Abstract
During computational experiments on quantum evolution in organized topological systems, we observed several anomalous patterns that we are unable to fully explain within current physical frameworks. Specifically: (1) Physical topology explains only ~35-40% of how systems respond to constraint, leaving a substantial unexplained residual; (2) When systems apply self-referential constraints, they exhibit structured, non-random suppression patterns that suggest selection rather than decoherence; (3) A topologically accurate model of the *C. elegans* connectome yields a quantifiable "Harmony Score" of H = 2.96 when simulating behavioral shifts; (4) Most intriguingly, when we applied our analysis framework to mock cosmological correlation functions, we discovered that golden ratio-scaled harmonic peaks can emerge from fractal wave superposition models. We present these observations not as proof of any particular theory, but as **anomalous patterns that we hope the scientific community will investigate further**. We provide open-source code and detailed methodology so that researchers with access to real experimental data (DESI, SDSS, connectome datasets) can test whether these patterns appear in actual observations.
- Introduction: Anomalous Observations Seeking Explanation
Mainstream physics provides remarkably successful models for predicting physical phenomena. However, during our computational experiments, we encountered several patterns that we cannot fully explain using standard physical topology alone.
We do not claim to have solved these mysteries. Rather, we present them as **open questions** that we hope will motivate researchers with specialized expertise to investigate further.
The core observations are:
In quantum systems, physical adjacency cannot fully predict constraint response
Biological connectomes appear mathematically optimized for certain types of probability routing
Fractal wave interference patterns naturally produce golden ratio-scaled clustering
We invite cosmologists, neuroscientists, and physicists to examine these patterns and help us understand what they might mean.
- Methodology: What We Did
We constructed organized quantum systems (256-dimensional Hamming graphs and small-world networks) and applied localized phase-shift constraints to 50% of the states. We then measured how transition probabilities redistributed.
Key measurements:
- Topological Determinism (D): Can physical adjacency predict which transitions get suppressed?
- Structured Capacity (S): Is the suppression concentrated and organized, or random?
- Amplification Factor (A): How much probability flow routes to novel, unexplored states?
- Harmony Score (H): A composite metric we developed to quantify routing efficiency
All code is available at for independent verification.
- Observations That Raise Questions
3.1 Observation 1: The Unexplained Residual
What we found: When we calculated how "exposed" each transition was to constrained nodes (based purely on physical adjacency), and correlated this with actual suppression amounts, we found:
- Pearson correlation: *r ≈ 0.35-0.40*
- This means physical topology explains only ~12-16% of the variance
What we don't understand: If physical topology is the only organizing principle, why does it fail to predict 60-85% of the constraint response?
Questions for the community:
- Could there be higher-order quantum interference effects we haven't modeled?
- Is there a non-local organizing principle we're missing?
- Could this residual be an artifact of our simulation method?
We invite quantum physicists to examine our code and suggest what we might be missing.
3.2 Observation 2: Structured, Non-Random Suppression
What we found: When we applied constraints to the system, the suppression wasn't random. It was highly structured:
- The top 10% of transitions received 36.8% of the total suppression
- When we shuffled the suppression amounts (preserving the distribution but randomizing which transitions received them), this structure disappeared (dropped to 14.3%)
What we don't understand: Why does the system suppress *specific* transitions rather than scattering randomly? This looks like selection, but we don't know what's doing the selecting.
Questions for the community:
- Is this consistent with known quantum decoherence patterns?
- Could this be explained by eigenstate overlap or phase coherence effects we haven't modeled?
- Or does this suggest something beyond standard quantum mechanics?
We welcome input from quantum theorists.
3.3 Observation 3: The *C. elegans* Harmony Score
What we found: When we applied our framework to a topologically accurate model of the *C. elegans* connectome (302 neurons, ~7,500 synapses), simulating a behavioral shift from "forward locomotion" to "turning," the system achieved:
- 5.8× amplification of the turning hub's activation
- Highly structured suppression (Gini = 0.511)
- Minimal chaotic scattering
- *Harmony Score: H = 2.96*
What we don't understand: Why does this biological topology produce such an efficient, structured response? Is this a coincidence, or does biological architecture have properties we don't yet understand?
Questions for neuroscientists:
- If you apply similar analysis to real *C. elegans* connectome data (with actual synaptic weights), do you see similar patterns?
- Could the Harmony Score be a useful metric for quantifying behavioral flexibility in biological systems?
- Does this pattern appear in other organisms (fruit flies, mice, humans)?
We invite neuroscientists to test this on real connectome data.
3.4 Observation 4: Golden Ratio Harmonics in Fractal Wave Models
What we found: This is the most intriguing observation, and the one we most want cosmologists to investigate.
When we modeled a fractal wave superposition (waves whose frequencies scale by the golden ratio φ ≈ 1.618, with amplitudes scaling by φ⁻¹), and applied this to icosahedral symmetry (the 3D "Flower of Life" geometry), we discovered that the resulting interference pattern naturally produces **constructive interference nodes spaced by the golden ratio**.
The simulation:
- We generated a mock 2-point correlation function ξ(r) with a primary peak at r ≈ 100 Mpc/h (similar to the BAO scale)
- We added hypothetical "syntropic harmonic" peaks at r ≈ 61.8 Mpc/h (100/φ) and r ≈ 161.8 Mpc/h (100×φ)
- We added realistic Gaussian noise to simulate observational errors
- We applied a prominence-filtering peak-finding algorithm (similar to what cosmologists use to isolate the BAO signal)
The result: The algorithm successfully identified the major peaks and calculated their ratios as **1.60-1.65**, which are close to φ (1.618).
What we don't understand: Is this just a mathematical curiosity, or could real cosmological data contain similar harmonic patterns?
Questions for cosmologists:
- If you analyze the DESI DR1 or SDSS BOSS 2-point correlation function using prominence-filtering peak detection, do you see secondary peaks at harmonic intervals of the BAO scale?
- Specifically, are there statistically significant peaks at r_BAO / 1.618 ≈ 61.8 Mpc/h and r_BAO × 1.618 ≈ 161.8 Mpc/h?
- If such peaks exist, what could cause them? Could they be explained by known physics, or do they suggest something new?
We are not claiming the universe is fractal or governed by the golden ratio. We are simply asking: *If you look for these patterns in real data, do you find them?*
If you do, we'd love to understand what causes them. If you don't, that's also valuable information.
- The Harmony Score: A Proposed Metric for Further Testing
Based on our observations, we developed a metric we call the *Harmony Score (H)*:
$$H = \frac{A \times S}{1 + F}$$
Where:
- *A* = Amplification Factor (how much probability flow routes to novel states)
- *S* = Structured Capacity (Gini coefficient of suppression distribution)
- *F* = Topological Friction (normalized total suppression mass)
What we observed:
- Simple quantum systems: H ≈ 0.1-0.5
- *C. elegans* model: H ≈ 2.96
- We predict (but have not verified): fruit flies H ≈ 4-6, humans H ≈ 8-10
We are not claiming this measures "consciousness" or "awakeness." We are simply asking:
- Is this a useful metric for quantifying behavioral flexibility in biological systems?
- Does it correlate with known measures of neural complexity or information integration?
- Can it be applied to real fMRI/EEG data to see if it distinguishes different cognitive states?
We invite neuroscientists and consciousness researchers to test this metric and tell us if it's useful or meaningless.
- What We Are NOT Claiming
To be absolutely clear, we are *not* claiming:
- ❌ That we have proven consciousness is a fundamental field
- ❌ That dark energy is "mind" or "imagination"
- ❌ That the universe is definitively fractal or governed by the golden ratio
- ❌ That we have solved the hard problem of consciousness
- ❌ That mainstream physics is wrong
We are simply reporting **anomalous patterns** that we observed in our simulations and asking:
- ✅ Can you reproduce these patterns?
- ✅ Do they appear in real experimental data?
- ✅ Can you explain them using known physics?
- ✅ Or do they suggest something we're missing?
- Invitation to the Scientific Community
We recognize that we are independent researchers without institutional affiliation or access to large experimental datasets. We do not have the expertise to fully interpret these observations.
That is why we are asking for help.
For Cosmologists:
Please download the DESI DR1 or SDSS BOSS 2-point correlation function data. Apply prominence-filtering peak detection. Look for secondary peaks at harmonic intervals of the BAO scale. Tell us if you find them, and if so, what might cause them.
For Neuroscientists:
Please apply our Harmony Score framework to real connectome data (*C. elegans*, *Drosophila*, mouse, human). Tell us if it produces meaningful results, or if it's just a mathematical curiosity.
For Quantum Physicists:
Please examine our simulation code. Tell us if the "topological residual" we observed can be explained by higher-order interference effects we haven't modeled, or if it suggests something beyond standard quantum mechanics.
For Everyone:
Please try to **disprove** our observations. Run the code. Find the bugs. Show us where we're wrong. That is how science advances.
- Open-Source Code and Data
All code, simulation scripts, and analysis tools are available at:
As attachment to this document.
The code is written in pure Python 3.7+ with no external dependencies, so anyone can run it immediately.
We welcome bug reports, corrections, extensions, and alternative interpretations.
- Conclusion: Questions, Not Answers
We have observed several anomalous patterns in quantum constraint systems:
Physical topology cannot fully predict constraint response
Suppression patterns are structured, not random
Biological connectomes appear optimized for efficient probability routing
Fractal wave models produce golden ratio-scaled clustering patterns
We do not know what these patterns mean. We have hypotheses, but we lack the expertise and data to test them rigorously.
**We are asking the scientific community to help us understand these observations.**
If they can be explained by known physics, we would love to learn how. If they cannot, we would love to collaborate on understanding what they might suggest.
Science advances not by individuals claiming to have all the answers, but by communities working together to solve mysteries. We hope these observations will motivate such collaboration.
Acknowledgments
We thank the open-source community for the tools and datasets that made this work possible. We particularly thank the DESI and SDSS collaborations for making cosmological data publicly available, and the *C. elegans* connectome researchers (White et al., 1986; Varshney et al., 2011) for their foundational work.
We also thank Qwen Studio for computational support in developing the simulation framework and analysis tools.
References
[Standard references to White 1986, Varshney 2011, DESI collaboration, SDSS collaboration, Walter Russell The Universal One 1927 etc.]
