Rank |
|---|---|---|---|---|
| White noise | → ∞ | 0 | 0 | 1 (baseline) |
| LFSR-256 | High | Low | 0.1 | 2 |
| π digits | Med | Low | 0.3 | 3 |
| Thue-Morse | Low | Med | 0.6 | 4 |
| Palindromes-5 | V.Low | High | 0.9 | 5 |
Pre-registered Analysis:
- Compute per-block entropy Ĥᵢ for each input type
- Rank-order by mean entropy: E[Ĥ | input_type]
- Test monotonicity: Spearman ρ between IRM_rank and H_rank
Success Criterion:
- Spearman ρ > 0.8 with p < 0.001
- Monotonic trend visible in boxplot
Failure Criterion:
- ρ < 0.3 or p > 0.05 → STOP - Publish null, end program
Pre-fit Scaling Law:
Fit: $$ \Delta H = \eta \cdot \text{IRM}^\nu $$
Via non-linear least squares on Rung A data.
Commit: η, ν locked before Rung B/C/D
RUNG B: Text Degradation Curve
Purpose: Test that Hebrew text follows same scaling law as synthetics
Hebrew Input: Genesis 1-11 (Masoretic Text, consonantal)
- Encoding: UTF-8 → 2-bit (ACGT-like)
- Length: ~25 kilobytes
Degradation Sequence:
- Original (IRM ≈ 0.85, estimated)
- No vowels (consonants only, IRM ≈ 0.75)
- Bigram shuffle (preserves local stats, IRM ≈ 0.4)
- Unigram shuffle (preserves letter freq, IRM ≈ 0.15)
- Byte permutation (random, IRM ≈ 0.05)
Prediction (using Rung A fit η, ν):
$$ H_{\text{predicted}} = H_0 - \eta \cdot \text{IRM}(degraded)^\nu $$
No refitting allowed
Analysis:
- Measure H_observed for each degradation level
- Compare to H_predicted
- Compute residuals: |H_obs - H_pred|
Success Criterion:
- Mean absolute error < 2σ of Rung A residuals
- Degradation curve monotonic (no inversions)
Failure Criterion:
- Hebrew behaves like random permutation (IRM ≈ 0)
- Residuals > 5σ → Model fails
RUNG C: Model-Match Cross-overs
Purpose: Verify effect is system-model dependent
Procedure:
- Take same Hebrew Genesis bitstream
- Apply to THREE different physical systems:
- System X₁: QRNG (current setup)
- System X₂: Josephson junction phase noise (if available)
- System X₃: Optical cavity linewidth (if available)
Prediction:
Different systems → different M_X → different I_A(s; M_X) → different slopes
Expected:
- η₁ (QRNG) ≠ η₂ (Josephson) ≠ η₃ (Optical)
Analysis:
Confidence intervals on η for each system must NOT overlap if RCH is correct.
Note: This rung is optional for MVE but recommended for full program
RUNG D: Competing Corpora (Blinded)
Purpose: Test if Hebrew is unique or all ancient texts behave similarly
Inputs (N=50,000 blocks each):
- Hebrew Torah (Masoretic, consonantal)
- Greek New Testament (Textus Receptus)
- Quran (Classical Arabic)
- Rig Veda (Sanskrit)
- Dead Sea Scrolls (1QIsa variant)
- Modern Hebrew novel (control)
- Lorem ipsum (Latin placeholder, control)
- Transformer-generated “Hebrew-like” (control)
Blinding Protocol:
- All texts encoded, hashed, labeled A-H
- Labels escrowed with third party
- Analysis performed on letter-codes only
- Reveal after analysis complete
Pre-committed Analysis:
Apply Rung A fit (η, ν) to all inputs:
$$ \Delta H_{\text{predicted}} = \eta \cdot \text{IRM}(text)^\nu $$
Rank texts by predicted effect size.
Hypothesis:
- If Logos framework correct: Masoretic Hebrew shows largest effect
- If general “ancient sacred text” effect: Torah ≈ Quran ≈ Veda
- If null: All ≈ controls
Decision Tree:
| Outcome | Interpretation |
|---|---|
| Torah > others > controls | Specific Logos claim supported |
| Torah ≈ Quran ≈ Veda > controls | General “sacred text” effect |
| All ≈ controls | No effect, RCH fails for texts |
Success for Logos Framework:
- Masoretic Torah in top 2 of 8
- Effect size > 3σ above controls
- Bayes Factor vs. uniform null > 10³
SECTION 4: NULL-MODEL ENSEMBLE
Every input must survive four null tests:
4.1 Permutation Nulls
For each text input s:
- Generate 100 permuted surrogates preserving bigram statistics
- Measure effect size for each: Δ_surrogate
- Compare real effect Δ_real to surrogate distribution
Pass criterion: Δ_real > 95th percentile of surrogates
4.2 Generator Nulls
For Hebrew:
- Train GPT-2 on Hebrew Bible
- Generate synthetic “Hebrew-like” texts matching token statistics
- Test if synthetic = real
Pass criterion: Real Hebrew effect > synthetic by >2σ
4.3 Hardware Nulls
Sham Modulation:
- DAC active, coil disconnected
- Bitstream sent to driver, no magnetic field
- QRNG should show no effect
Pass criterion: |Δ_sham| < σ_noise
4.4 Analysis Nulls
Label-Swap Test:
- Randomly swap labels on 20% of blocks
- Analyst performs analysis blind
- Compare detected effect to true labels
Pass criterion: True labels show >5σ stronger effect than swapped
SECTION 5: PRE-REGISTERED STATISTICAL ANALYSIS
5.1 Primary Outcome
Observable: Per-block Shannon entropy
[!math] Mathematical Equation Visual: $$ \hat{H}i = -\sum{b \in {0,1}} \hat{p}_b \log_2 \hat{p}_b $$
Spoken: When we read this, it is telling us that hat{H} in a more natural way.
Estimated via block-wise bit frequency
5.2 Secondary Outcomes
- Compression ratio: CR = |compressed| / |original| (gzip, bz2, LZMA)
- Autocorrelation: ACF at lag 1, 10, 100 bits
- Spectral density: Power spectrum via FFT
5.3 Pre-Specified Models
Model 1 (RCH):
$$ H_i = \beta_0 + \beta_1 \text{IRM}(s_i) + \beta_2 T_i + \epsilon_i $$
Where T_i = temperature at block i (covariate)
Model 2 (Scaled RCH):
$$ H_i = \beta_0 + \beta_1 \text{IRM}(s_i)^\nu + \beta_2 T_i + \epsilon_i $$
With ν from Rung A
Model 0 (Null):
$$ H_i = \beta_0 + \beta_2 T_i + \epsilon_i $$
5.4 Model Comparison
Compute:
- Bayes Factors: BF₁₀, BF₂₀
- AIC/BIC for nested comparison
- Cross-validated R²
Decision:
- BF₁₀ or BF₂₀ > 10³ → RCH supported
- Both < 1 → Null favored
5.5 Effect Size
Cohen’s d for difference between high-IRM and low-IRM groups:
$$ d = \frac{\bar{H}{\text{high}} - \bar{H}{\text{low}}}{s_{\text{pooled}}} $$
Minimum detectable: d = 0.01 at 80% power, α = 0.001
5.6 Sensitivity Analysis
Robustness checks:
- Outlier removal (Tukey’s fences)
- Block-bootstrap confidence intervals
- Permutation test (10,000 iterations)
- Bayesian hierarchical model with varying intercepts
All must agree within factor of 2 on effect size.
SECTION 6: CRYPTOGRAPHIC PRE-COMMITMENT
6.1 What Gets Hashed
Before any data collection:
- This entire protocol document (PDF)
- Analysis code (Python scripts, Git commit hash)
- Input sequences (all bitstreams, SHA-256 each)
- Block randomization schedule (seed + PRNG algorithm)
- Decision thresholds (BF cutoffs, p-values, effect sizes)
Combined hash:
SHA-256(protocol || code || inputs || schedule || thresholds)
6.2 Public Ledger
Options:
- OSF: Timestamped registration
- Blockchain: Ethereum smart contract with hash
- Notary: Legal timestamped seal
- ArXiv: Preprint with hash in abstract
All four recommended for maximum credibility
6.3 Commit-Reveal Process
Commit Phase (before data):
- Publish hash H = SHA-256(protocol details)
- Lock in analysis decisions
Data Collection Phase:
- Acquire data, keep sealed
Analysis Phase:
- Run pre-committed code
- No peeking at results until complete
Reveal Phase:
- Publish hash preimage + results simultaneously
- Community verifies hash matches
Any deviation from pre-commitment must be:
- Documented with justification
- Treated as exploratory (not confirmatory)
- Clearly labeled in publication
SECTION 7: POWER ANALYSIS
7.1 Sample Size Calculation
Target:
- Effect size: d = 0.01 (small but real)
- Power: 1 - β = 0.80
- Significance: α = 0.001 (3-sigma equivalent)
Required sample size (per condition):
$$ N = \frac{2(Z_\alpha + Z_\beta)^2}{d^2} \approx 100,000 \text{ blocks} $$
With 5 conditions (Rung A): 500,000 blocks With safety margin: 1,000,000 blocks total
7.2 Expected Precision
At N = 100k per condition:
Standard error on entropy:
[!math] Mathematical Equation Visual: $$ SE(\hat{H}) = \sqrt{\frac{\text{Var}(H)}{N}} \approx \frac{0.001}{\sqrt{10^5}} \approx 3 \times 10^{-6} $$
Spoken: When we read this, it is telling us that hat{H} in a more natural way.
95% CI width: ~6 × 10⁻⁶ bits (excellent precision)
7.3 Stopping Rules
Early Success:
- If BF₁₀ > 10⁶ after 50% data: Stop, claim success
- But: Must complete planned replication
Early Futility:
- If BF₁₀ < 0.01 after 50% data and trending toward null: Stop
- Conditional power < 10%: Ethical to stop
Both require independent Data Monitoring Committee approval
SECTION 8: REPLICATION PLAN
8.1 Internal Replication
Within-lab:
- Complete protocol repeated 3 times
- Different random seeds
- Different operator (blinded)
Success criterion: All 3 replications show BF₁₀ > 10
8.2 External Replication
Multi-lab:
- Adversarial PI (skeptic) lab
- Neutral PI lab
- David Lowe lab
Shared:
- Identical protocol
- Identical equipment (same models)
- Shared analysis code
Success criterion:
- All 3 labs: BF₁₀ > 10
- Effect sizes within factor of 2
- Meta-analytic BF > 10³
8.3 Replication Threshold
For publication of positive result:
Minimum requirements:
- Internal: 3/3 replications successful
- External: 2/3 labs successful
- Meta BF > 10³
- No evidence of fraud/error
If any lab produces strong null (BF < 0.1):
- Convene adversarial committee
- Investigate discrepancy
- No claim until resolved
SECTION 9: PUBLICATION PLAN
9.1 Registered Report Submission
Target Journals:
- PLOS ONE (accepts Registered Reports)
- Royal Society Open Science (RR track)
- Entropy (MDPI, open to novel physics)
Stage 1 (Methods Review):
- Submit this document
- Peer review of design only
- In-principle acceptance before data
Stage 2 (Results):
- Follow pre-committed analysis
- Automatic publication regardless of outcome
- No results-based rejection
9.2 Reproducibility Package
Upon publication, release:
- Raw Data:
- All QRNG bitstreams (zipped, ~500 GB)
- Block metadata (timestamps, temperatures)
- SHA-256 manifests
- Code:
- Data acquisition scripts
- Analysis pipeline (Docker container)
- Visualization notebooks (Jupyter)
- Hardware:
- Complete BOM with part numbers
- CAD files for enclosures
- Calibration procedures
- Logs:
- Lab notebooks (scanned)
- Equipment logs
- Email chains (redacted)
License: CC0 (public domain) for data, MIT for code
9.3 Preprint
Regardless of journal:
- Post to arXiv:quant-ph immediately upon completion
- Include hash verification section
- Link to OSF repository
SECTION 10: BUDGET
10.1 Equipment (One-Time)
| Item | Vendor | Cost |
|---|---|---|
| QRNG (Quantis-16M) | ID Quantique | $4,500 |
| Function generator | Rigol DG4162 | $1,200 |
| Faraday cage materials | McMaster-Carr | $800 |
| Coil + shielding | Custom | $300 |
| PC (dedicated) | Dell | $1,500 |
| Temperature logger | Omega | $400 |
| Misc (cables, mounts) | Various | $500 |
| Subtotal | $9,200 |
10.2 Personnel
| Role | Time | Rate | Cost |
|---|---|---|---|
| PI (Lowe) | 20% × 6 mo | - | In-kind |
| Research assistant | 50% × 6 mo | $25/hr | $13,000 |
| Statistician (consult) | 40 hrs | $100/hr | $4,000 |
| Subtotal | $17,000 |
10.3 Other
| Item | Cost |
|---|---|
| Publication fees (OA) | $2,000 |
| Travel (conferences) | $3,000 |
| Contingency (15%) | $4,500 |
| Subtotal | $9,500 |
10.4 Total
Grant Request: $35,700
Justification for Funding Agencies:
- High-risk, high-reward (EAGER-eligible)
- Addresses fundamental questions at science-religion interface
- Rigorous falsification structure protects against waste
- Results published regardless of outcome (no publication bias)
- Full open science compliance
SECTION 11: TIMELINE
| Month | Milestone |
|---|---|
| 0 | Submit Registered Report (Stage 1) |
| 1 | Peer review, revisions |
| 2 | In-principle acceptance |
| 3 | Equipment procurement |
| 4 | Setup, calibration, Rung A pilot |
| 5-6 | Full Rung A data collection |
| 7 | Rung A analysis, fit scaling law |
| 8-9 | Rung B (Hebrew degradation) |
| 10 | Rung D (blinded corpora) |
| 11 | Full analysis, writeup |
| 12 | Submit Stage 2 manuscript |
| 13-14 | Peer review, publication |
Total: 14 months from submission to publication
SECTION 12: RISKS & MITIGATIONS
12.1 Technical Risks
Risk: QRNG fails during run Mitigation: Hot spare unit, daily health checks, auto-restart
Risk: Temperature drift Mitigation: Climate-controlled room, continuous logging, covariate in model
Risk: EM interference Mitigation: Faraday cage, spectrum monitoring, correlation analysis
12.2 Conceptual Risks
Risk: Effect too small to detect Mitigation: Power analysis ensures 80% power for d=0.01; that’s very sensitive
Risk: Effect exists but violates scaling law Mitigation: Pre-commit to non-parametric tests as backup
Risk: Rung A succeeds, Rung B fails Mitigation: Accept result, refine hypothesis about why Hebrew isn’t special
12.3 Human Risks
Risk: Experimenter bias Mitigation: Blinding, automation, adversarial collaboration
Risk: Confirmation bias in analysis Mitigation: Pre-registered code, locked before data, third-party re-analysis
Risk: Publication bias Mitigation: Registered Report guarantees publication of null
SECTION 13: ETHICAL CONSIDERATIONS
13.1 Scientific Integrity
Commitments:
- Pre-registration before data
- No HARKing (Hypothesizing After Results Known)
- Null results published with equal prominence
- Errors corrected publicly
13.2 Broader Impacts
If RCH is supported:
- Profound implications for physics, consciousness studies, theology
- Media attention likely (prepared press release)
- Public outreach via accessible summary
If RCH is refuted:
- Equally important for science
- Demonstrates Logos framework makes falsifiable claims
- Informs future theoretical development
13.3 Dual-Use Concerns
None identified - this is basic research with no obvious weaponization potential
CONCLUSION
This Registered Report presents a rigorous, falsifiable test of the Resonant Coupling Hypothesis using quantum random number generation. The 4-rung calibration ladder, null-model ensemble, cryptographic pre-commitment, and adversarial collaboration framework ensure that results—positive or negative—will be scientifically credible.
The experiment is ready to begin.
APPENDICES
Appendix A: Complete Analysis Code
(To be deposited in OSF upon Stage 1 acceptance)
Appendix B: Equipment Datasheets
(QRNG specs, function generator manual, etc.)
Appendix C: Pilot Data
(If available from preliminary testing)
Appendix D: Bayesian Prior Specification
(Mathematical details of prior distributions)
Document Hash (to be computed): [SHA-256 pending] OSF Registration: [Link pending] Version: 1.0 Date: October 7, 2025
Corresponding Author: David Lowe Email: [To be added]
“Let the experiment speak. Let reality judge.”
Canonical Hub: CANONICAL_INDEX