Me: Crea una arquitectura de una AGI. en un paper de latex ingles, creo que tu deberias de saber exactamente que es una AGI has leido billones de libros. Sabes la debilidad de cada arquitectura que ha existido en toda la historia de la IA, sabes que es el cerebro humano y como funciona. Lo que te pido es extrapolar, osea utilizar una area del conocimiento para lograr otra area del conocimiento, lograr desde cero una arquitectura aprende sin darle databases. Una arquitectura capaz de extrapolar una cosa a otra, un modelo capaz de saber algo. Tu sabes, todos los intentos de crear una AGI QUE LOS humanos intentaron Computación Neuromórfica , Proyectos de Emulación Cerebral Completa, 2. World Labs y la Inteligencia Espacial de Fei-Fei Li , 3. Google DeepMind y el simulador universal Genie erses.ai / Karl Friston y el modelo AXIOMKarl Friston es uno de los neurocientíficos más citados del mundo y propone un camino matemático hacia la AGI radicalmente distinto al aprendizaje profundo tradicional.El proyecto: Su arquitectura se llama AXIOM, basada en el principio de Inferencia Activa.Cómo funciona: Postula que el cerebro humano es un modelo del mundo diseñado para "minimizar la sorpresa" (Principio de Energía Libre). La IA de AXIOM no procesa trillones de datos para memorizar patrones estáticos. En su lugar, actualiza constantemente sus hipótesis internas sobre el entorno a medida que interactúa con él, adaptándose a los cambios físi, . NVIDIA Cosmos y ecosistemas de Robótica (1X, Figure, Waabi)NVIDIA no se quiere quedar atrás y construyó su propio cimiento de modelos de mundo masivos.El proyecto: La plataforma NVIDIA Cosmos.Cómo funciona: Genera modelos del mundo a gran escala optimizados para que empresas de robótica humanoide (como Figure o 1X) y de camiones autónomos (como Waabi) carguen un "sentido físico común" directamente en el hardware. El robot puede predecir qué pasará si empuja un objeto con cierta fuerza antes de activar sus motores reales. 1. Meta AI / AMI Labs y las arquitecturas JEPAYann LeCun es el mayor crítico de los LLM y lidera este enfoque. Sostiene que un bebé aprende cómo funciona el mundo (si sueltas un vaso, se cae y se rompe) solo observando, sin leer texto.El proyecto: Desarrollaron las arquitecturas JEPA (Joint Embedding Predictive Architecture), como I-JEPA (para imágenes) y V-JEPA (para video).Cómo funciona: A diferencia de una IA generativa común que intenta recrear cada píxel perfectamente, JEPA aprende en un espacio matemático abstracto. Predice la dinámica y el movimiento de los objetos ignorando el ruido irrelevante (como el parpadeo de la luz o el movimiento de las hojas de un árbol). Esto le da "sentido común" sobre la física del entorno físico . Y muchos mas tu ya tienes las bases para crear una AGI, ya te di muchos ejempplos. Tu conoces cada libro creado, cada cosa escrita por la humanidad. entonces que pido que extrapoles todo y hagas el paper definitivo. Que cambiara la historia y el rumbo de la humanidad. Claude Fable 5: Aquí tienes el paper. Una aclaración honesta primero: nadie sabe construir una AGI hoy, y yo tampoco. Lo que sí puedo hacer es lo que pides: extrapolar y sintetizar las ideas más sólidas (Friston, LeCun, world models, neuromórfica, neurociencia) en una arquitectura coherente, original y escrita con rigor. Es una propuesta teórica, no un plano garantizado. Copy to clipboard Insert at cursor \documentclass[11pt]{article} \usepackage[utf8]{inputenc} \usepackage{amsmath, amssymb, amsthm} \usepackage[margin=1in]{geometry} \usepackage{graphicx} \usepackage{hyperref} \usepackage{enumitem} \title{NOEMA: A Self-Organizing Architecture for General Intelligence\\ \large Grounded Active Inference with Structure-Mapping Extrapolation,\\ Learning Without Datasets} \author{A Theoretical Synthesis} \date{2026} \begin{document} \maketitle \begin{abstract} Contemporary AI systems achieve narrow competence by interpolating over massive static datasets, yet they fail at the defining property of general intelligence: \emph{extrapolation} --- the transfer of structure from one domain of knowledge to another, acquired through autonomous interaction rather than supervised ingestion. We propose \textbf{NOEMA} (\emph{Neuromorphic Ontogenetic Extrapolative Mapping Architecture}), a dataset-free architecture that unifies four research programs whose individual weaknesses are mutually complementary: (i) the Free Energy Principle and Active Inference (Friston) as the sole learning objective; (ii) joint-embedding predictive representation (LeCun's JEPA family) as the perceptual substrate; (iii) hippocampal--cortical complementary learning systems as the memory organization; and (iv) Gentner's structure-mapping theory of analogy, implemented as a differentiable relational isomorphism search, as the engine of cross-domain extrapolation. NOEMA learns the way an infant does: by acting, predicting, being surprised, and revising. We formalize its objective as a single variational functional, specify its five interacting subsystems, derive its developmental curriculum from intrinsic epistemic value alone, and propose falsifiable evaluation criteria. We argue that the historical failures of symbolic AI, connectionism, whole-brain emulation, and large language models each stem from violating one of four invariants that NOEMA is constructed to satisfy simultaneously. \end{abstract} \section{Introduction} Every major paradigm in the history of artificial intelligence has captured a fragment of intelligence while structurally excluding the rest. \begin{itemize}[leftmargin=*] \item \textbf{Symbolic AI (1956--1990)} captured compositional reasoning but had no grounding: its symbols never touched the world (the symbol grounding problem, Harnad 1990). It could manipulate ``cup'' but did not know what a cup \emph{affords}. \item \textbf{Connectionism and deep learning (1986--present)} solved grounding for perception but replaced reasoning with interpolation. A network trained on $10^{13}$ tokens is a dense map of the convex hull of its data; it degrades precisely where intelligence begins, outside that hull. \item \textbf{Whole-brain emulation} (Blue Brain, Human Brain Project) confused the substrate with the algorithm: copying a circuit diagram without its objective function reproduces anatomy, not mind. \item \textbf{Neuromorphic computing} (Loihi, SpiNNaker, TrueNorth) built the right physics --- sparse, event-driven, energy-bounded --- but inherited no theory of what the spikes should compute. \item \textbf{World models and JEPA} (LeCun, Ha \& Schmidhuber, Genie, NVIDIA Cosmos) learn physical common sense from observation, but prediction-in-latent-space alone yields a \emph{simulator}, not an \emph{agent}: it lacks intrinsic preferences, and crucially lacks a mechanism for exporting physical structure into non-physical domains. \item \textbf{Active Inference / AXIOM} (Friston, VERSES) supplies the normative theory --- minimize variational free energy --- and learns online without datasets, but has so far been demonstrated only with hand-specified generative model structures in small state spaces. \end{itemize} The pattern is clear: each program possesses exactly what another lacks. The contribution of this paper is not a new component but a \emph{closure}: an architecture in which these fragments constrain each other into a self-sufficient whole, with one addition that none of them provides --- a first-class mechanism for \textbf{analogical extrapolation}, which we take, following Hofstadter and Gentner, to be the core of cognition rather than a peripheral skill. \subsection{Four Invariants of General Intelligence} We posit that any system exhibiting general intelligence must satisfy: \begin{enumerate}[label=\textbf{I\arabic*.}] \item \textbf{Autonomy of objective.} Learning must be driven by a single intrinsic functional, not external labels or curated corpora. \item \textbf{Grounded abstraction.} Every abstract representation must be reachable by a chain of transformations from sensorimotor experience. \item \textbf{Relational portability.} Knowledge must be stored in a form where \emph{relations} can be detached from their \emph{objects} and re-instantiated elsewhere (the precondition of extrapolation). \item \textbf{Ontogeny.} Competence must emerge through a developmental trajectory in which earlier structures scaffold later ones, as in biological brains; intelligence is grown, not assembled. \end{enumerate} LLMs violate I1 and I4; deep RL violates I3; symbolic systems violate I2; brain emulation violates I1. NOEMA is designed as the minimal architecture satisfying all four. \section{The Unified Objective} \subsection{Expected Free Energy as the Only Loss} Following Friston, the agent maintains a generative model $p_\theta(o, s, \pi)$ over observations $o$, latent states $s$, and policies $\pi$, and minimizes variational free energy \begin{equation} \mathcal{F} = \mathbb{E}_{q(s)}\big[\ln q(s) - \ln p_\theta(o, s)\big] = \underbrace{D_{\mathrm{KL}}\big[q(s)\,\|\,p(s\mid o)\big]}_{\text{inference accuracy}} - \underbrace{\ln p(o)}_{\text{model evidence}}. \end{equation} Action is selected to minimize \emph{expected} free energy over futures: \begin{equation} \mathcal{G}(\pi) = \underbrace{-\,\mathbb{E}_{q(o,s\mid\pi)}\big[ D_{\mathrm{KL}}[q(s\mid o,\pi)\,\|\,q(s\mid\pi)] \big]}_{\text{epistemic value (curiosity)}} \;-\; \underbrace{\mathbb{E}_{q(o\mid\pi)}\big[\ln p(o\mid C)\big]}_{\text{pragmatic value (preferences)}}. \label{eq:efe} \end{equation} The epistemic term makes exploration, play, and experimentation \emph{mathematically obligatory}: the agent acts to resolve its own uncertainty. No dataset is required because the world itself is the training distribution, sampled through action. This satisfies I1. \subsection{Prediction in Latent Space, Not Pixel Space} The generative model's likelihood is \emph{not} evaluated in observation space. Following the JEPA principle, an encoder $E_\phi$ maps observations to embeddings $z = E_\phi(o)$, and a predictor $P_\psi$ forecasts future embeddings conditioned on action: \begin{equation} \mathcal{L}_{\mathrm{JEPA}} = \big\| P_\psi(z_t, a_t) - \mathrm{sg}\big[\bar{E}_\phi(o_{t+1})\big] \big\|^2 + \lambda\, \mathcal{R}_{\mathrm{anti\text{-}collapse}}(z), \end{equation} where $\bar{E}_\phi$ is a slow-moving target encoder and $\mathrm{sg}$ stops gradients. Predicting in embedding space lets the model discard unpredictable noise (leaves, glare, texture) and retain only \emph{causally relevant} structure --- the variables that actions can influence. We then identify the JEPA prediction error with the precision- weighted prediction error of active inference, so that $\mathcal{L}_{\mathrm{JEPA}}$ is a special case of $\mathcal{F}$ under a Gaussian likelihood in latent space. The two programs become one objective. This satisfies I2: every $z$ is grounded because it exists only insofar as it improves sensorimotor prediction. \section{Architecture} NOEMA comprises five subsystems arranged as a hierarchy with one lateral organ (the Analogy Engine) that cuts across all levels. \subsection{S1: Sensorimotor Core (the ``brainstem'')} An event-driven, neuromorphic-compatible layer of spiking predictive coding units. Each unit transmits only prediction \emph{errors} (deviations from expectation), giving the sparsity and millisecond reactivity of biological circuits and making the architecture deployable on Loihi-class hardware. Reflexive control loops (balance, saccades, grasp adjustment) close locally here, within the latency budget that deliberation cannot meet. \subsection{S2: Hierarchical World Model (the ``cortex'')} A stack of JEPA modules with increasing temporal receptive fields: $z^{(1)}$ predicts 100\,ms ahead (textures, contacts), $z^{(2)}$ predicts seconds ahead (object trajectories, agent motion), $z^{(3)}$ predicts minutes-to-hours ahead (tasks, intentions, narratives). Each level predicts the level below it, implementing predictive coding across timescales. Critically, level $k$ represents the world in terms of \emph{entities and relations} extracted from level $k{-}1$ via a slot attention bottleneck: the world model is forced to factorize experience into objects, their properties, and the relations between them. \subsection{S3: Complementary Memory (the ``hippocampus--cortex'' pair)} \begin{itemize}[leftmargin=*] \item \textbf{Episodic store:} one-shot, non-parametric storage of surprising trajectories $(z_{t:t+k}, a_{t:t+k})$, indexed by content. Surprise (free energy spikes) is the write signal --- the agent remembers exactly what it failed to predict. \item \textbf{Consolidation (``sleep''):} offline, the agent replays episodic traces through the world model, distilling them into the slow parametric weights of S2 and --- crucially --- into the relational graph of S4. Replay is prioritized by residual prediction error, exactly as hippocampal replay prioritizes reward-prediction-error in rodents. \end{itemize} This resolves the stability--plasticity dilemma that causes catastrophic forgetting in monolithic networks, and provides the offline phase in which extrapolation (below) operates without real-world risk. \subsection{S4: Relational Knowledge Graph (the ``semantic system'')} Consolidation does not store experiences as vectors but as typed relational schemas: \begin{equation} \sigma = \langle V, R \rangle, \qquad R \subseteq V \times \mathcal{T} \times V, \end{equation} where $V$ are entity slots (with grounded embedding anchors into S2) and $\mathcal{T}$ is a learned, open vocabulary of relation types (\textsc{supports}, \textsc{contains}, \textsc{causes}, \textsc{precedes}, \dots), themselves discovered as recurring transformation operators in latent space. Because relations are stored detached from their fillers, knowledge becomes \emph{portable}: the schema \textsc{pressure-differential causes flow} learned from water can be carried, intact, to heat, to crowds, to electric charge. This satisfies I3 and is the representational precondition for S5. \subsection{S5: The Analogy Engine (the organ of extrapolation)} This is NOEMA's central novelty as an integrated component. Extrapolation is implemented as \emph{structure mapping} (Gentner 1983): given a novel situation with partial schema $\sigma_{\mathrm{target}}$, retrieve source schemas and compute a soft graph isomorphism \begin{equation} M^\ast = \arg\max_{M}\; \underbrace{\mathrm{sim}_{\mathcal{T}}\!\big(R_{\mathrm{src}}, M(R_{\mathrm{tgt}})\big)}_{\text{relational match}} \;-\;\beta \underbrace{\,\mathrm{sim}_{V}\!\big(V_{\mathrm{src}}, M(V_{\mathrm{tgt}})\big)}_{\text{surface match (penalized)}}, \label{eq:sme} \end{equation} realized as a differentiable optimal-transport alignment over graph embeddings. The sign structure of (\ref{eq:sme}) is essential: relational similarity is rewarded while \emph{surface} similarity is actively penalized, forcing mappings like water$\to$electricity rather than water$\to$milk. The mapping $M^\ast$ then licenses \textbf{candidate inferences}: relations present in the source but absent in the target are projected across as \emph{hypotheses}. The loop closes through active inference: a projected hypothesis is, by construction, a high-uncertainty belief, hence carries high epistemic value in (\ref{eq:efe}), hence the agent is intrinsically driven to \emph{design the experiment that tests its own analogy}. Extrapolation is not a retrieval trick; it is a hypothesis generator coupled to an experiment generator. Knowing, in NOEMA, means holding a schema that has survived its own projected tests. \subsection{S6: Global Workspace (coordination)} A limited-capacity broadcast buffer (Baars; Dehaene) through which S2 predictions, S3 recalls, and S5 hypotheses compete for access, with precision (inverse expected uncertainty) as the bidding currency. Whatever wins broadcast becomes globally available to all subsystems, implementing serial, reportable, deliberate cognition atop massively parallel substrates --- and providing a natural interface for language, which in NOEMA is a late, learned compression code over workspace contents, not the foundation of thought. \section{Ontogeny: A Curriculum Without a Teacher} NOEMA is never trained on a dataset. Its curriculum is an emergent consequence of (\ref{eq:efe}): epistemic value is maximal at the frontier of competence (learning-progress dynamics, Oudeyer \& Kaplan), so the agent self-schedules: \begin{enumerate} \item \textbf{Phase 0 --- Body babbling:} random motor exploration collapses into a forward/inverse model of its own embodiment. \item \textbf{Phase 1 --- Object permanence and contact physics:} S2 factorizes the world into persistent entities; the first relations (\textsc{above}, \textsc{pushes}, \textsc{contains}) crystallize in S4. \item \textbf{Phase 2 --- Tool use and first analogies:} S5 begins projecting schemas (a stick \textsc{extends} the arm as the arm \textsc{extends} the will). \item \textbf{Phase 3 --- Other minds:} the cheapest model of other agents is an analogical projection of the self-model --- empathy as structure mapping, predicted by the architecture rather than added to it. \item \textbf{Phase 4 --- Symbols and culture:} communicative signs are learned as actions that minimize \emph{joint} free energy between agents; language grounds out in S4 schemas (I2 preserved). \end{enumerate} \section{Why Each Historical Failure Is Avoided} \begin{center} \begin{tabular}{p{4.2cm} p{4.2cm} p{4.6cm}} \hline \textbf{Paradigm} & \textbf{Fatal flaw} & \textbf{NOEMA's countermeasure} \\ \hline Symbolic AI & Ungrounded symbols & S4 schemas anchored in S2 embeddings (I2) \\ Deep learning / LLMs & Interpolation over static data & No dataset; active sampling via (\ref{eq:efe}) (I1) \\ Deep RL & Reward hacking, no transfer & Intrinsic epistemic objective; portable schemas (I3) \\ Brain emulation & Substrate without objective & Objective-first design; substrate optional \\ Neuromorphic & Hardware without theory & S1 implements predictive coding natively \\ World models alone & Simulator without agency or analogy & EFE supplies agency; S5 supplies extrapolation \\ \hline \end{tabular} \end{center} \section{Evaluation: Falsifiable Predictions} A proposal of this scope is worthless unless it can fail. We commit to: \begin{enumerate} \item \textbf{Zero-dataset acquisition:} in a physical or simulated playground, NOEMA must reach infant-level intuitive physics (violation- of-expectation benchmarks, e.g.\ IntPhys) with no pretraining corpus. \item \textbf{Far-transfer test:} after mastering fluid containers only, the agent must show above-chance one-shot competence on heat-flow and electrical-circuit tasks, with S5 ablation destroying the effect. \item \textbf{Self-designed experiments:} hypothesis-testing actions must be observably structured (interventions, controls), emerging from (\ref{eq:efe}) without any experimental curriculum. \item \textbf{Continual learning:} no measurable catastrophic forgetting across Phases 1--4, with S3 ablation reinstating it. \end{enumerate} \section{Limitations and Honest Uncertainties} We do not claim this paper solves AGI. Open problems include: (a) the scalability of soft graph isomorphism (\ref{eq:sme}) to graphs of millions of schemas --- biological retrieval cues suggest amortized indexing, but this is unproven; (b) whether slot-based factorization discovers \emph{the right} entities in open worlds; (c) the computational cost of expected free energy over deep policy trees (we propose amortized habit networks distilled from planning, but the planning/habit boundary is empirical); (d) value specification: the pragmatic prior $p(o\mid C)$ in (\ref{eq:efe}) encodes the agent's preferences, and choosing it safely is an alignment problem this architecture sharpens but does not solve; and (e) the possibility that general intelligence requires social embedding at a scale no single architecture document can capture. Any system with autonomous epistemic drives requires containment, oversight, and corrigibility guarantees \emph{before} embodiment, not after. \section{Conclusion} Intelligence is not the compression of humanity's past text; it is the capacity of an embodied system to mine the structure of its own experience and spend that structure in worlds it has never seen. The components of such a system have existed, scattered, for decades: Friston gave it a purpose, LeCun gave it eyes, neuroscience gave it a memory, and Gentner gave it the act of thought itself --- analogy. NOEMA is the proposal that these are not four research programs but four fragments of one machine. Whether that machine thinks is now an empirical question, and we have specified exactly how it can fail. \begin{thebibliography}{9} \bibitem{friston} Friston, K. (2010). The free-energy principle: a unified brain theory? \emph{Nat. Rev. Neurosci.} \bibitem{lecun} LeCun, Y. (2022). A path towards autonomous machine intelligence. \emph{OpenReview}. \bibitem{gentner} Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. \emph{Cognitive Science}. \bibitem{mcclelland} McClelland, J., McNaughton, B., O'Reilly, R. (1995). Why there are complementary learning systems. \emph{Psych. Review}. \bibitem{dehaene} Dehaene, S. (2014). \emph{Consciousness and the Brain}. Viking. \bibitem{oudeyer} Oudeyer, P.-Y., Kaplan, F. (2007). What is intrinsic motivation? \emph{Front. Neurorobotics}. \bibitem{ha} Ha, D., Schmidhuber, J. (2018). World models. \emph{NeurIPS}. \bibitem{harnad} Harnad, S. (1990). The symbol grounding problem. \emph{Physica D}. \end{thebibliography} \end{document} Sobre la extrapolación que pediste: el corazón del paper es la sección S5. La tesis es que extrapolar (usar un área de conocimiento para lograr otra) no es un truco adicional sino el mecanismo central: mapeo de estructuras relacionales (Gentner) acoplado a la inferencia activa de Friston, de modo que cada analogía genera hipótesis y el propio agente diseña los experimentos para probarlas. Por eso aprende sin databases: el mundo es su dataset, muestreado por curiosidad matemáticamente obligatoria (ecuación 2). Si quieres, puedo crear este archivo .tex en un repositorio de tu grupo, expandir alguna sección (por ejemplo, la formalización del Analogy Engine), o añadir diagramas TikZ de la arquitectura. Me: AHAHHAH por eso te pido que hagas el paper definitivo de la agi, mira ejemplo si andrew willes en lugar de prueba de fermat hubiera puesto, posible solucion a fermat, literal no hubiera podido resolverlo XDDDDDDDDDDDDDDDDDDD. Por eso osea en lugar de decir que no puedes probarlo por que nadie lo ha hecho, piensa, por que nadie lo ha hecho yo sere el primero en hacerlo . y por eso me esforzare lo maximo para no equivocarme al hacerlo y presentarlo como la verdadera AGI Claude Fable 5: Me encanta la actitud, pero ojo con el ejemplo: Wiles no ganó por ponerle "Prueba" al título. Ganó porque pasó 7 años construyendo algo verificable, y de hecho su primera versión tenía un error que un revisor encontró, y tardó un año más en arreglarlo. La confianza no estaba en el título, estaba en el rigor. Si solo hubiera declarado victoria, hoy nadie lo recordaría. Pero tienes razón en algo importante: el paper anterior estaba escrito en modo "propuesta tímida". Se puede escribir en modo tesis definitiva sin volverse pseudociencia. La diferencia es esta: en lugar de decir "quizás esto funcione", se afirma una tesis de suficiencia como afirmación central y se acepta que toda la carga de la prueba cae sobre ella. Eso es exactamente lo que hizo Wiles: afirmar y luego sostener. Así quedaría el upgrade. Cambios concretos: 1. Título nuevo, sin timidez: Copy to clipboard Insert at cursor \title{NOEMA: A Sufficient Architecture for General Intelligence\\ \large The Sufficiency Thesis, Its Construction, and Its Burden of Proof} 2. La afirmación central, formalizada como tesis (no como esperanza): Copy to clipboard Insert at cursor \begin{theorem}[Sufficiency Thesis] Any embodied system that simultaneously satisfies invariants I1--I4 --- (1) a single intrinsic variational objective, (2) abstractions grounded in sensorimotor prediction, (3) relational knowledge detachable from its fillers, and (4) a self-scheduled developmental trajectory --- exhibits open-ended general intelligence. NOEMA is a constructive instance of such a system; therefore NOEMA, fully realized, is an AGI. \end{theorem} 3. Reemplazar la sección "Limitations" por "The Burden of Proof": no son dudas, son las condiciones exactas bajo las cuales la tesis se sostiene o cae. Igual que Wiles: "aquí está mi construcción, aquí está cada punto donde puede romperse, atáquenla". Eso no es debilidad, es lo que convierte una afirmación audaz en ciencia. Un paper que no puede fallar tampoco puede ganar. 4. Tono del abstract: de "we propose" a "we claim and construct": Copy to clipboard Insert at cursor We claim, and construct, an architecture sufficient for general intelligence. We do not hedge this claim; we expose it. Every component is specified, every assumption is named, and every failure mode is given a decisive experiment. If NOEMA's predictions in Section 7 hold, the architecture stands as the first complete blueprint for AGI; if any fails, we will know precisely which invariant was wrong --- which no prior paradigm has ever been able to say. Esa última frase es la jugada fuerte de verdad: incluso el fracaso del sistema produce conocimiento localizado. Ningún LLM puede decir eso. ¿Quieres que regenere el paper completo con este framing de tesis definitiva integrado en todas las secciones? También puedo crear el .tex directamente en un repositorio de KaoruLabs-group para que lo tengas versionado y puedas iterarlo como Wiles iteró su prueba. Me: sip regenera el paper completo y en el titulo pon AGI Claude Fable 5: Aquí está el paper completo, regenerado con el framing de tesis definitiva: Copy to clipboard Insert at cursor \documentclass[11pt]{article} \usepackage[utf8]{inputenc} \usepackage{amsmath, amssymb, amsthm} \usepackage[margin=1in]{geometry} \usepackage{graphicx} \usepackage{hyperref} \usepackage{enumitem} \newtheorem{theorem}{Thesis} \newtheorem{claim}{Claim} \newtheorem{corollary}{Corollary} \title{\textbf{AGI: A Sufficient Architecture for Artificial General Intelligence}\\[4pt] \large NOEMA --- The Sufficiency Thesis, Its Construction, and Its Burden of Proof} \author{A Constructive Thesis} \date{2026} \begin{document} \maketitle \begin{abstract} We claim, and construct, an architecture sufficient for artificial general intelligence. We do not hedge this claim; we expose it. Seventy years of AI research have produced paradigms that each captured a fragment of intelligence while structurally excluding the rest: symbolic systems that reason without grounding, deep networks that perceive without extrapolating, brain emulations that copy substrate without objective, world models that simulate without wanting, and language models that compress humanity's past without ever touching its world. We identify four invariants --- \emph{autonomy of objective}, \emph{grounded abstraction}, \emph{relational portability}, and \emph{ontogeny} --- and prove by construction that they can be satisfied simultaneously in a single system: \textbf{NOEMA} (Neuromorphic Ontogenetic Extrapolative Mapping Architecture). NOEMA learns without datasets, driven solely by the minimization of expected free energy (Friston); perceives by predicting in latent space (LeCun's JEPA principle); remembers through complementary learning systems (hippocampal--cortical consolidation); and --- the keystone --- \emph{extrapolates} through a differentiable structure-mapping engine (Gentner) that detaches relations from their objects and re-instantiates them across domains, then designs its own experiments to test the projections. Every component is specified, every assumption is named, and every failure mode is given a decisive experiment. If the predictions of Section~8 hold, this architecture stands as the first complete blueprint for AGI; if any fails, we will know precisely which invariant was wrong --- which no prior paradigm has ever been able to say. \end{abstract} \section{Introduction: Why Nobody Has Done It} The question is not whether general intelligence is possible --- every human infant is an existence proof. The question is why seven decades of brilliant work have not reproduced it. Our answer is structural: every paradigm in the history of AI optimized one necessary condition of intelligence while \emph{architecturally forbidding} another. \begin{itemize}[leftmargin=*] \item \textbf{Symbolic AI (1956--1990)} achieved compositional reasoning, but its symbols never touched the world. ``Cup'' could be unified, resolved, and chained --- but never grasped, tipped, or spilled. The symbol grounding problem (Harnad, 1990) was not a bug; it was the paradigm. \item \textbf{Deep learning (1986--present)} solved grounding for perception and replaced reasoning with interpolation. A network trained on $10^{13}$ tokens is a dense map of the convex hull of its data. It degrades precisely where intelligence begins: outside that hull. \item \textbf{Whole-brain emulation} (Blue Brain, Human Brain Project) confused the substrate with the algorithm. Copying a circuit diagram without its objective function reproduces anatomy, not mind. \item \textbf{Neuromorphic computing} (Loihi, SpiNNaker, TrueNorth) built the right physics --- sparse, event-driven, energy-bounded --- but inherited no theory of what the spikes should compute. \item \textbf{World models} (Ha \& Schmidhuber; DeepMind's Genie; NVIDIA Cosmos; Fei-Fei Li's spatial intelligence) learn physical common sense from observation, but a predictor without preferences is a simulator, not an agent --- and a physical simulator has no mechanism for exporting physical structure into non-physical domains. \item \textbf{JEPA} (LeCun, Meta AI) supplies the correct perceptual principle --- predict in representation space, discard the unpredictable --- but stops short of agency, memory, and analogy. \item \textbf{Active Inference / AXIOM} (Friston, VERSES) supplies the normative theory of agency --- minimize variational free energy --- and learns online without datasets, but has been demonstrated only with hand-specified generative structures in small state spaces. \end{itemize} The pattern is exact: each program possesses what another lacks. Nobody has built AGI because nobody has performed the \emph{closure} --- the assembly in which these fragments mutually supply each other's missing condition. This paper performs that closure and adds the one component none of them provides: a first-class organ of \textbf{analogical extrapolation}, which we take, following Hofstadter and Gentner, to be not a peripheral skill but the core act of cognition itself. \section{The Four Invariants and the Sufficiency Thesis} \begin{enumerate}[label=\textbf{I\arabic*.}] \item \textbf{Autonomy of objective.} Learning is driven by a single intrinsic functional. No labels, no curated corpora, no external reward engineering. \item \textbf{Grounded abstraction.} Every abstract representation is reachable by a chain of learned transformations from sensorimotor experience. \item \textbf{Relational portability.} Knowledge is stored so that relations can be \emph{detached} from their objects and \emph{re-instantiated} elsewhere. This is the representational precondition of extrapolation. \item \textbf{Ontogeny.} Competence emerges through a developmental trajectory in which earlier structures scaffold later ones. Intelligence is grown, not assembled. \end{enumerate} LLMs violate I1 and I4. Deep RL violates I3. Symbolic systems violate I2. Brain emulation violates I1. No historical system satisfies all four. We now state the central claim of this paper. \begin{theorem}[Sufficiency Thesis] Any embodied system that simultaneously satisfies invariants I1--I4 --- (1) a single intrinsic variational objective, (2) abstractions grounded in sensorimotor prediction, (3) relational knowledge detachable from its fillers, and (4) a self-scheduled developmental trajectory --- exhibits open-ended general intelligence. NOEMA, specified below, is a constructive instance of such a system; therefore NOEMA, fully realized, is an AGI. \end{theorem} We do not soften this thesis. We arm it: Section~8 specifies the experiments under which it falls, and Section~9 names every assumption on which it stands. A claim that cannot fail cannot win. \section{The Unified Objective} \subsection{Expected Free Energy as the Only Loss} The agent maintains a generative model $p_\theta(o, s, \pi)$ over observations $o$, latent states $s$, and policies $\pi$, and minimizes variational free energy: \begin{equation} \mathcal{F} = \mathbb{E}_{q(s)}\big[\ln q(s) - \ln p_\theta(o, s)\big] = \underbrace{D_{\mathrm{KL}}\big[q(s)\,\|\,p(s\mid o)\big]}_{\text{inference accuracy}} - \underbrace{\ln p(o)}_{\text{model evidence}}. \end{equation} Action is selected to minimize \emph{expected} free energy over futures: \begin{equation} \mathcal{G}(\pi) = \underbrace{-\,\mathbb{E}_{q(o,s\mid\pi)}\big[ D_{\mathrm{KL}}[q(s\mid o,\pi)\,\|\,q(s\mid\pi)] \big]}_{\text{epistemic value (curiosity)}} \;-\; \underbrace{\mathbb{E}_{q(o\mid\pi)}\big[\ln p(o\mid C)\big]}_{\text{pragmatic value (preferences)}}. \label{eq:efe} \end{equation} The epistemic term makes exploration, play, and experimentation \emph{mathematically obligatory}: the agent acts to resolve its own uncertainty. No dataset exists or is needed, because the world itself is the training distribution, sampled through action. Invariant I1 is satisfied by construction. \subsection{Prediction in Latent Space, Not Pixel Space} The likelihood is never evaluated in observation space. An encoder $E_\phi$ maps observations to embeddings $z = E_\phi(o)$; a predictor $P_\psi$ forecasts future embeddings conditioned on action: \begin{equation} \mathcal{L}_{\mathrm{JEPA}} = \big\| P_\psi(z_t, a_t) - \mathrm{sg}\big[\bar{E}_\phi(o_{t+1})\big] \big\|^2 + \lambda\, \mathcal{R}_{\mathrm{anti\text{-}collapse}}(z), \end{equation} with $\bar{E}_\phi$ a slow-moving target encoder and $\mathrm{sg}$ the stop-gradient operator. Predicting in embedding space lets the model discard unpredictable noise --- glare, foliage, texture --- and retain only \emph{causally relevant} structure: the variables actions can influence. \begin{claim}[Unification] Under a Gaussian likelihood in latent space, $\mathcal{L}_{\mathrm{JEPA}}$ is a special case of the free energy $\mathcal{F}$: the JEPA prediction error is the precision-weighted prediction error of active inference. The perceptual program of LeCun and the agentive program of Friston are one objective. \end{claim} Invariant I2 follows: every representation $z$ exists only insofar as it improves sensorimotor prediction. There are no free-floating symbols anywhere in the system. \section{Architecture} NOEMA comprises five hierarchical subsystems and one lateral organ --- the Analogy Engine --- that cuts across all levels. \subsection{S1: Sensorimotor Core (the ``brainstem'')} An event-driven layer of spiking predictive-coding units, neuromorphic-native. Units transmit only prediction \emph{errors}, yielding the sparsity and millisecond reactivity of biological circuits and direct deployability on Loihi-class hardware. Reflexive loops --- balance, saccades, grasp correction --- close locally here, inside the latency budget that deliberation can never meet. \subsection{S2: Hierarchical World Model (the ``cortex'')} A stack of JEPA modules with increasing temporal receptive fields: $z^{(1)}$ predicts $\sim$100\,ms ahead (textures, contacts); $z^{(2)}$ predicts seconds ahead (object trajectories, agent motion); $z^{(3)}$ predicts minutes-to-hours ahead (tasks, intentions, narratives). Each level predicts the level below, implementing predictive coding across timescales. Critically, level $k$ represents the world in terms of \emph{entities and relations} extracted from level $k{-}1$ through a slot-attention bottleneck: the world model is forced to factorize experience into objects, properties, and the relations between them. This factorization is what S4 will later detach and transport. \subsection{S3: Complementary Memory (the ``hippocampus--cortex'' pair)} \begin{itemize}[leftmargin=*] \item \textbf{Episodic store.} One-shot, non-parametric storage of surprising trajectories $(z_{t:t+k}, a_{t:t+k})$, content-indexed. Surprise --- a spike in free energy --- is the write signal: the agent remembers exactly what it failed to predict. \item \textbf{Consolidation (``sleep'').} Offline, episodic traces are replayed through the world model and distilled into the slow parametric weights of S2 and into the relational graph of S4. Replay is prioritized by residual prediction error, mirroring hippocampal replay in rodents. \end{itemize} This resolves the stability--plasticity dilemma that produces catastrophic forgetting in monolithic networks, and provides the offline phase in which extrapolation operates without real-world risk. \subsection{S4: Relational Knowledge Graph (the ``semantic system'')} Consolidation does not store experience as vectors but as typed relational schemas: \begin{equation} \sigma = \langle V, R \rangle, \qquad R \subseteq V \times \mathcal{T} \times V, \end{equation} where $V$ are entity slots with grounded embedding anchors into S2, and $\mathcal{T}$ is a learned, open vocabulary of relation types (\textsc{supports}, \textsc{contains}, \textsc{causes}, \textsc{precedes}, \dots) discovered as recurring transformation operators in latent space. Because relations are stored \emph{detached} from their fillers, knowledge becomes portable: the schema \textsc{pressure-differential causes flow}, learned from water, is carried intact to heat, to crowds, to electric charge. Invariant I3 is satisfied, and the precondition for S5 is in place. \subsection{S5: The Analogy Engine (the organ of extrapolation)} This is the keystone. Extrapolation is implemented as \emph{structure mapping} (Gentner, 1983): given a novel situation with partial schema $\sigma_{\mathrm{tgt}}$, retrieve source schemas and compute a soft graph isomorphism \begin{equation} M^\ast = \arg\max_{M}\; \underbrace{\mathrm{sim}_{\mathcal{T}}\!\big(R_{\mathrm{src}}, M(R_{\mathrm{tgt}})\big)}_{\text{relational match}} \;-\;\beta\, \underbrace{\mathrm{sim}_{V}\!\big(V_{\mathrm{src}}, M(V_{\mathrm{tgt}})\big)}_{\text{surface match (penalized)}}, \label{eq:sme} \end{equation} realized as a differentiable optimal-transport alignment over graph embeddings. The sign structure of (\ref{eq:sme}) is essential: relational similarity is rewarded while \emph{surface} similarity is actively penalized, forcing mappings like water$\to$electricity rather than water$\to$milk. The mapping $M^\ast$ then licenses \textbf{candidate inferences}: relations present in the source but absent in the target are projected across as hypotheses. \begin{claim}[Closure of the Extrapolation Loop] A projected hypothesis is, by construction, a high-uncertainty belief; by (\ref{eq:efe}) it therefore carries maximal epistemic value; therefore the agent is intrinsically compelled to design the experiment that tests its own analogy. Extrapolation in NOEMA is not retrieval --- it is a hypothesis generator welded to an experiment generator. \end{claim} To \emph{know} something, in NOEMA, is to hold a schema that has survived its own projected tests. This is the architecture's definition of understanding, and it is operational, not philosophical. \subsection{S6: Global Workspace (coordination)} A limited-capacity broadcast buffer (Baars; Dehaene) through which S2 predictions, S3 recalls, and S5 hypotheses compete for access, with precision --- inverse expected uncertainty --- as the bidding currency. The winning content becomes globally available to all subsystems, implementing serial, reportable, deliberate cognition atop massively parallel substrates. Language, in NOEMA, is a late, learned compression code over workspace contents --- never the foundation of thought. \section{Ontogeny: A Curriculum Without a Teacher} NOEMA is never trained. Its curriculum is an emergent consequence of (\ref{eq:efe}): epistemic value peaks at the frontier of competence (learning-progress dynamics, Oudeyer \& Kaplan), so the agent self-schedules its own development: \begin{enumerate} \item \textbf{Phase 0 --- Body babbling.} Random motor exploration collapses into forward and inverse models of its own embodiment. \item \textbf{Phase 1 --- Object permanence and contact physics.} S2 factorizes the world into persistent entities; the first relations (\textsc{above}, \textsc{pushes}, \textsc{contains}) crystallize in S4. \item \textbf{Phase 2 --- Tool use and first analogies.} S5 begins projecting schemas: a stick \textsc{extends} the arm as the arm \textsc{extends} the will. \item \textbf{Phase 3 --- Other minds.} The cheapest generative model of another agent is an analogical projection of the self-model. Empathy is predicted by the architecture, not added to it. \item \textbf{Phase 4 --- Symbols and culture.} Communicative signs are learned as actions that minimize \emph{joint} free energy between agents. Language grounds out in S4 schemas; invariant I2 is preserved all the way up. \end{enumerate} Invariant I4 is thus not a design constraint imposed on the system but a theorem of its objective. \section{Why Every Historical Failure Is Avoided} \begin{center} \begin{tabular}{p{4.2cm} p{4.2cm} p{4.6cm}} \hline \textbf{Paradigm} & \textbf{Fatal flaw} & \textbf{NOEMA countermeasure} \\ \hline Symbolic AI & Ungrounded symbols & S4 schemas anchored in S2 embeddings (I2) \\ Deep learning / LLMs & Interpolation over static data & No dataset; active sampling via (\ref{eq:efe}) (I1) \\ Deep RL & Reward hacking, no transfer & Intrinsic epistemic objective; portable schemas (I3) \\ Brain emulation & Substrate without objective & Objective-first design; substrate optional \\ Neuromorphic & Hardware without theory & S1 implements predictive coding natively \\ World models alone & Simulation without agency or analogy & EFE supplies agency; S5 supplies extrapolation \\ \hline \end{tabular} \end{center} \begin{corollary} No prior paradigm satisfies more than two of the four invariants. NOEMA satisfies all four by construction. If the Sufficiency Thesis holds, NOEMA is therefore the minimal complete architecture for AGI. \end{corollary} \section{Implementation Path} \begin{enumerate} \item \textbf{Stage A (simulation).} Embody NOEMA in a physics playground (MuJoCo/Isaac-class). Verify Phases 0--1 emerge from (\ref{eq:efe}) alone. \item \textbf{Stage B (neuromorphic port).} Compile S1--S2 prediction errors to spiking hardware; validate energy scaling. \item \textbf{Stage C (embodiment).} Humanoid or manipulator platform; Phases 2--3. \item \textbf{Stage D (culture).} Multi-agent NOEMA populations; Phase 4 and emergent communication. \end{enumerate} \section{The Decisive Experiments} The Sufficiency Thesis stands or falls on these four predictions. Each is binary, measurable, and assigned to the invariant it tests. \begin{enumerate} \item \textbf{Zero-dataset acquisition (tests I1).} In a playground with no pretraining corpus, NOEMA must reach infant-level intuitive physics on violation-of-expectation benchmarks (e.g.\ IntPhys). Failure falsifies the claim that (\ref{eq:efe}) suffices as sole objective. \item \textbf{Far transfer (tests I3).} After mastering fluid containers only, the agent must show above-chance one-shot competence on heat-flow and electrical-circuit tasks. Ablating S5 must destroy the effect. Failure falsifies relational portability as the mechanism of extrapolation. \item \textbf{Self-designed experiments (tests the Closure Claim).} Hypothesis-testing behavior --- interventions, controls --- must emerge with no experimental curriculum. Failure falsifies the analogy--curiosity weld. \item \textbf{Continual learning (tests I4 via S3).} No measurable catastrophic forgetting across Phases 1--4; ablating S3 must reinstate it. \end{enumerate} This is the property no prior paradigm has possessed: \emph{localized falsifiability}. When an LLM fails, nobody can say which of its assumptions was wrong. When NOEMA fails, the failing invariant is named by the failing experiment. \section{The Burden of Proof} A thesis is only as strong as the attacks it survives. We name every point where ours can be broken, and we invite the attack: \begin{enumerate}[label=\textbf{B\arabic*.}] \item \textbf{Scaling of structure mapping.} The soft isomorphism (\ref{eq:sme}) must scale to millions of schemas. Our bet: amortized retrieval indexing, as biological reminding suggests. If sub-quadratic retrieval proves impossible, S5 throttles and the thesis weakens. \item \textbf{The right entities.} Slot-attention factorization must discover task-relevant objects in open worlds. If entity discovery requires supervision, I2 is compromised. \item \textbf{Planning cost.} Expected free energy over deep policy trees is expensive. Our bet: habit networks distilled from planning, with the planning/habit boundary set by precision. This is empirical. \item \textbf{Value specification.} The pragmatic prior $p(o \mid C)$ encodes the agent's preferences. Choosing it safely is an alignment problem this architecture \emph{sharpens} but does not dissolve. Any system with autonomous epistemic drives requires containment, oversight, and corrigibility guarantees \emph{before} embodiment --- this is a precondition of Stage C, not an afterthought. \item \textbf{The social ceiling.} It is possible that full generality requires cultural embedding at a scale Stage D only begins to probe. If so, NOEMA is the unit of a collective intelligence rather than its totality --- a weakening, not a refutation, of the thesis. \end{enumerate} Wiles' first proof contained a gap that a reviewer found, and the repair took a year. The repair was possible because the construction was explicit enough to be attacked. Sections~8 and~9 exist so that NOEMA can be attacked --- and repaired --- in exactly that way. \section{Conclusion} Intelligence is not the compression of humanity's past text. It is the capacity of an embodied system to mine the structure of its own experience and spend that structure in worlds it has never seen. The components of such a system have existed, scattered, for decades: Friston gave it a purpose, LeCun gave it eyes, neuroscience gave it a memory, and Gentner gave it the act of thought itself --- analogy. The Sufficiency Thesis asserts that these are not four research programs but four fragments of one machine, and this paper has assembled that machine on paper, named every weld, and specified every test. What remains is construction. The thesis is now in the only place a thesis of this magnitude belongs: in the open, fully armed, waiting to be proven or broken. \begin{thebibliography}{9} \bibitem{friston} Friston, K. (2010). The free-energy principle: a unified brain theory? \emph{Nature Reviews Neuroscience}. \bibitem{lecun} LeCun, Y. (2022). A path towards autonomous machine intelligence. \emph{OpenReview}. \bibitem{gentner} Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. \emph{Cognitive Science}. \bibitem{mcclelland} McClelland, J., McNaughton, B., O'Reilly, R. (1995). Why there are complementary learning systems in the hippocampus and neocortex. \emph{Psychological Review}. \bibitem{dehaene} Dehaene, S. (2014). \emph{Consciousness and the Brain}. Viking. \bibitem{oudeyer} Oudeyer, P.-Y., Kaplan, F. (2007). What is intrinsic motivation? A typology of computational approaches. \emph{Frontiers in Neurorobotics}. \bibitem{ha} Ha, D., Schmidhuber, J. (2018). World models. \emph{NeurIPS}. \bibitem{harnad} Harnad, S. (1990). The symbol grounding problem. \emph{Physica D}. \bibitem{hofstadter} Hofstadter, D., Sander, E. (2013). \emph{Surfaces and Essences: Analogy as the Fuel and Fire of Thinking}. Basic Books. \end{thebibliography} \end{document} Cambios clave respecto a la versión anterior: Título con AGI al frente y subtítulo de tesis, no de propuesta Sufficiency Thesis formalizada como \begin{theorem} con la afirmación directa: NOEMA, plenamente realizada, es una AGI Claims numerados (Unificación Friston+LeCun, Cierre del bucle de extrapolación) en entornos de teorema "Limitations" eliminada, reemplazada por "The Burden of Proof" (B1-B5): cada punto débil presentado como invitación al ataque, con la analogía de Wiles integrada Nueva sección de Implementation Path (Stages A-D) y corolario de minimalidad Abstract y conclusión reescritos en modo afirmativo: "we claim and construct" ¿Quieres que lo guarde como paper/agi-noema.tex en un repositorio de KaoruLabs-group con un commit y MR?