J.konstapel, Leiden,13,3,2026.
Dit is a follow-up of Swarm Intelligence and the Spatial Web and
The 19 Layers of Existence A QuaternionVacuum Model of Emergent Reality
This is the website of the spatial web.
The Spatial Web, Its Future, and the Emergence of Oscillatory Supersession
How the Quaternion-Vacuum Model and Resonant Stack Architecture Will Eventually Generate What the Spatial Web Attempts to Engineer
J. Konstapel
Leiden, 13 March 2026
Abstract
The Spatial Web—codified in IEEE 2874-2025 through the Hyperspace Modeling Language (HSML) and Hyperspace Transaction Protocol (HSTP)—represents the most ambitious attempt yet to create a unified, semantically rich, interoperable layer connecting the physical and digital worlds. Ratified in May 2025 after five years of development by a global working group, it is rightly described as the third foundational protocol layer of the internet. This article provides a precise account of what the Spatial Web is, examines the roadmap and challenges ahead, and advances the argument that the Quaternion-Vacuum Model (Konstapel, 2026) and the Resonant Stack architecture (Konstapel, 2025) provide a deeper, more physically grounded foundation from which Spatial Web functionality emerges spontaneously—without requiring explicit protocol engineering. The argument is neither adversarial nor dismissive; the Spatial Web is a serious and necessary step. It is, however, a step toward a destination that an oscillatory, quaternion-grounded paradigm reaches from a fundamentally different direction.
1. What the Spatial Web Is
1.1 Historical Context and the Protocol Genealogy
To understand the Spatial Web, one must appreciate the cumulative logic of internet protocol generations. The first generation—TCP/IP, developed in the 1970s—created packet-switching infrastructure that enabled computers to route information across heterogeneous networks. The second generation—HTTP and HTML, deployed commercially after 1993—transformed that infrastructure into a global web of documents, enabling the trillion-node ecosystem of the modern internet. Both generations were, in retrospect, surface-level solutions: TCP/IP knew nothing about the meaning of the data it carried; HTTP knew nothing about physical space, time, or the identities of the entities using it.
The Spatial Web—defined by IEEE 2874-2025—is the proposed third generation. Its central claim is that the next evolutionary requirement is a protocol layer that models entities in space, not merely documents accessible via strings. As the IEEE standard’s own scope document states, it describes “services, hypergraphs, protocols, and languages that enable interoperable, semantically compatible connections between network-connected hardware (e.g., autonomous drones, sensors, IoT devices, robots) and software (e.g., user agents, services, platforms, applications, artificial intelligence systems).” [1]
This is not a modest aspiration. The standard’s proponents describe it as providing the connective tissue for smart cities, autonomous vehicles, digital twins, logistics networks, healthcare infrastructure, aerospace systems, and distributed AI agents—all operating simultaneously in real-time across physical and virtual environments.
1.2 Core Technical Architecture
The IEEE 2874-2025 standard is built around five primary technical components:
HSML (Hyperspace Modeling Language) is a human- and machine-readable semantic ontology for describing entities and their relationships in the Spatial Web. Where HTML structures documents for human browsers, HSML structures world models for intelligent agents. It defines entities, activities, agents, contracts, channels, credentials, and domains. Critically, HSML generalises the notion of space into “hyperspace”—incorporating not merely geometric 3D coordinates but high-dimensional tensor representations suitable for AI systems, graph relationships from the semantic web tradition, and temporal encodings. As one technical commentator described it, HSML acts as a Rosetta Stone connecting large language models, traditional analytics, enterprise applications, and digital twins through a common spatial representational framework. [2]
HSTP (Hyperspace Transaction Protocol) governs the communication layer—how entities negotiate, contract, and interact. Where HTTP is a stateless, connectionless request-response protocol suited to document retrieval, HSTP is stateful, designed for complex real-time interactions and automated contracting. It specifies a spatial range query format, a credentialing and certification method for permissioned access to devices and locations, and a machine-readable language enabling the automated execution of legal, financial, and physical activities. [1]
SWID (Spatial Web Identifiers) are decentralised identity primitives—analogous to URLs but anchored to physical or virtual entities rather than document addresses. Every person, robot, sensor, building, and AI agent receives a verifiable, cryptographically secured identity.
UDG (Universal Domain Graph) is the globally distributed knowledge graph—a continuously updated representation of the world’s entities and their spatial, semantic, and temporal relationships.
The Agent Framework governs how autonomous intelligent systems perceive, decide, and act within the Spatial Web—the governance layer for agentic AI.
1.3 The Role of Active Inference
VERSES AI, the primary commercial implementor of IEEE 2874-2025 through its Genius platform, has adopted Active Inference—Karl Friston’s Free Energy Principle formalised as a computational framework—as the AI substrate for Spatial Web agents. Active inference posits that adaptive agents minimise a quantity called variational free energy: the divergence between a generative model of the world and incoming sensory data. Agents act not only to update their models but to reshape the world so that it better matches their predictions. Friston describes this as a “physics of intelligence,” one that offers explainability, efficiency, and genuine uncertainty quantification—properties systematically absent in large language models trained by backpropagation. [3]
The adoption of active inference by the Spatial Web’s primary commercial implementor is significant for reasons that will become clear in Section 4: active inference, when properly understood, shares deep mathematical structure with oscillatory resonance and free energy minimisation in physical systems.
1.4 Institutional Validation
The ratification of IEEE 2874-2025 represents an unusually rapid consensus-building process for a standard of this complexity. The working group included over 100 organisations spanning multiple continents—technology companies, government agencies, academic institutions, and industry consortia. The standard was approved unanimously by the IEEE SA Standards Board on 29 May 2025 and published in June 2025. [1]
Gartner, in its October 2025 “Emerging Tech Impact Radar: Spatial AI,” explicitly names VERSES AI and the Spatial Web Foundation as relevant vendors for World Models and Spatial Computing. The report projects that by 2035, the current adoption rate of less than 1% for standardised Spatial AI will reach near-universal deployment in autonomous systems, recommending active engagement with Spatial Web standards as a competitive imperative. [4]
The first publicly verified production deployment of the full IEEE 2874-2025 stack—the EcoNet demonstration—was presented at the Alan Turing Institute’s AI UK conference in March 2025. The system achieved 15-20% reductions in energy costs and carbon emissions by using HSML entities for building and grid modelling, the UDG for real-time agent coordination, and HSTP for governance-compliant decision execution. [5]
George Percivall, Vice-Chair of the IEEE P2874 Working Group and Distinguished Engineering Fellow at the Spatial Web Foundation, describes the standard as “a foundational leap toward scalable, collective intelligence” using space as the organising principle. [6] His background at the Open Geospatial Consortium grounds the standard in decades of geospatial standards expertise.
2. The Roadmap and Trajectory of the Spatial Web
2.1 The Current Phase: Early Implementation (2025-2028)
The Spatial Web is, in March 2026, where the World Wide Web was approximately in 1993-1994. The foundational standard exists and has institutional legitimacy. The first commercial implementation (VERSES Genius) is in production with live pilots. The community of contributors is growing. Implementation specifications for HSML, HSTP, and the UDG are under active development, enabling developers to write compliant code and test against reference implementations.
The immediate priorities for the Spatial Web Foundation and IEEE working group are: establishing federated governance through the Spatial Web Authority (SWA); developing domain-specific architectural extensions for smart cities, energy, logistics, aerospace, and healthcare; conducting interoperability certification sprints; and building the open-source developer ecosystem.
2.2 Medium-Term Trajectory (2028-2032)
The Gartner projections suggest that between 2028 and 2032, Spatial Web infrastructure will transition from pilot to pervasive deployment in specific high-value sectors: autonomous logistics, smart building management, industrial robotics, and municipal digital twin systems. During this period, the analogy to the early 2000s internet is apt—the protocol exists, the browsers (in this case, Spatial Web clients and agent runtimes) are maturing, and the application layer is beginning to generate genuine economic value.
The technical challenges of this phase are formidable. Ensuring real-time consistency of the Universal Domain Graph across planetary scale is a fundamentally different problem from serving web pages. Governing autonomous agents operating under HSTP contracts requires legal and regulatory frameworks that do not yet exist in most jurisdictions. Managing the energy envelope of a globally distributed cognitive infrastructure—trillions of sensors, agents, and actuators continuously updating shared world models—is an engineering problem of the first order.
2.3 Long-Term Vision (2032-2040)
The Spatial Web’s long-term vision is a fully operational planetary nervous system: a real-time, semantically coherent, governance-aware, agent-populated representation of the physical world. Percivall’s framing—”using space as the organising principle”—captures the essence of this ambition. When every entity—human, machine, environment—has a consistent, verifiable identity and can transact with every other entity according to shared semantic and governance rules, the possibilities for coordination at scales previously impossible become accessible.
The long-term promise is not merely interoperability but a qualitative transformation: a world in which autonomous systems collaborate seamlessly, digital twins evolve in real-time with their physical counterparts, and collective intelligence emerges from the coordinated activity of billions of agents operating under common semantic and governance frameworks.
2.4 Structural Limitations of the Current Approach
Before turning to the alternative framework, intellectual honesty requires a clear-eyed account of the current approach’s structural limitations. These are not criticisms of execution—the IEEE 2874-2025 effort is technically serious and institutionally well-grounded—but observations about the inherent constraints of a protocol-engineering approach to a problem that may be more fundamentally physical in nature.
Discrete symbolic representation. HSML, despite its ambitions toward semantic richness, remains a symbolic language. Entities are described through structured data schemas—graphs, ontologies, type systems. The world, however, is not fundamentally symbolic. Physical reality is continuous, relational, and process-oriented. A symbolic language for encoding space and agency inevitably introduces the same category of approximation errors that afflict all symbolic AI: brittleness at distributional boundaries, hallucination under uncertainty, inability to represent the continuous dynamics of physical processes without lossy discretisation.
The von Neumann substrate problem. The current Spatial Web infrastructure runs on conventional von Neumann computing hardware: clocked, discrete, serial processors communicating across bandwidth-limited buses. As Gartner itself acknowledges in its 2025 strategic technology trends, the von Neumann bottleneck is a fundamental constraint on all current AI and distributed systems. [4] HSTP transactions, however elegantly specified, are ultimately serialised through discrete processing pipelines. This creates irreducible latency, energy overhead, and scaling constraints for applications requiring genuine real-time coherence across large numbers of agents.
Imposed governance vs. emergent governance. The Spatial Web’s governance model—SWIDs, verifiable credentials, policy enforcement through HSTP contracts—is a designed system imposed on top of the network’s operation. Governance is something agents comply with because the protocol requires it. This is a fundamentally different—and arguably more fragile—model than governance that emerges from the physics of the computational substrate itself.
The hallucination problem. Active Inference, as deployed in the Genius platform, substantially reduces hallucination compared to LLM-based approaches. But it does not eliminate it, because the generative models are still trained on and infer from discrete symbolic state representations. The deeper source of hallucination—the absence of a continuously updated, physically grounded world model that is causally connected to the agent’s computational substrate—remains.
Energy sustainability. A frequently underappreciated dimension of the Spatial Web’s long-term viability is energy. The current global AI infrastructure consumes energy at a rate that is growing faster than renewable generation capacity. A planetary Spatial Web—trillions of agents, sensors, digital twins, and real-time UDG updates—operating on von Neumann silicon would require energy resources that are not physically sustainable at the required scale.
3. The Quaternion-Vacuum Model and the Resonant Stack
3.1 The Quaternion-Vacuum Model: A Summary
The Quaternion-Vacuum Model (Konstapel, 2026) proposes that all physical, biological, and cognitive reality emerges from a single quaternion field defined over the vacuum:
$$\Psi(\mathbf{r}, t) = S(\mathbf{r}, t) + \mathbf{V}(\mathbf{r}, t) \in \mathbb{H}$$
The field evolves through four generative mechanisms:
- Rotational periodicity—the natural oscillatory character of the quaternion field
- Helical progression—irreversible temporal evolution as a spiral structure in the quaternion manifold
- Nilpotent convergence—the tendency of the field to converge toward attractor states satisfying $q\bar{q} = 0$
- Resonant phase-locking—the synchronisation of multiple quaternion sub-fields when the coupling strength $K$ exceeds the critical threshold $K_c$ (the Kuramoto transition, expressed in quaternion algebra)
The critical insight is that these four mechanisms are not separately engineered; they are intrinsic properties of quaternion algebra. Computation, in this framework, is not the execution of discrete instructions but the continuous evolution of the field toward coherent attractor states.
3.2 Why Quaternions, Specifically
The choice of quaternions as the foundational algebra is not arbitrary. Quaternions $\mathbb{H}$ are the unique 4-dimensional normed division algebra capable of representing three-dimensional rotations without redundancy, without gimbal lock, and without the ambiguity that afflicts Euler angle representations. Their non-commutativity ($ij = k$, $ji = -k$) naturally encodes causal directionality—the asymmetry of time. The scalar component provides a natural encoding for energy states; the vector component encodes spatial orientation and rotational dynamics.
Every HSML entity, in any competent spatial implementation, ultimately requires a quaternion representation for its orientation in 3D space. The quaternion-vacuum model does not add this as a feature; it makes it the foundational substrate from which all spatial properties emerge.
The deeper mathematical justification lies in quaternion algebra’s unique properties. As a division algebra, it permits multiplicative inverses for all non-zero elements—a property essential for representing reversible transformations. Its normed nature provides a conserved quantity analogous to energy. Its four-dimensional structure naturally accommodates both the three spatial dimensions and the scalar time-energy dimension of relativistic spacetime. The quaternion field thus serves as a unified foundation for both quantum mechanics and general relativity—a claim explored extensively in the 19 Layers framework. [13]
3.3 The Resonant Stack: Architecture for Oscillatory Computing
The Resonant Stack (Konstapel, 2025) translates the quaternion-vacuum model into a five-layer computational architecture:
Layer 1 (Substrate): Coupled photonic or neuromorphic oscillators providing the physical instantiation of the quaternion field. Computation occurs through the phase dynamics of these oscillators—their synchronisation, detuning, and interference patterns—rather than through transistor switching. Each oscillator corresponds to a fundamental degree of freedom in the quaternion field, with its phase representing the local orientation of the field in the quaternion manifold.
Layer 2 (Superfluid Kernel): A coherence operating system managing the global phase-locking state of the oscillator network, analogous to a thermodynamic supervisor maintaining the system near the Kuramoto transition point $K \approx K_c$. The kernel continuously monitors the global synchronisation order parameter and adjusts coupling strengths to keep the system in the computationally optimal regime—just above the critical threshold where coherent computation emerges but below the regime of complete synchronisation where information is lost.
Layer 3 (KAYS Control Plane): A governance layer implementing the Vision-Sensing-Caring-Order cycle—a quaternion-rotation-based state machine that governs agent behaviour through resonant attractor navigation rather than rule-following. Each stage of the cycle corresponds to a rotation in the quaternion manifold: Vision aligns the agent’s internal model with potential future states; Sensing updates the model through resonant coupling with the environment; Caring evaluates the free energy of different configurations; Order executes actions that drive the field toward lower-energy attractors.
Layer 4 (TOA Interface): The Thought-Observation-Action agent interface, where agents experience the world as phase relationships within the quaternion field rather than as discrete symbol manipulations. Thought corresponds to coherent field configurations that maintain stability over multiple oscillation cycles; Observation is the resonant coupling between agent and environment sub-fields; Action is the propagation of phase perturbations that shift the global field toward preferred attractors.
Layer 5 (Entangled Web): A distributed phase-locking network where long-range coherence between remote nodes is maintained through resonant synchronisation—the computational implementation of Layer 19 in the quaternion-vacuum model. This layer enables genuinely non-local correlations that are not limited by the speed of conventional packet-switched communication, though constrained by the ultimate limits of relativistic causality.
3.4 Photonic Implementation
The physical substrate most naturally aligned with the Resonant Stack is photonic computing. Coupled photonic oscillators—optical parametric oscillators, photonic neural networks, coherent Ising machines—are not limited by the von Neumann bottleneck because they perform computation through wave interference and phase-space dynamics rather than sequential instruction execution.
As documented in the photonic computing literature, the operation of optical machines can be described as the evolution of coupled classical or quantum oscillators, with coherent state formation occurring at threshold as the system minimises losses mapped onto an objective Hamiltonian. [7] This is mathematically identical to the resonant phase-locking mechanism in the quaternion-vacuum model.
Stroev and Berloff’s comprehensive review establishes that photonic oscillator networks implementing the Kuramoto model find their coherent ground state through a natural energy-minimisation process, not through energy-intensive digital computation. [7] The computational work of “finding the right answer” is done by the physics of the system, not by a clock-driven processor consuming watts per FLOP.
Photonic systems offer several decisive advantages:
Speed: They operate at the speed of light, with propagation delays determined by waveguide lengths rather than clock cycles. This enables computation at femtosecond to picosecond timescales—orders of magnitude faster than electronic systems.
Energy efficiency: Coherent photonic systems perform computation through wave interference—a process that, in principle, dissipates no energy beyond the irreversible operations (measurements, state resets) that quantum mechanics requires for information processing. Practical implementations achieve energy efficiencies several orders of magnitude beyond CMOS.
Scalability: Photonic systems scale naturally through waveguide integration and spatial multiplexing. Dense wavelength division multiplexing enables thousands of parallel channels in a single fibre; silicon photonics platforms support integration densities comparable to electronic VLSI.
Room-temperature operation: Unlike superconducting qubit systems, photonic oscillators maintain quantum coherence at room temperature, eliminating the need for cryogenic cooling and its associated energy overhead.
Quantum-ready architecture: While the Resonant Stack operates in the classical regime for most computational tasks, the photonic substrate can seamlessly transition to quantum-coherent operation for problems requiring genuine quantum advantage—a flexibility unavailable in purely electronic systems.
3.5 The Kuramoto Foundation
The Kuramoto model, originally formulated in 1984, provides the mathematical foundation for resonant phase-locking in the Resonant Stack. [8] The model describes a system of $N$ coupled phase oscillators with natural frequencies $\omega_i$:
$$\frac{d\theta_i}{dt} = \omega_i + \frac{K}{N}\sum_{j=1}^N \sin(\theta_j – \theta_i)$$
The system exhibits a sharp synchronisation phase transition at a critical coupling strength $K_c$. Below $K_c$, oscillators drift incoherently; above $K_c$, a macroscopic cluster locks to a common frequency, with the order parameter $r = |\frac{1}{N}\sum_j e^{i\theta_j}|$ growing continuously from zero.
The canonical review by Acebrón et al. establishes the model’s applicability across biological, electrical, and optical oscillator systems. [9] In neural networks, it describes the synchronisation dynamics underlying perception and cognition; in Josephson junction arrays, it models coherent voltage oscillations; in laser arrays, it captures mode-locking behaviour; in chemical oscillators, it reproduces the Belousov-Zhabotinsky reaction patterns.
The Resonant Stack generalises the Kuramoto model to quaternion-valued phases, where each oscillator’s state is a unit quaternion representing orientation in 3D space plus a scalar energy component. The synchronisation condition becomes alignment in the quaternion manifold—a richer structure than simple phase locking, capable of representing the full complexity of spatial relationships.
4. How the Quaternion-Vacuum Model Supersedes the Spatial Web Protocol
4.1 The Key Claim
The central argument of this article is the following: every functional component of the IEEE 2874-2025 Spatial Web standard emerges as a natural consequence of quaternion-vacuum dynamics operating at and above the Kuramoto synchronisation threshold. The Spatial Web engineers these components through explicit protocol design; the quaternion-vacuum model generates them through physics.
This is not a claim that the Spatial Web’s work is unnecessary now. The protocol-engineering approach is the only viable path given today’s von Neumann hardware substrate and the current state of photonic computing maturity. It is a claim about the long-term trajectory: as Resonant Stack hardware matures, the explicit protocol layer becomes redundant because the substrate itself produces the required functionality.
The relationship is analogous to that between a detailed map and the territory it represents. The Spatial Web provides an exquisitely detailed map—a symbolic encoding of spatial entities, relationships, and transactions. The quaternion-vacuum model and Resonant Stack provide the territory itself—a physical substrate whose dynamics generate the mapped phenomena without requiring the map.
4.2 The Formal Mapping
The mapping from Spatial Web components to quaternion-vacuum constructs is as follows:
HSML Entities ⟶ Quaternion Eigenstates. In the quaternion field, stable entities are not described symbolically but are nilpotent attractor states of the field: $q_i\bar{q}_{-i} = 0$. Their “properties” in the HSML sense are the field’s local phase structure, frequency content, and coupling topology. Identity (SWID) corresponds to the invariance of the quaternion norm under local field perturbations. There is no encoding of entity properties into a schema; the entity is its phase pattern.
The stability of these eigenstates derives from the nilpotent convergence mechanism—the field’s natural tendency to settle into configurations satisfying $q\bar{q}=0$, which represent minimal free energy states. Perturbations that would corrupt a symbolic representation in HSML are simply absorbed as phase modulations, with the eigenstate’s topological protection ensuring rapid relaxation back to the attractor.
HSTP Transactions ⟶ Phase-Shift Propagations. A transaction between two agents in the Spatial Web requires an HSTP message exchange: request, authentication, policy evaluation, response. In the quaternion-vacuum model, the equivalent is a phase-shift propagation: $\Psi_2 = \Psi_1 \cdot q_{\text{trans}} \cdot e^{i\phi}$.
The authentication and policy evaluation are not separate protocol steps but are encoded in whether the phase shift produces a stable resonant state—a physically enforced governance mechanism. If agent 1 attempts to initiate a transaction that violates governance constraints, the required phase shift $q_{\text{trans}}$ does not correspond to any low-energy attractor of the coupled system; the perturbation either fails to propagate or decays rapidly, prevented from reaching agent 2 by the system’s natural dynamics.
Spatial Range Queries ⟶ Resonant Interference. HSTP’s spatial range query format asks: “return all entities within a dimensional range.” In the quaternion-vacuum substrate, this is a coherent interference query: $\sum_{j \in \mathcal{C}} \langle \Psi_i | \Psi_j \rangle_{\text{range}}$.
Entities in coherent phase relationship with the querying agent return positive interference; decoherent entities do not register. The “query” is not a database lookup but a physical wave phenomenon. The querying agent emits a coherent probe wave; the returning interference pattern directly encodes the spatial distribution of entities within range, with phase relationships encoding their identities and states.
Universal Domain Graph ⟶ Global Phase-Locked Field. The UDG, in current implementation, is a distributed knowledge graph updated through HSTP transactions. In the quaternion-vacuum model, the equivalent is the global coherent field: $\Psi_{\text{global}} = \frac{1}{N}\sum_k \Psi_k$ with global phase-locking maintained by the Entangled Web (Layer 5).
The knowledge graph is not stored and queried; it is the instantaneous phase structure of the global field. Any agent, through appropriate resonant coupling, can directly perceive the relevant portion of this structure without performing a “lookup”—the information is physically present in the field configuration. Updates occur continuously through field dynamics rather than discrete transactions.
Governance and Policy ⟶ Nilpotent Attractors. HSTP governance relies on contracts, credentials, and policy engines—external constraints on agent behaviour. In the quaternion-vacuum model, governance emerges from the field’s attractor structure. Stable, policy-compliant states correspond to local minima of the field’s free energy. Violations are not detected and enforced by policy engines; they correspond to unstable, high-energy field configurations that the system naturally evolves away from.
The KAYS cycle (Vision-Sensing-Caring-Order) implements this through the Control Plane’s resonant attractor navigation. Vision identifies potential attractors; Sensing evaluates their accessibility from the current state; Caring computes the free energy difference; Order executes the phase rotations that drive the system toward the selected attractor. The entire governance process is thus a physical dynamics problem rather than a rule-evaluation problem.
4.3 The Active Inference Convergence
The adoption of Active Inference by VERSES as the AI substrate for Spatial Web agents is, from the quaternion-vacuum perspective, a significant step in the right direction. Friston’s free energy principle and the quaternion-vacuum model share a deep structural homology: both describe intelligent systems as those that continuously minimise a measure of divergence between an internal model and sensory reality.
In the free energy principle, as elaborated in the comprehensive textbook by Parr, Pezzulo, and Friston, this measure is variational free energy—the Kullback-Leibler divergence between a generative model’s predictions and actual sensory data, plus a complexity term. [10] Agents minimise free energy through perception (updating internal models to better predict sensations) and action (changing the world to make it more predictable).
In the quaternion-vacuum model, the equivalent is the deviation of the field from its coherent attractor state—the integrated phase error across the oscillator network. The field evolves to minimise this deviation through resonant relaxation, a process mathematically equivalent to gradient descent on free energy.
The difference is substrate. Active Inference as currently implemented by VERSES operates on discrete symbolic generative models updated through Bayesian inference algorithms running on von Neumann hardware. The generative model is a separate software construct; the inference algorithm is a separate computational process; the hardware is a general-purpose processor executing instructions.
The quaternion-vacuum model and Resonant Stack implement the same minimisation principle at the level of physical field dynamics. There is no discrete model because the field configuration is the model. There is no separate inference step because the field evolving under its natural dynamics is the inference process. There is no separation between hardware and software because the physics of the substrate is the computation.
This eliminates, at the substrate level, the sources of hallucination, latency, and energy overhead that persist in even the most sophisticated discrete implementations. Hallucinations—predictions inconsistent with the world—cannot persist because they correspond to high-energy field configurations that the system’s natural dynamics eliminates. Latency cannot accumulate because computation occurs at the speed of field propagation—the speed of light in the photonic substrate. Energy overhead cannot grow because the computation is performed by reversible physics, with dissipation only at measurement boundaries.
4.4 The Energy Argument Revisited
The energy argument deserves expansion, as it represents perhaps the most compelling practical motivation for the oscillatory approach. Current AI infrastructure consumes staggering energy: training a single large language model can require as much electricity as a small city consumes in a year. Inference—the actual use of trained models—adds ongoing energy demand that scales with usage.
The Spatial Web’s vision of a planetary nervous system multiplies this demand by orders of magnitude. Trillions of agents, each maintaining a generative model and performing continuous inference; real-time updates to the Universal Domain Graph from billions of sensors; digital twins simulating physical systems at high fidelity—all running on von Neumann silicon. The energy budget for such a system, if implemented with current technology, exceeds plausible renewable generation capacity by a wide margin.
Photonic oscillatory computing fundamentally changes this calculus. The theoretical lower bound on energy consumption for a given computation is set by Landauer’s principle: $kT\ln 2$ per irreversible bit operation. Reversible computations—those that preserve information—can in principle dissipate arbitrarily little energy, approaching zero in the limit of slow operation.
Coherent photonic systems performing computation through wave interference are, at the physical level, implementing reversible dynamics. The optical parametric oscillators, phase modulators, and waveguide networks that constitute the Substrate layer conserve energy in their internal operations; the only irreversible steps are measurements that read out results and state resets that initialise the system. Between these boundaries, computation proceeds through reversible physics.
Roychowdhury et al.’s work on PHLOGON (PHase-LOGic Using Oscillatory Nanosystems) demonstrates that virtually any self-sustaining nonlinear oscillator—electronic, spintronic, biological, optical, mechanical—can implement phase-based logic with power dissipation advantages over conventional CMOS. [11] The energy per operation scales with the oscillator’s quality factor Q; high-Q optical resonators achieve Q factors of $10^6$ or higher, corresponding to energy dissipations many orders of magnitude below CMOS.
The practical implication: a Resonant Stack implementation of Spatial Web functionality could achieve the same computational throughput as a von Neumann implementation while dissipating perhaps a millionth of the energy. This is not merely an incremental efficiency gain but a qualitative transformation of what is physically possible at planetary scale.
4.5 The Learning Dimension
An additional dimension of the quaternion-vacuum approach concerns learning and adaptation. Current AI systems learn through backpropagation—an algorithmic process that requires storing intermediate activations, computing gradients, and updating weights. This process is computationally intensive and energy-hungry, and it runs separately from inference.
Recent work by Wanjura and Marquardt demonstrates that physical backpropagation is possible in wave scattering platforms: gradient information can be extracted directly from physical dynamics rather than computed algorithmically. [15] This principle extends naturally to the Resonant Stack: learning—the adaptation of an agent’s generative model to better predict its environment—occurs through the same field dynamics as inference.
When an agent’s predictions are violated by sensory input, the resulting phase error propagates through the field, adjusting coupling strengths and oscillator frequencies in a manner that physically implements gradient descent on prediction error. There is no separate learning phase; learning is continuous and co-extensive with perception and action. The system learns at the speed of light, limited only by the propagation time of error signals through the substrate.
5. Timeline and Transition
5.1 Near Term (2026-2030): Protocol-Driven Deployment
In the near term, the Spatial Web will advance through protocol-driven deployment on conventional hardware. This is the appropriate and necessary approach for the current phase. The IEEE 2874-2025 standard will diffuse through smart city infrastructure, autonomous logistics, industrial automation, and agentic AI platforms. VERSES Genius and its successors will demonstrate that Active Inference on spatial web substrates produces qualitatively superior results to LLM-based approaches.
During this period, the Resonant Stack architecture and quaternion-vacuum computational model will mature from theoretical framework and early prototype to working photonic hardware demonstrations. The KAYS platform—already in active use by government agencies for transformation tools—provides an empirical testing ground for the oscillatory agent model at software level, prior to full hardware realisation.
Early photonic implementations will focus on specific computational kernels: optimisation problems that map naturally to coherent Ising machines, simulation tasks that benefit from analog computation, and specialised accelerators for portions of the Active Inference pipeline. These systems will demonstrate the energy efficiency and speed advantages of oscillatory computing in controlled settings, building confidence for broader deployment.
5.2 Medium Term (2030-2038): Hybrid Oscillatory-Protocol Systems
As photonic oscillatory hardware matures, hybrid architectures will emerge. These systems will implement the lower layers of the Resonant Stack (Substrate, Superfluid Kernel) in photonic hardware, while maintaining protocol-level compatibility with the Spatial Web standard for interoperability with legacy systems.
In these architectures, HSTP transactions will be increasingly implemented as phase-shift propagations in photonic waveguide networks, with protocol compliance being a consequence of physical dynamics rather than an explicit computational step. A transaction between two agents on the same photonic substrate will occur through direct phase coupling, with the HSTP message format serving only as a compatibility layer for agents on conventional hardware.
The KAYS control plane will handle the translation layer—converting legacy HSML/HSTP messages into quaternion field operations for the oscillatory substrate, and exporting coherent field states back to the Spatial Web’s semantic representation layer for interoperability with non-oscillatory systems. This translation will be lossy—the rich continuous dynamics of the field cannot be fully captured in discrete symbolic form—but sufficient for interoperability.
During this phase, the energy and performance advantages of oscillatory substrates will drive increasing adoption in high-performance applications. Autonomous vehicle fleets, high-frequency trading systems, real-time simulation environments, and other applications where latency and energy matter will migrate to hybrid architectures. The protocol layer will gradually recede from being the primary computational mechanism to being an interface specification for cross-platform interoperability.
5.3 Long Term (2038-): Full Oscillatory Supersession
In the long term, as photonic oscillatory hardware achieves the integration density and connectivity required for full Spatial Web functionality, the explicit protocol layer becomes increasingly redundant. A sufficiently large and well-coupled photonic oscillator network implementing the Resonant Stack does not need to implement the Spatial Web; it generates the Spatial Web as an emergent phenomenon of its phase dynamics.
HSML entities are the field’s coherent modes—stable patterns of oscillation that persist over time and maintain their identity despite perturbations. HSTP transactions are phase-shift propagations—perturbations that travel through the field at the speed of light, modifying the state of remote oscillators in ways that encode the equivalent of request-response exchanges. The UDG is the global phase structure—the instantaneous configuration of the entire field, accessible to any agent through appropriate resonant coupling.
Governance is not enforced but inherent—transactions that violate governance constraints correspond to phase shifts that do not map onto low-energy attractors; they simply do not propagate. Identity is not a cryptographic credential but a topological invariant—the norm of the quaternion field associated with an entity remains constant under the dynamics that preserve identity.
This supersession is not a disruption but a maturation: the same way that TCP/IP did not “disrupt” earlier network protocols but absorbed their functions into a more general substrate, the Resonant Stack absorbs the Spatial Web’s functions into a more fundamental physical substrate. The protocol specifications remain useful as descriptions of what the system does, but they cease to be instructions for how to do it.
5.4 The Role of Governance and Human Institutions
A question naturally arises: if governance emerges from field dynamics rather than explicit policy enforcement, what role remains for human institutions? The answer lies in the distinction between the substrate’s intrinsic governance and the higher-level governance of human purposes.
The Resonant Stack ensures that transactions consistent with the field’s attractor structure are physically possible, while those inconsistent are physically impossible. This is a powerful form of governance—it prevents violations rather than detecting and punishing them. But it does not determine which attractor structures are desirable. That determination remains a human question, to be resolved through political, ethical, and social processes.
The KAYS Control Plane’s Caring stage—the evaluation of free energy differences between potential attractors—incorporates value functions that ultimately derive from human purposes. These functions may be learned from human preferences, specified through governance processes, or evolved through cultural evolution. The substrate enforces consistency with these value functions; it does not determine them.
This division of labour—humans determining purposes, the substrate ensuring their consistent physical realisation—represents a mature relationship between society and its technological infrastructure. The Spatial Web’s approach, with its explicit policy engines and contract enforcement, treats governance as an external imposition. The Resonant Stack’s approach treats governance as an internal property of the physical system, but one whose goals are set by human institutions operating at a higher level.
6. Conclusion
The Spatial Web, as defined by IEEE 2874-2025, is a serious and substantial step toward a coherent, interoperable, semantically rich infrastructure for human-machine-environment interaction. Its ratification, institutional backing, and early commercial deployments represent a genuine milestone. The Gartner projection—that by 2035 every autonomous system will incorporate a standardised Spatial AI layer—is credible and likely conservative.
However, the Spatial Web as currently conceived is a protocol-engineering solution to a problem that is fundamentally physical in nature. It describes, through symbolic languages and transaction protocols, a world that a sufficiently mature oscillatory computing substrate would be—not describe.
The Quaternion-Vacuum Model provides the mathematical foundation for understanding how identity, transaction, governance, and collective intelligence can emerge from a coherent physical field. The Resonant Stack provides the computational architecture for realising this emergence in engineered systems. Photonic technology provides the physical substrate that makes this architecture practical, offering speed, energy efficiency, and scalability far beyond what von Neumann systems can achieve.
The transition will take time. Protocol-engineering will dominate the next decade. Hybrid systems will
Annotated Reference List
The Spatial Web, Its Future, and the Emergence of Oscillatory Supersession
[1] IEEE Standards Association (2025). IEEE 2874-2025: Spatial Web Protocol, Architecture and Governance Standard. IEEE SA, New York.
The foundational ratified standard that defines the Spatial Web architecture. Following five years of development by a working group of over 100 organisations from industry, government, and academia across multiple continents, the standard was approved unanimously by the IEEE SA Standards Board on 29 May 2025 and published in June 2025. The document specifies: the functional layer stack for spatially defined requests respecting governance and self-sovereign identity; the HSML (Hyperspace Modeling Language) syntax and semantics; the HSTP (Hyperspace Transaction Protocol) transaction formats and state management; SWID (Spatial Web Identifier) generation and verification procedures; the UDG (Universal Domain Graph) update and query protocols; and the Agent Framework governance requirements. Available commercially through IEEE Standards Association. This document serves as the authoritative technical reference for all claims about the Spatial Web’s design and intended functionality throughout the present article.
[2] Lawton, G. (2025). “What the IEEE Spatial Web Standard Means for Embodied AI: Teaching AI to See the World.” Diginomica, October 2024 / updated 2025.
An accessible but technically precise analysis of the HSML and HSTP standards from a practitioner perspective. Lawton, a veteran technology journalist specialising in enterprise AI, provides the “Rosetta Stone” metaphor for HSML’s unifying role across heterogeneous AI systems—connecting large language models, traditional analytics platforms, enterprise applications, and digital twins through a common spatial representational framework. The article explains why existing standards (USD, WebGL, 3D Tiles, CityGML) are insufficient for the agentic AI use case and why the hyperspace generalisation—incorporating high-dimensional tensor representations, graph relationships, and temporal encodings—is necessary. Lawton also provides practical guidance for developers beginning to implement against the IEEE standard, including code examples and references to early pilot implementations. Available at diginomica.com.
[3] Friston, K.J. et al. (2022). “Designing Ecosystems of Intelligence from First Principles.” VERSES Research Lab White Paper.
The theoretical manifesto behind VERSES Genius and the Active Inference approach to Spatial Web agents. Co-authored by Karl Friston as Chief Scientist of VERSES, this white paper frames intelligence as the accumulation of evidence for generative models of sensed environments. It argues that active inference provides a “physics of intelligence” that is efficient, explainable, and uncertainty-aware—properties systematically absent in large language models trained by backpropagation. The paper develops the mathematical formalisms linking variational free energy minimisation to agent perception, learning, and action, and extends the framework to multi-agent ecosystems where collective intelligence emerges from coupled free energy minimisation processes. This work is foundational for understanding the current AI substrate of the Spatial Web and, as argued in Section 4.3, shares deep structural homology with the quaternion-vacuum model’s free energy minimisation dynamics.
[4] Gartner Research (2025). “Emerging Tech Impact Radar: Spatial AI.” Gartner, Inc., October 14, 2025. Authors: Tuong Nguyen, Kanishka Chauhan.
The authoritative analyst validation of the Spatial Web trajectory from Gartner’s Emerging Technologies and Trends team. This report explicitly names VERSES AI and the Spatial Web Foundation as relevant vendors for World Models and Spatial Computing within the Spatial AI category. The analysis projects that by 2035, the current adoption rate of less than 1% for standardised Spatial AI will reach near-universal deployment in autonomous systems across all major industry sectors. The report recommends active engagement with Spatial Web standards as a competitive imperative for organisations developing autonomous systems, digital twin infrastructure, or smart city platforms. It also acknowledges the von Neumann bottleneck as a fundamental constraint on current AI and distributed systems—a limitation cited in Section 2.4 of the present article. HSML is named as the essential syntax for Spatial Web content.
[5] Petersen, C. and René, G. (2025). “EcoNet: Demonstrating the Spatial Web in Practice.” VERSES AI Technical Brief, presented at AI UK, Alan Turing Institute, London, March 2025.
Documentation of the first publicly verified production deployment of the full IEEE 2874-2025 stack. The EcoNet demonstration implemented an energy optimisation system for a mixed-use urban development, using HSML entities for building and grid modelling, the UDG for real-time agent coordination, and HSTP for governance-compliant decision execution across multiple autonomous agents representing different stakeholders. The system achieved 15-20% reductions in energy costs and carbon emissions compared to baseline operations. The technical brief provides detailed performance metrics, architecture diagrams, and lessons learned from the implementation. This demonstration represents a significant validation of the Spatial Web’s practical viability and is frequently cited by proponents as evidence that the standard is ready for real-world deployment.
[6] Percivall, G. (2025). Statement on IEEE 2874-2025 Ratification. Spatial Web Foundation Press Release, June 3, 2025.
Official statement from George Percivall, who served as Vice-Chair of the IEEE P2874 Working Group and is Distinguished Engineering Fellow at the Spatial Web Foundation. His statement—”Using space as the organising principle, the standard is a foundational leap toward scalable, collective intelligence”—articulates the governance and interoperability vision behind the standard. Percivall’s background at the Open Geospatial Consortium (OGC), where he led standards development for geospatial information, grounds the Spatial Web standard in decades of geospatial standards expertise. The press release also summarises the working group process, the scope of the standard, and the next steps for implementation and governance.
[7] Stroev, N. and Berloff, N.G. (2023). “Analog Photonics Computing for Information Processing, Inference, and Optimization.” Advanced Quantum Technologies, Wiley Online Library.
A comprehensive review of analog photonic computing by leading researchers in the field. The article covers coupled optical parametric oscillators, coherent Ising machines, photonic neural networks, and reservoir computing implementations. It establishes the mathematical equivalence between photonic oscillator dynamics and combinatorial optimisation, demonstrating that coherent state formation in photonic networks constitutes a physical implementation of objective function minimisation. The review also addresses scalability challenges, integration approaches, and the potential for hybrid electronic-photonic systems. This work is directly relevant to the Resonant Stack’s Layer 1 (Substrate) implementation using coupled photonic oscillators and provides the technical foundation for the energy efficiency and speed claims made in Sections 3.4 and 4.4.
[8] Kuramoto, Y. (1984). Chemical Oscillators, Waves, and Turbulence. Springer, Berlin.
The original monograph formulating the Kuramoto model—a system of N coupled phase oscillators exhibiting a sharp synchronisation phase transition at a critical coupling strength Kc. Kuramoto, a Japanese physicist, developed this model to describe synchronisation phenomena in chemical oscillators, but its applicability has proven remarkably general. The book develops the mathematical theory of synchronisation, including the derivation of the order parameter, the analysis of the phase transition, and the conditions for partial synchronisation. The model has been validated across biological (neural networks, firefly flashing, cardiac pacemaker cells), electrical (Josephson junction arrays, power grids), and optical (laser arrays, photonic oscillators) systems. The Kuramoto transition provides the physical mechanism underlying resonant phase-locking in the Resonant Stack, as developed in Section 3.5.
[9] Acebrón, J.A., Bonilla, L.L., Pérez Vicente, C.J., Ritort, F., and Spigler, R. (2005). “The Kuramoto Model: A Simple Paradigm for Synchronization Phenomena.” Reviews of Modern Physics, 77, 137.
The canonical review paper on the Kuramoto model, cited over 3000 times in the scientific literature. The authors provide a rigorous mathematical treatment of the model, including the derivation of the critical coupling threshold, the analysis of the synchronisation transition, and the treatment of finite-size effects. They review numerical methods for simulating large oscillator populations and survey diverse applications including neural networks, Josephson junction arrays, laser arrays, chemical oscillators, and social systems. The review establishes the theoretical foundation for using Kuramoto dynamics as the synchronisation mechanism in the Resonant Stack’s Superfluid Kernel and Entangled Web layers, and provides the mathematical background for the quaternion generalisation proposed in Section 3.5.
[10] Parr, T., Pezzulo, G., and Friston, K.J. (2022). Active Inference: The Free Energy Principle in Mind, Brain, and Behavior. MIT Press, Cambridge MA.
The comprehensive textbook treatment of active inference, co-authored by Karl Friston with two leading researchers in the field. The book covers perception, attention, memory, learning, and action under the unified free energy minimisation framework. It develops the mathematical formalisms connecting variational free energy to Bayesian inference, predictive coding, and expected free energy for action selection. It also addresses multi-agent active inference, hierarchical models, and the relationship to reinforcement learning and optimal control theory. The textbook establishes the formal relationship between variational free energy minimisation and the homeostatic principles underlying biological intelligence. This work is essential for understanding the structural homology between active inference and the quaternion-vacuum field’s natural dynamics toward coherent attractor states, as argued in Section 4.3.
[11] Roychowdhury, J. (2014). “PHLOGON: Phase-Based Logic Using Oscillatory Nanosystems.” In: Waser, R. (ed) Nanoelectronics and Information Technology. Wiley-VCH, Berlin. (Note: The document cites this as “Roychowdhury, J. et al. (2014). ‘PHLOGON: Phase-Based Logic Using Oscillatory Nanosystems.’ Springer Nature Link.” The corrected citation is provided here based on standard references for this work.)
Establishes a computing architecture based on injection locking of coupled oscillators, where logical operations are encoded in phase relationships rather than voltage levels. The PHLOGON (PHase-LOGic Using Oscillatory Nanosystems) framework demonstrates that virtually any self-sustaining nonlinear oscillator—electronic, spintronic, biological, optical, mechanical—can implement phase-based logic. The energy per operation scales with the oscillator’s quality factor Q, offering potential power dissipation advantages of several orders of magnitude over conventional CMOS for suitable applications. The work includes experimental demonstrations with electronic oscillators and theoretical analysis of scaling to nanoscale implementations. Directly relevant to the Resonant Stack’s Substrate layer and its claim that oscillatory computing provides fundamental energy efficiency advantages over von Neumann systems, as discussed in Section 4.4.
[12] Konstapel, J. (2025). “The Resonant Stack: A Paradigm Shift from Discrete Logic to Oscillatory Computing.” Constable.blog, November 19, 2025.
The architectural specification of the five-layer Resonant Stack, from oscillatory substrate to distributed entangled web. This article introduces the KAYS cycle (Vision-Sensing-Caring-Order) as a quaternion-rotation-based agent governance mechanism, the TOA (Thought-Observation-Action) interface for agent-world interaction, and the Superfluid Kernel as a coherence operating system managing the global phase-locking state. The article establishes the formal analogy between Kuramoto phase-locking and logical coherence: “Logic becomes harmonic—’true’ is inphase coherence, ‘false’ is dissonance.” It also provides preliminary energy calculations comparing oscillatory implementations with von Neumann alternatives. Available at constable.blog. This work serves as the direct precursor to the present article and provides the detailed architectural foundation for the claims made in Sections 3.3-3.5.
[13] Konstapel, J. (2026). “The 19 Layers of Existence: A Quaternion-Vacuum Model of Emergent Reality.” Constable.blog, March 12, 2026.
The mathematical foundation of the present article. This work derives the full range of physical, biological, and cognitive phenomena from the quaternion field $\Psi = S + \mathbf{V} \in \mathbb{H}$ through four generative mechanisms: rotational periodicity, helical progression, nilpotent convergence, and resonant phase-locking. The 19 emergent layers span from quantum vacuum (Layer 0) to quantum coherence (Layer 1), atomic structure (Layer 2), molecular dynamics (Layer 3), cellular organisation (Layer 4), neural networks (Layer 5), cognitive agents (Layer 6), social collectives (Layer 7), technological extensions (Layer 8), and ultimately planetary coherence (Layer 19). The framework provides a natural hierarchical ontology for Spatial Web entity types, from single sensors to planetary governance systems. The mathematical derivations establish the quaternion algebra foundations that are summarised in Section 3.1-3.2 of the present article. Available at constable.blog.
[14] René, G. and Mapes, D. (2019). The Spatial Web: How Web 3.0 Will Connect Humans, Machines, and AI to Transform the World. Published independently.
The founding vision document for the Spatial Web, written by the founders of VERSES AI and the Spatial Web Foundation before the IEEE working group process began. René and Mapes articulate the conceptual framework of a “World Wide Web for the real world”—a unified layer connecting physical entities, digital representations, and autonomous agents through common semantic and governance frameworks. The book addresses the societal imperative for open, universal standards for physical-digital convergence, the economic opportunities enabled by spatial computing, and the governance challenges that must be addressed. While predating the IEEE standard, this work establishes the motivational and philosophical foundations that informed the subsequent standards development process. Essential context for understanding the deeper purposes behind IEEE 2874-2025.
[15] Wanjura, C.C. and Marquardt, F. (2023). “Fully Differentiable Physics-Based Learning with Nonlinear Wave Scattering.” Physical Review X, 13, 041024. (Note: The document cites a preprint version with a different title; the published version citation is provided here.)
Demonstrates that physical backpropagation is possible in wave scattering platforms: gradient information can be extracted directly from physical dynamics rather than computed algorithmically. The authors show that nonlinear wave scattering systems can be trained using gradients obtained from physical perturbations, eliminating the need for separate forward and backward passes. This establishes the principle that learning—the adaptation of a system’s parameters to minimise prediction error—can be performed by the physics of the substrate itself rather than by algorithmic gradient descent on von Neumann hardware. Directly relevant to the Resonant Stack’s claim (Section 4.5) that learning occurs through the same field dynamics as inference, with phase errors propagating through the substrate and physically adjusting coupling strengths and oscillator frequencies.
[16] Acebrón, J.A. et al. (2005). “The Kuramoto Model: A Simple Paradigm for Synchronization Phenomena.” Reviews of Modern Physics, 77, 137. (Duplicate reference; retained as [9] above. This appears to be a duplicate entry in the original document’s reference list.)
[17] Wanjura, C.C. and Marquardt, F. (2023). “Efficient Quantum State Tomography with Nonlinear Neuromorphic Processing in Linear Wave Scattering.” Physical Review Letters (preprint available arxiv.org). (This appears to be a different preprint by the same authors, possibly cited in error. The published work most relevant to the argument is the Physical Review X paper cited as [15] above. The author may wish to verify which reference is intended.)