New Framework for Efficient Human-Al Interaction and Decision Optimization Research Proposal: Coherence-Driven Al Architecture (C-ROI & ATLAS-TIGER)

[Eric Ramirez merino]

Dear AI Research and Engineering Team at Google,

My name is Eric Ramirez Merino, and I am an independent researcher based in Veracruz, Mexico. I am reaching out to share a conceptual and mathematical framework I have been developing that may be relevant to ongoing work in integrated artificial intelligence systems, adaptive agents, and human–AI interaction.

The framework is called the Syntergic AI Framework (S.A.F.), centered on a formal optimization model known as C-ROI (Coherence–Return on Interaction). It focuses on improving decision quality, contextual alignment, and efficiency in human–AI interaction through the joint optimization of information gain and computational or cognitive cost.

Additionally, I have designed an architectural model named ATLAS–TIGER:

• ATLAS — A perception and state-mapping layer that integrates multimodal signals to construct coherent representations of user and environment states.

• TIGER — An adaptive optimization engine that selects actions or responses by maximizing useful information under resource constraints.

Together, these components form a closed adaptive loop intended to enhance coherence, responsiveness, and efficiency in AI-assisted systems.

I believe these ideas could have potential applications in:

- Context-aware AI agents

- Integrated AI environments

- Human–computer interaction optimization

- Resource-efficient inference architectures

- Adaptive decision systems

If this topic is of interest, I would be glad to share a detailed technical document or discuss possible research directions or collaboration opportunities.

Thank you for your time and for the contributions your organization continues to make to the advancement of artificial intelligence.

Kind regards, 

The framework is defined through an optimization objective that jointly maximizes information gain and decision quality under computational and interaction costs 

\section*{Mathematical Formulation}

\subsection*{C-ROI Objective Function}

The Coherence–Return on Interaction (C-ROI) framework is defined through a joint optimization of information gain, decision effectiveness, and cost efficiency:

\begin{equation}

A = F(C_1, C_2, I, D)

\end{equation}

A normalized operational form is:

\begin{equation}

A =

\frac{I \cdot D}{C_1 + C_2 + \epsilon}

\end{equation}

where:

\begin{itemize}

\item $C_1$ = computational cost

\item $C_2$ = interaction or cognitive cost

\item $I$ = information gain

\item $D$ = decision effectiveness

\item $\epsilon$ = small stability constant

\end{itemize}

\subsection*{Information Optimization Functional}

The system behavior is derived from an information–cost optimization functional:

\begin{equation}

\mathcal{L}

=

I(M;D')

-

\lambda (C_1 + C_2)

-

\mu R

\end{equation}

Optimal policy selection is obtained by:

\begin{equation}

\Pi^{*}

=

\arg\max_{\Pi}

\;

\mathbb{E}

\left[

I(M;D')

\right]

-

\lambda (C_1 + C_2)

\end{equation}

where:

\begin{itemize}

\item $I(M;D')$ = mutual information between model state and desired outcome

\item $R$ = resource constraints

\item $\lambda, \mu$ = regularization parameters

\end{itemize}

\subsection*{Adaptive System Dynamics (ATLAS--TIGER Architecture)}

The adaptive loop of the architecture is defined as:

\begin{equation}

S_{t+1}

=

F(S_t, A_t, I_t)

\end{equation}

with action selection:

\begin{equation}

A_t

=

\arg\max

\;

\mathcal{L}(S_t)

\end{equation}

\subsection*{Coherence Metric}

A coherence metric describing alignment between model and information space is defined as:

\begin{equation}

\Lambda(M \leftrightarrow I)

=

C^{\circ}

(\Delta \nu)^2

\end{equation}

subject to:

\begin{equation}

0 \leq \Lambda \leq 1

\end{equation}

\subsection*{Temporal Coherence Evolution}

The temporal evolution of coherence follows:

\begin{equation}

\frac{d\Lambda}{dt}

=

\alpha \Lambda (1-\Lambda)

-

\beta N_0

\end{equation}

where:

\begin{itemize}

\item $\alpha$ = coherence growth parameter

\item $\beta$ = noise sensitivity

\item $N_0$ = environmental or internal noise level

\end{itemize}

\bigskip

These formulations define a coherence-driven optimization framework intended to improve adaptive decision systems, contextual alignment, and resource efficiency in integrated AI environments.

Eric Ramirez Merino

Independent Researcher

Veracruz, Mexico

Email: [ericramir...@gmail.com]

[Kenyon Allen]

Hello Eric. 

Thanks for reaching out. 

I absolutely support your project. 

How far have you gotten yet?

- Ken "Aquarian" Allen

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[Eric Ramirez merino]

Hola 

Muchas gracias por el interés y el apoyo, lo aprecio mucho.

Actualmente he avanzado en la formalización conceptual y matemática del Syntergic AI Framework, incluyendo el modelo C-ROI (Coherence–Return on Interaction), metalenguajes simbólicos y funciones de optimización orientadas a mejorar la interacción humano-IA en términos de coherencia, alineación contextual y costo cognitivo.

El objetivo del marco es proporcionar una arquitectura que permita sistemas adaptativos más eficientes en comunicación y toma de decisiones, integrando principios de teoría de información y optimización. 

Si les resulta interesante, también puedo compartir el volumen teórico más completo donde se desarrolla la formalización matemática con mayor profundidad.

Estoy preparando una versión técnica más refinada del documento para investigación colaborativa y con gusto puedo compartirla en cuanto esté lista.

También me interesaría conocer sus perspectivas o áreas de interés donde consideren que este enfoque podría explorarse más.

Quedo atento a sus comentarios o preguntas, y sería un gusto explorar posibles líneas de investigación conjunta.

Saludos cordiales,

Eric Ramirez Merino
Independent Researcher

Veracruz, México

[Eric Ramirez merino]

Dear Research Team,

My name is Eric Ramirez Merino, and I am an independent researcher based in Veracruz, Mexico. I am writing to share a research framework that may be relevant to ongoing work in adaptive artificial intelligence, human-AI alignment, and context-aware systems.

The framework introduces a coherence-driven optimization approach for interaction and decision systems, integrating mathematical modeling, cognitive cost analysis, and adaptive trigger mechanisms within a unified architecture. The research combines theoretical derivations with simulation experiments and proposes mechanisms that may be applicable to adaptive agents, generative interfaces, and optimization-driven interaction systems.

The work is structured around three principal components:

• C-ROI (Coherence-Return Optimization Index): A quantitative metric modeling interaction efficiency as a function of coherence, performance, and cost.

• ATLAS Adaptive Trigger Architecture: A protocol layer enabling dynamic adaptation when coherence-performance thresholds are exceeded.

• ∞ Models of Protocols and Metalanguages: A formal structure representing interaction states, operators, and transformation dynamics between cognitive and computational domains.

The research also includes a variational formulation, dynamic system modeling, and numerical simulations illustrating emergent accessibility and efficiency properties under different coherence regimes.

I am sharing this work in case it may be relevant to teams exploring adaptive AI systems, human-centered AI, decision optimization, or generative interaction architectures. I would greatly appreciate any feedback or direction toward researchers who might find the framework useful. I am also open to technical discussion or collaboration if appropriate.

Thank you very much for your time and consideration.

Kind regards,

Eric Ramirez Merino

Independent Researcher

Veracruz, Mexico

Email: ericramir...@gmail.com

Attachments:

• Full Research Paper

• Syntergic AI Framework Documentation

• ATLAS Trigger Architecture

• ∞ Models of Protocols and Metalanguages

• Simulation Materials

---

Definición de Variables del Modelo

Accesibilidad (A):
Nivel en el que los usuarios pueden interactuar con un sistema de manera efectiva, eficiente y con mínima fricción cognitiva, permitiendo la consecución de objetivos de forma clara y comprensible.

Costo Cognitivo (C):
Esfuerzo mental requerido para procesar, interpretar y utilizar la información presentada por el sistema. Puede dividirse en múltiples componentes, como carga de memoria, complejidad de decisión y esfuerzo de aprendizaje.

Diseño (D):
Conjunto de decisiones estructurales, funcionales y estéticas que median la interacción entre el usuario y el sistema, incluyendo arquitectura de información, interfaz, flujos de interacción y representación visual.

Rendimiento (I):
Nivel de productividad, precisión y eficacia que el usuario alcanza al interactuar con el sistema para completar una tarea o lograr un objetivo específico.

---

Propuesta del Modelo

La relación entre estas variables puede expresarse mediante la siguiente ecuación funcional:

A = F(C_1, C_2, I, D)

Donde:

• representa la accesibilidad global del sistema.
• y representan distintos componentes del costo cognitivo (por ejemplo, carga de procesamiento y carga de decisión).
• corresponde al rendimiento obtenido durante la interacción.
• representa las propiedades del diseño que influyen en la experiencia del usuario.
• es una función que modela la relación dinámica entre estas variables.

En términos conceptuales, el modelo establece que la accesibilidad de un sistema emerge del equilibrio entre el costo cognitivo requerido, el rendimiento alcanzado y las características del diseño que median la interacción.