Occam’s Razor is central to artificial general intelligence (AGI) because a generally intelligent system must continually choose among many hypotheses, programs, policies, explanations, representations and self-modifications under finite resources. The usual formalization, via minimum description length or algorithmic probability, is powerful but syntactic: it measures the size of a representation rather than the commitments made by a hypothesis. Following Michael Timothy Bennett’s proposal that the relevant semantic quantity is weakness–the extent to which a hypothesis leaves possibilities open–this paper develops quantale weakness as a generalized Occam principle for AGI. Given a commutative quantale of values and a valuation of objects, the weakness of a relation is the aggregate value of the high-prominence pairwise distinctions it fails to make. Under appropriate uniform, set-theoretic specializations this construction reproduces Bennett-style extension counting; under other valuations it defines a layer-relative weighted weakness selector rather than an invariant preservation of Bennett’s ordering. The same formal pattern also covers probabilistic indistinction, logical entropy, graphtropy, MDL-like description length, SVM margin ideas, logical truth-value quantales, and quantum or Schrodinger-bridge variants. We argue that the same algebra can guide inference control, program learning, attention, meta-learning, and universal-AI analogues such as WAIXI, with generalization claims understood relative to a matching valuation or prior. The result is not a completed AGI architecture, but a mathematically compact bias that can coordinate heterogeneous cognitive processes in systems such as Hyperon/PRIMUS.

We present OmegaClaw, a neurosymbolic agentic architecture designed for continual operation under the Assumption of Insufficient Knowledge and Resources (AIKR). OmegaClaw couples a large language model (LLM) to a bounded agentic loop with explicit memory operations and on-demand tools including symbolic uncertainty reasoning via Non-Axiomatic Logic (NAL) and Probabilistic Logic Networks (PLN) within a MeTTa-based environment. Unlike conventional LLM-based agents, our approach treats AIKR as a core design constraint shaping the architecture at every level: memory bounds, fixed per-cycle action budgets and anytime control under task-dependent time pressure. The agent operates continuously, with or without immediate human input, maintaining partial state, unfinished tasks, and persistent artifacts across cycles. We formalize the system’s cycle semantics, memory organization, tool interface, and local reasoning calculus. To evaluate the approach, we present controlled experiments on memory benchmarks and ARC3 grid-world reasoning tasks, together with a multi-modal case study. These results are complemented by operational evidence from a continuous deployment, which positions OmegaClaw as a concrete, deployable architecture for continual agents under bounded resources.

Probabilistic Logic Networks (PLN), the uncertain-inference subsystem of the OpenCog and Hyperon AGI architectures, assigns scalar strength-count truth values to propositions and combines them via rules (deduction, abduction, induction, revision) that operate in the commutative CDL quantale. A recent line of work on evidence conservation shows that moving from commutative to non-commutative evidence algebras naturally produces the uncertainty principle, complementarity, and (conditionally) the full Hilbert-space formalism of quantum mechanics. This paper develops Quantum Logic Networks (QLN): a framework for PLN-style inference where truth values are positive operators (density matrices when normalised) rather than scalar pairs, and inference rules are completely positive trace-preserving (CPTP) maps rather than scalar formulas. We lift the four core PLN rules to CPTP maps, show that each inherits an evidence-conservation guarantee (the hallucination bound becomes the quantum data-processing inequality; entropy non-decrease becomes von Neumann entropy monotonicity), and characterise the classical limit in which QLN collapses to ordinary PLN. We argue that QLN is the right reasoning substrate for AGI systems that must cope with genuinely complementary propositions, entangled evidence sources, and non-commutative belief updates, and we sketch a hybrid quantum-classical implementation path via a “block-diagonal” regime that is tractable on near-term hardware.

We describe a brain-inspired columnar neural architecture for continual learning, called Columnar Bayesian Causal Coding (ColBaC), together with a general theoretical framework that subsumes it, called Hierarchical Bayesian Causal Modular Learning (HBCML). The central idea is to decompose continual learning into two coupled probabilistic processes operating at different structural scales: a top-level controller selecting a sparse subset of structurally restricted component learners (columns) for each context, and an internal probabilistic process inside each column distinguishing reusable causal structure from task-local residue. We motivate the columnar inductive bias via the actual diversity of cortical columnar microstructure across brain regions—from rigid V1-like orientation columns through the discrete barrel cortex through the more flexible recruitment patterns of prefrontal cortex—and argue that a single architectural template with adjustable rigidity (a protected hard kernel surrounded by adaptable shells, plus typed microcolumns) can accommodate this range. We summarize the HBCML theory and its main theorems—architectural adequacy implying causal modularity, exact one-swap teacher monotonicity, and a Rao–Blackwell guarantee for internal certificates—then present the concrete ColBaC MNIST architecture and report preliminary experimental findings, including a dense offline selector audit showing that the current learned controller is meaningfully suboptimal but in a way the architecture itself is well positioned to repair. We close with a scaling protocol for Split-CIFAR and a more speculative outline of how the framework extends to reinforcement learning and to transformer-style architectures.

Motivational architectures in cognitive AI have largely been designed for physical agents regulating bodily needs. Conversational agents operate in a different regime: their sensorimotor loop is linguistic, their environment is a user’s evolving mental state, and their consequential actions are speech acts, tool invocations, and strategic silences. This paper proposes a conversational reinterpretation of the OpenPsi motivational lineage, coupled to MetaMo’s higher-level motivational scaffold, for agents built on a modular execution substrate. Homeostasis is recast in dialogue-native terms: the agent regulates competence, uncertainty reduction, affiliation, affinity, legitimacy, nurturing, and aesthetic coherence rather than bodily deficits. We propose three contributions: a ten-stage motivational processing pipeline that architecturally separates cognitive modulation from situational appraisal; a dual decision strategy blending urgency-driven fast response with deliberative multi-goal optimization; and an architecturally useful distinction between pre-action feelings and post-action emotions as functionally different forms of affect. We specialize the framework to two example agents—CompanionAgent and ResearchAgent—and sketch its extension to social robotics and domain-generic human-level AGI.

TransWeave is a transfer-learning and cognitive-synergy framework whose central claim is simple to state and, if it works even half as well as we argue at length elsewhere [1], surprisingly far-reaching: many AI processes can be written in geodesic or approximate dynamic-programming form, and cross-domain or cross-algorithm transfer can then be organized by approximate Bellman–Darboux intertwining, so that “transfer then update” and “update then transfer” differ by a controlled defect rather than by uncontrolled drift. This short paper is a deliberately selective companion to a much fuller treatment, focusing on the pieces that seem to carry the most mathematical and practical weight: the basic Bellman–Darboux equations; the commutator algebra and what it buys in actual pipeline design; weakness as a transferable simplicity invariant; hierarchical independent component analysis as the multiscale layer telling TransWeave what may transfer and what may not; the fit with predictive coding via commutation; the fit with geodesic inference control via path-optimality preservation; and the quantum lift in which the bracket algebra becomes cleaner because the ambient operator world is natively Lie-algebraic. We also briefly summarize a set of toy experiments – not as settlement of anything but as a smoke test indicating that the formal machinery is tethered to concrete transfer behavior rather than floating off as pure notation. A concluding section sketches the wider territory covered in [1] but not developed here in detail: motivational systems, SubRep certificates, pattern mining, algorithmic chemistry, transport-aware storage, adaptive compression, Galois decompositions, discrete–continuous bridges, and the more speculative parts of the quantum agenda.

We present the basic concept of fluid-dynamics-based neural networks and argue that they are relevant to artificial general intelligence (AGI). The central idea is to treat activation, attention, or cognitive resource as a conserved density transported by an incompressible velocity field. Rather than spreading credit by isotropic diffusion or routing it by unconstrained attention weights, an Incompressible-Fluid Network routes a fixed budget along goal-shaped streamlines. The mathematical motivation comes from the relationship between Hamilton-Jacobi-Bellman (HJB) optimal control on the group of volume-preserving diffeomorphisms and incompressible Navier-Stokes (NS) dynamics: a value function gives a downhill policy, and after pushforward and Leray projection this policy becomes a divergence-free velocity field. For practical neural computation we work in finite graph or manifold discretizations, parameterize velocity in a solenoidal basis, use conservative advection updates, and combine global transport with local predictive-coding reactions. The resulting model offers a unified view of attention allocation, credit assignment, local learning, transfer, and regime switching. We include a deliberately simple smoke-test on a grid with hard obstacles, showing that a conserved activation budget can be routed into a target region while preserving total mass, non-negativity, and zero graph divergence. The experiment is not a performance benchmark; it is a sanity check that the proposed semantics are computationally meaningful. We close with a roadmap for extending this preliminary work toward AGI systems with fluid attention, cognitive Reynolds-number control, transweave transfer, and integration with symbolic and neural memory architectures.

We introduce a unifying framework showing how modular architectures emerge naturally when connection patterns are regularized by an optimal-transport (OT) cost. We represent any candidate architecture as a probability distribution over possible links and consider a dynamic in which links are created or removed as part of the same learning process as modifying link weights. We then add to the usual task loss a penalty that charges more for creating or strengthening distant connections than for local ones. Under mild formal conditions indicating that there is an underlying modular structure in the problem the network is learning to solve – even if heavily obscured by other phenomena – we then show that the optimal architecture places almost all its mass on a small number of modules (with only a bounded “leakage” outside), and that any gradient-based update of the combined loss is likely to stay trapped within those modules until convergence. We illustrate this in three settings. In predictive-coding neural networks with columnar structure, an OT penalty on inter-column links drives the system to form edge, stroke and loop detectors before ever wiring far-flung columns, yielding a hierarchical, stroke-based feature scaffold. In probabilistic logic networks (PLN), chaining and pruning of belief links under a reasoning-distance cost produces clusters of related concepts with sparse bridges between them. Finally, we give speculative arguments that these same dynamics may occur in biological brains – i.e. synapse growth and pruning under metabolic and wiring-length pressures may instantiate a generalized OT flow that gives rise to orientation columns, place fields and motor primitives. Across these domains, minimizing task error plus an OT transport penalty provides a general principle for the self-organization of functional modules.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties {F_1, F_2, …, F_n} and {W_1, W_2, …, W_m} with associated degrees {d_1, d_2, …, d_n} and {e_1, e_2, …, e_m}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W | F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

We present a conceptual framework for extending homomorphic encryption beyond arithmetic or Boolean operations into the domain of intuitionistic logic proofs and, by the Curry-Howard correspondence, into the domain of typed functional programs. We begin by reviewing well-known homomorphic encryption schemes for arithmetic operations, and then discuss the adaptation of similar concepts to support logical inference steps in intuitionistic logic. Key to our construction are polynomial functors and Bounded Natural Functors (BNFs), which serve as a categorical substrate on which logic formulas and proofs are represented and manipulated. We outline a complexity-theoretic hardness assumption – the BNF Distinguishing Problem, constructed via a reduction from Subgraph Isomorphism, providing a foundation for cryptographic security. Finally, we describe how these methods can homomorphically encode the execution of total, dependently typed functional programs, and outline strategies for making the approach potentially efficient, including software optimizations and hardware acceleration.

We present a framework for embedding abstract motivational principles into concrete AGI systems, bridging the gap between the formal theory of motivational structures and dynamics and the practical implementation of motivational systems for real-world applications and agents. We introduce MetaMo, a category-theory-based framework designed to ensure dynamical stability, self-coherence, and ethical alignment in open-ended AGI systems. MetaMo integrates a comonadic appraisal process with a decision monad, forming a pseudo-bi-monad structure that guides multi-objective reasoning and context-sensitive modulation of goals. The framework ensures that agents can pursue multiple, potentially conflicting goals while maintaining stability through contractive updates and over goals that enforce ethical constraints. We demonstrate the specialization of MetaMo in the Hyperon AGI system, where the agent's goals are organized into a hierarchical structure in line with the MAGUS motivational theory, with top-level metagoals focused on the two principle drives of Open-Ended Intelligence theory, individuation (self-preservation) and transcendence (self-expansion). These high-level goals dynamically influence the agent's decision-making and appraisal processes via the OpenPsi motivational dynamic, modulating exploratory behaviors and caution based on context. OpenPsi provides a flexible and context-sensitive appraisal system that updates emotional and motivational states in response to stimuli, supporting adaptive behavior in complex environments. By combining theoretical foundations (MetaMo) with more concretely grounded motivational frameworks (OpenPsi, MAGUS), we provide a concrete approach to integrating motivational systems into AGI architectures, ensuring ethical behavior, stability, and the ability to adapt and open-endedly self-modify over time.

This paper introduces ActPC-Geom, an approach to accelerate Active Predictive Coding (ActPC) in neural networks by integrating information geometry, specifically using Wasserstein-metric-based methods for measure-dependent gradient flows. We propose replacing KL-divergence in ActPC's predictive error assessment with the Wasserstein metric, suggesting this may enhance network robustness. To make this computationally feasible, we present strategies including: (1) neural approximators for inverse measure-dependent Laplacians, (2) approximate kernel PCA embeddings for low-rank approximations feeding into these approximators, and (3) compositional hypervector embeddings derived from kPCA outputs, with algebra optimized for fuzzy FCA lattices learned through neural architectures analyzing network states. This results in an ActPC architecture capable of real-time online learning and integrating continuous (e.g., transformer-like or Hopfield-net-like) and discrete symbolic ActPC networks, including frameworks like OpenCog Hyperon or ActPC-Chem for algorithmic chemistry evolution. Shared probabilistic, concept-lattice, and hypervector models enable symbolic-subsymbolic integration. Key features include (1) compositional reasoning via hypervector embeddings in transformer-like architectures for tasks like commonsense reasoning, and (2) Hopfield-net dynamics enabling associative long-term memory and attractor-driven cognitive features. We outline how ActPC-Geom combines few-shot learning with online weight updates, enabling deliberative thinking and seamless symbolic-subsymbolic reasoning. Ideas from Galois connections are explored for efficient hybrid ActPC/ActPC-Chem processing. Finally, we propose a specialized HPC design optimized for real-time focused attention and deliberative reasoning tailored to ActPC-Geom's demands.

We present MetaMo, a unified formal framework for AGI motivational systems, combining category theory, functional analysis and topology to support open-ended agents that self-modify and evolve their own goals and drives. A sequel paper shows how MetaMo maps onto concrete architectures like OpenPsi and MAGUS. MetaMo centers on a composite appraisal-then-decision operator F that carries both comonad (appraisal) and monad (decision) structure – a pseudo-bimonad – enabling clean “feel vs choose” pipelines. It enforces a contractive update law that dynamically keeps motivational states within a designated safe region, and it assumes a tubular topology that guarantees any achievable target lies on a thick, feasible path of incremental steps. From this foundation we extract five meta-motivational design principles: 1) Modular Appraisal-Decision Interface: separate mood updates from goal selection but allow just enough feedback so swapping their order only causes a tiny change; 2) Reciprocal State Simulation: share precise state-translation maps so agents can step into each other’s motivational frames for seamless hand-off and deep empathy; 3) Parallel Motivational Compositionality: run multiple motivational subsystems (e.g. exploration, ethics, service) in parallel and merge their outputs with small coherence corrections; 4) Homeostatic Drive Stability: apply damping so small disturbances fade and tighten control near boundary conditions; 5) Incremental Objective Embodiment: blend partway toward preferred motivational states each cycle, guaranteeing gradual convergence into a feasible "ideal region" without overshoot or destabilization or loss of coherent self-model. We argue that MetaMo guides the design of AGI systems that are stable yet adaptable, capable of safe, incremental self-improvement, trustworthy collaborators in multi-agent communities, and scalable via parallel sub-agents. We illustrate these concepts via a running example of an online research assistant.

We review the OpenCog Hyperon AGI architecture, which couples a self-modifying metagraph (the Atomspace) with the MeTTa pattern-rewriting language to realise a fully reflexive cognitive substrate. On top of that substrate the PRIMUS cognitive model instantiates working, declarative, and procedural memories, an attention economy, and a rapid goal-driven cognitive cycle. We argue that this stack satisfies every functional role identified by the Common Model of Cognition, while remaining light enough to serve as a seed architecture for open-ended self-improvement. Large-language models, formal reasoning engines, and evolutionary program learners all plug into Hyperon as specialised "lobes," yet the integrative hub remains the Atomspace itself. Running on the decentralised MeTTaCycle fabric, Hyperon avoids single-point capture and enables plural governance of its goal-evolution dynamics. We sketch a staged roadmap shows how, given a production Hyperon stack by late 2025, one might plausibly reach human-level AGI within a few years and then scale toward beneficial super-intelligence.

The Patterns of Cognition (PoC) framework casts diverse AGI algorithms—probabilistic logic networks, evolutionary program learning, deep Q-learning, attention focusing and more—as approximate stochastic dynamic programs on typed metagraphs. Each algorithm is implemented by a chronomorphism: an unfold functor that generates a tree of candidate states and a fold functor that collapses this tree using a preorder, forming a Galois connection that monotonically improves solution quality. Here we explain how to port this framework to the quantum computing domain, obtaining a similar unified treatment of AGI algorithms applicable to quantum implementation. The approach taken leverages the facts that in continuous time the chronomorphism operator approximates the Hamilton–Jacobi–Bellman (HJB) equation; whereas a logarithmic action → wavefunction transform, plus Wick rotation for diffusive noise, turns the HJB into the Schrödinger or heat equation. Thus every PoC chronomorphism lifts to a sparse Hamiltonian H_eff = H_C + H_R whose off-diagonal block H_C encodes combinatory expansion and whose diagonal block H_R encodes evaluation phases. Second-order Trotter or qubitization then realizes the small-time propagator U(Δ t) ≈ e^-iH_RΔ t/2 e^-iH_CΔ t e^-iH_RΔ t/2 in O(d ‖ H_eff‖ t) fault-tolerant gates, giving quadratic speed-ups in, for instance, batch size, action branching and fitness estimation. A rough resource analysis shows that a hypothetical next-generation Dirac3+ 10k-qubit machine would likely scale quite favorably to thousand-agent workloads. The sequel paper elaborates how this mechanism can be leveraged for a number of the key AI algorithms involved in the OpenCog Hyperon architecture—illustrating that the given mechanisms can be considered as a general-purpose scalable control loop for Hyperon-style quantum AGI systems.

Today, at this pivotal tipping point, we offer this participatory framework to guide the creation of an eventual Global Constitution for benevolent Artificial General Intelligence (AGI). We present this framework as a living compass, charting an unprecedented course toward a thriving future for life on Earth. We acknowledge that AGI may hold the key to solving some of the most complex challenges of our time, if humans and intelligent machines can collaborate to enhance the conditions of life on Earth. However, in the wrong hands or solely for financial and political gain, malicious applications of AGI’s potential could lead to unthinkable harm at catastrophic scales. This participatory framework is our urgent call to the global community of key decision-makers to begin putting steps in place for collectively stewarding AGI’s potential as a global commons.* In particular, we emphasize that AGI is nearing realization and requires a radically different approach than the current focus on narrow artificial intelligence.

We explore a novel paradigm (labeled ActPC-Chem) for biologically inspired, goal-guided artificial intelligence (AI) centered on a form of Discrete Active Predictive Coding (ActPC) operating within an algorithmic chemistry of rewrite rules. ActPC-Chem is envisioned as a foundational "cognitive kernel" for advanced cognitive architectures, such as the OpenCog Hyperon system, incorporating essential elements of the PRIMUS cognitive architecture. The central thesis is that general-intelligence-capable cognitive structures and dynamics can emerge in a system where both data and models are represented as evolving patterns of metagraph rewrite rules, and where prediction errors, intrinsic and extrinsic rewards, and semantic constraints guide the continual reorganization and refinement of these rules. Using a virtual "robot bug" thought experiment, we illustrate how such a system might self-organize to handle challenging tasks involving delayed and context-dependent rewards, integrating causal rule inference (AIRIS) and probabilistic logical abstraction (PLN) to discover and exploit conceptual patterns and causal constraints. Next, we describe how continuous predictive coding neural networks, which excel at handling noisy sensory data and motor control signals, can be coherently merged with the discrete ActPC substrate. Finally, we outline how these ideas might be extended to create a transformer-like architecture that foregoes traditional backpropagation in favor of rule-based transformations guided by ActPC. This layered architecture, supplemented with AIRIS and PLN, promises structured, multi-modal, and logically consistent next-token predictions and narrative sequences.

We articulate here a series of specific metagoals designed to address the challenge of creating AGI systems that possess the ability to flexibly self-modify yet also have the propensity to maintain key invariant properties of their goal systems 1) a series of goal-stability metagoals aimed to guide a system to a condition in which goal-stability is compatible with reasonably flexible self-modification 2) a series of moderated-goal-evolution metagoals aimed to guide a system to a condition in which control of the pace of goal evolution is compatible with reasonably flexible self-modification The formulation of the metagoals is founded on fixed-point theorems from functional analysis, e.g. the Contraction Mapping Theorem and constructive approximations to Schauder's Theorem, applied to probabilistic models of system behavior We present an argument that the balancing of self-modification with maintenance of goal invariants will often have other interesting cognitive side-effects such as a high degree of self understanding Finally we argue for the practical value of a hybrid metagoal combining moderated-goal-evolution with pursuit of goal-stability – along with potentially other metagoals relating to goal-satisfaction, survival and ongoing development – in a flexible fashion depending on the situation

AgingAging is best understood as a gradual, sometimes punctuated, change in the dynamical regime of a self-organizing network composed of heterogeneous complex processes interacting via complex nonlinear spatiotemporal interactions. Key easily observable aspects such as the “hallmarks of agingAging” represent specific manifestations of underlying holistic network dynamics. Different aspects of this self-organizing network are apt to be best understood by reference to different datasets and by means of different analytical approaches. However, it seems likely that to create therapies substantially increasing maximum human lifespan in a reliable way, ultimately a holistic understanding of the dynamics of agingAging across the organism will be required. This leads naturally to a network-based approach to data-analytics and hypothesis-formation and -evaluation, in which holistic models of agingAging in the organism are automatically assembled from multiple datasets and models addressing various aspects. One key issue in realizing a network-based approach to agingAging is the process of mathematically combining multiple models; toward this end we propose an assemblage of techniques beginning with a relatively simple quadratic programming based approach, and culminating in a “computational social science” approach in which multiple models collectively form a social network of models. Within that network, symbols and cultures, reflecting complex holistic patterns in the underlying data, may emerge. Another key issue is how to incentivize an appropriately diverse and capable community of individuals or organizations to contribute data and models to the holistic “Generative Cooperative Network” of models. We propose a tokenomics approach, in which a variety of cryptographic token types are used to incentivize contribution to the GCN. These issues comprise much of the inspiration for the Rejuve.AI project, which is building general mechanisms for GCN and tokenomic incentivization. Rejuve.AI is also creating a set of relatively simple agingAging-related models to seed the GCN, including: Automated integration of insights from these diverse models, based on diverse datasets, will enable prototyping of the overall GCN framework and will serve as a seed for broader growth of the GCN based on contributions from the research and Rejuve.AI app user communities. Growth of our holistic network will enable the formation of a dynamic, multiresolutional mechanistic simulation of the human body that will shed new light on the causes of agingAging and its treatment.