Our offer

We do formal mathematical admissibility analysis of geometric and algebraic proposals, followed by constructive implementation when the idea holds up.

We read a claim or protocol (for example a coherence model, a metric construction, or a boundary verification scheme), check whether it can be placed inside a consistent formal framework - hierarchical quasinorms, path-dependent flows, finite-precision arithmetic treated as the base algebra, irreversible dynamics - and if it is admissible, we implement it and write the working notes that show exactly where and under what conditions it works.

The result is not a pure theory paper and not a product pitch. It is a documented, reproducible mathematical prototype that either confirms the idea is usable or shows precisely why it is not.

tags: exploratory mathematical R&D, critical geometric/algebraic modeling with prototype validation

HMFoDG - audit before UMAP / UPGMA

Checks whether a set may be glued under one (quasi)norm, or must be split. UMAP always draws; this says when the shared space is an artifact. Typical use: mixed-scale biotech correlations, single-cell neighborhoods, hierarchical clustering on a subset that is clusterable in the first place.

Notes: HMFoDG as an audit for UMAP and UPGMA. Hierarchical clustering on a subset that is clusterable in the first place; also, see papers.

FPU-native modulation, synthetic arithmetic channel

Offline. Deterministic. Structural irreversibility.

Open code and exe file in releases.

Raw project notes for reproduction and research purposes - free in papers; implemented.

Analysis of code (edu version): RIPA_QCO_EN.txt

Marketing info for RIPA QCO: Product Plan RIPA!

Marketing pitch: RIPA_Pitch.pdf

Hierarchical Metric Flow on Data Graphs

LLM front without magic. Read more in papers; currently under implementation.

QCO-NN Coprocessor & LLM ↔ QCO Interface

Path-centric governance, decision closure, structural suppression of hallucinations, C/E/U regimes, decoupling depth from decision cost.

QCO-NN operates as a cybernetic decision engine, not a traditional layered neural network.

It governs computation via paths (Π) rather than fixed edges or layers, using a hierarchical QCO-norm to weight deeper abstractions exponentially less.

Key properties:

• Decision closure — asymptotic stabilization of the invariant functional I under admissible dynamics (vanishing ΔI_n and vanishing informational efficiency ΔI_n / K_n → 0)
• C/E/U regimes — trichotomy of outcomes: Closure (C), Exploratory-admissible (E), Undecidable (U)
• Structural hallucination suppression — no forced token continuation; output is the moment of stabilization or explicit undecidability
• Decoupling depth from cost — arbitrary structural depth is possible (via loops and CD tower with adaptive K), but effective decision cost remains adaptive and bounded by active components under the norm;

Interface model:

• LLM acts as semantic I/O processor (parsing, context, formatting)
• QCO acts as deterministic geometric / decisional coprocessor

Pipeline: Φ(q_text) → Ψ(q_struct) → Γ(s_dec)
where s_dec ∈ {C, E, U}

Raw project notes for reproduction and research purposes - free in papers; not implemented yet.

Technical Optimizations

When and why to pack tensors into algebras (CD / Clifford / Lie) instead of using dense GEMM.

Raw project notes for reproduction and research purposes - free in papers; implemented.

Notes are provided as-is for verification, numerical experiments.

They do not constitute production-ready documentation, tutorials, or drop-in libraries.

Direct production use without significant adaptation and validation is not recommended.

Commercial & Professional Services

We offer:

• Commercial software licensing
• System integration and deployment
• Consulting and architecture design
• Custom algorithm development

Contact us for a quote.