Harmonic coherence as an alternative to JOINs for relationship detection — has this been explored?

[atech-hub]

I'm not a developer — I'm a sysadmin who fell down a mathematical rabbit hole. I ended up with a question that I think is relevant to CozoDB's approach to relational algebra.
The idea: encode values as phases on a unit circle, then use cos(n × Δθ) to detect typed relationships. When n=2 you find pairs, n=3 finds triples, n=4 finds quadrants — all from a single parameterised function instead of explicit JOINs or traversals.
What caught my attention about CozoDB is your position that relational algebra should be composable. This approach reduces the relational query to one function where the "type" of relationship is just the harmonic number. It feels algebraically composable in a way that graph traversals and SQL JOINs aren't.
I built a proof of concept in Rust with AI assistance (~530 lines, zero dependencies, 10 tests passing). In one test, a single scan with n=3 found 75 entities across 3 groups — something that would typically need 2-3 JOINs.
Has anything like this been explored in Datalog or relational algebra literature?
MIT license: https://github.com/atech-hub/Wave-Coherence-as-a-Computational-Primitive

[ConstantinVasilev]

Hi @atech-hub I find your work really interesting, could you please email me, I would like to collab:
konstantin.vasilev.phd@gmail.com

[atech-hub]

Hi Constantin,

Thanks for reaching out.

Full transparency: I'm not an academic — I'm a systems administrator who spots patterns across different domains. This work came from extended conversations with AI (Claude) about alternatives to static vector representations in databases and LLMs. The core idea is representing meaning as orbital elements — phases in cycles with structural relationships — rather than points in high-dimensional space requiring brute-force computation.

That line of thinking connected orbital mechanics (6 parameters describing any orbit) with the limitations of 12,000–16,000 arbitrary vector dimensions, and eventually led to the Wave-Based Semantic Memory paper (Listopad, 2025) and the Defierithos architecture, which explore similar ground from different angles.

I want to be honest about how I work: my strength is cross-domain pattern recognition and asking questions. The formal mathematics is developed through dialogue with AI, where I push toward specific insights and work to understand them at a practical level. The computational validation passes, but I'd need someone with rigorous mathematical training to properly assess the foundations.

I've shared everything I have in the paper and repository — the data and the framework are all there. This isn't my field, so I don't have much more to add beyond what's published. But the fact that someone with your background finds it worth a conversation tells me there may be something here worth exploring further. I'm happy to talk and answer any questions about how the ideas developed.

Best regards,
Marco

[atech-hub]

My apologies, I did forgot to add citation to the paper that glued everyhthing into place. I have updated the docs in GitHub.
[1] Listopad, S. (2025). Wave-Based Semantic Memory: A Phase-Aware Alternative to Vector Retrieval. arXiv:2509.09691. https://arxiv.org/abs/2509.09691