Navier–Stokes Existence & Smoothness

The work develops a new diagnostic framework for analysing the existence and smoothness of threedimensional incompressible Navier–Stokes flows. Two localized, scale-invariant quantities are introduced: a localized energy functional that measures kinetic-energy concentration in parabolic cylinders, and a vorticity-coherence functional that quantifies alignment of vorticity structures at critical scales. Together, these diagnostics unify small-data global regularity theory, ε-regularity criteria, and partial regularity results within a single formulation.

Current Preprint DOI: https://doi.org/10.5281/zenodo.18040834
Status: Ongoing

Yang–Mills Mass Gap (Constructive Proof)

A constructive proof of the Yang–Mills mass gap for four-dimensional SU(𝑁) Yang– Mills theory in a weak-coupling regime, formulated through a gauge-invariant Hamiltonian and Euclidean lattice framework. At fixed cutoff, we establish a gauge-invariant Hilbert-space formulation, self-adjointness of the cutoff Hamiltonian, a strictly positive lower spectral bound on the vacuum-orthogonal sector, and a reflection-positive Euclidean Wilson measure with associated transfer-operator structure. The continuum problem is organized through blocked transfer operators at fixed physical Euclidean time thickness and a bounded gauge-invariant physical-channel formulation. The continuum step is completed by combining the internal reduction framework with imported multiscale results that provide boundary-uniform logarithmic Sobolev control, interface and large-field estimates, volume-uniform transfer-gap control, uniqueness and universality of the Euclidean continuum limit, and restoration of continuous Euclidean covariance with Wightman reconstruction

Current Preprint DOI: https://doi.org/10.5281/zenodo.19166488

Status: Ongoing

Hodge Conjecture: Analytic–Spectral Reformulation

An analytic–spectral framework related to the Hodge Conjecture. An intrinsic elliptic operator is introduced whose kernel captures precisely the cohomology classes arising from algebraic Chern–Weil constructions. The Hodge Conjecture is shown to be logically equivalent to the absence of additional rational harmonic classes beyond this kernel, thereby isolating the remaining obstruction in analytic terms. The obstruction is proven to vanish for very general members of polarized families. No complete proof of the Hodge Conjecture is claimed

Current Preprint DOI: https://doi.org/10.5281/zenodo.17977164

Status: Ongoing

Riemann Hypothesis: A Spectral Determinant Proof

A spectral determinant framework for the Riemann Hypothesis based on a self-adjoint operator construction and Krein spectral shift theory. Starting from the completed Riemann xi-function, we define a family of regularized Schrödinger operators  as bounded perturbations of the harmonic oscillator, for which trace-class resolvent differences and perturbation determinants are rigorously available. Using spectral zeta regularization, we relate the logarithmic derivative of the perturbation determinant to a spectral shift function associated with the pair . The central result is a non-circular identification of this spectral shift function with the boundary phase of the xi-function, established via explicit trace and Fourier analysis in the regularized setting and normalized by high-energy asymptotics. This yields an exact determinant identity between the operator-theoretic perturbation determinant and the xi-function, up to a nonvanishing entire factor. Since zeros of the determinant correspond to eigenvalues of a self-adjoint operator, all zeros of the xi-function are shown to be real. The regularization is then removed by controlled trace-norm convergence.

Current Preprint DOI: https://doi.org/10.5281/zenodo.18135810

Status: Ongoing

Birch and Swinnerton-Dyer Conjecture: Hamiltonian–L-Function Mapping

Deriving a spectral operator whose trace asymptotics correspond to the analytic rank, linking elliptic curve invariants to energy eigenstructure.

Early Preprint DOI: https://doi.org/10.31219/osf.io/gnxza_v2

Status: Ongoing

The Timeless Energy-Space Framework

A reformulation of physics that removes time as a fundamental variable, replacing temporal evolution with deterministic transitions across entropy-structured gradients in energyspace. In this framework, all dynamical processes are governed by changes in energy-space coordinates rather than explicit time dependence, preserving conservation laws and causal coherence while offering a new foundation for classical and quantum theories. The mathematical structure is developed through an energy-space Hamiltonian, a reformulated Dirac equation, and entropy-gradient geodesics that define causal propagation without temporal parameters. This approach is contrasted with other timeless or entropic proposals—including Barbour’s relational dynamics, the Page–Wootters mechanism, Rovelli–Connes thermal time, and Verlinde’s entropic gravity—highlighting the distinct use of entropy gradients as causal drivers. The framework recovers standard physics as a limiting case: Newtonian and relativistic mechanics, quantum mechanics, and cosmological dynamics all emerge naturally when energy-space transitions are mapped back onto spacetime. Testable predictions include measurable deviations in atomic clock frequencies, interferometric phase shifts, and entanglement correlations, as well as potential imprints on cosmological observables such as CMB anisotropies. These falsifiable criteria provide an empirical route for assessing the framework. By shifting the basis of fundamental physics from time to energy-space, this work proposes a coherent and testable extension of physical law that addresses long-standing issues of causality, entropy, and unification.

Current Preprint DOI: https://doi.org/10.5281/zenodo.17984015

Energy-Space Gravity

A reformulation of gravity in which spacetime curvature emerges from entropy gradients in a generalized energy-space manifold, eliminating the need for fundamental time. Building on thermodynamic principles, we derive entropy-corrected Einstein field equations and modified geodesic motion from a covariant variational principle. The resulting framework predicts gravitational effects as a consequence of entropy divergence, offering a unified perspective on black hole thermodynamics, cosmic acceleration, and quantum gravity. Energy-space gravity predicts entropy-induced modifications to gravitational-wave propagation, black hole horizon structure, and cosmological observables, with the tensor-wave sector subject to strong constraints from high-coherence interferometric observations. We propose concrete experimental and observational tests—including pulsar timing anomalies, Casimir effect shifts, entropy-driven gravitational lensing, and entropy-modulated nucleosynthesis—to validate the theory. The framework integrates with loop quantum gravity and holography, suggesting a deeper entropic origin of quantum geometry. This work establishes energy-space gravity as a testable, time-free extension of General Relativity, capable of resolving longstanding tensions between gravitation, thermodynamics, and quantum theory.

Current Preprint DOI: https://doi.org/10.5281/zenodo.19153232

The Unified Energy-Space Deterministic Framework (UESDF)

Integrating entropy-driven attractor states across multiple domains, including quantum mechanics, biological evolution, societal dynamics, astrophysical structuring, and artificial intelligence cognition. Numerical simulations and AI-driven analyses indicate that entropy is not a measure of disorder but a structuring force that governs deterministic transitions across complex systems. Computational evidence is presented showing that entropy follows structured attractor pathways rather than increasing randomly, providing a theoretical basis for deterministic evolution at all scales. This challenges conventional interpretations of entropy, randomness and stochastic processes by proposing that what appears as randomness is often structured determinism operating in an imperceptible higher-dimensional energy-space framework.

Early Preprint DOI: Witheld

Entropy-Dependent Extension of General Relativity

We introduce a minimal entropy-dependent extension of General Relativity in which the spacetime metric becomes a member of a continuous family of manifolds indexed by an entropy coordinate S. The action incorporates a kinetic coupling between neighboring entropy manifolds through a quadratic term in ∂ₛg, producing modified Einstein equations that reduce exactly to GR when ∂ₛg = 0.

Early Preprint DOI: Witheld

An Entropic Multi-Manifold Origin for Dark Matter and Dark Energy

A geometric–entropic framework emerging from the Energy-Space framework that offers a unified explanation for dark matter and dark energy. By combining entropy gradients, cross-manifold curvature terms and multi-layer spacetime geometry, this research programme reveals how galactic rotation curves, halo profiles, black-hole core structure, and cosmic acceleration may arise from a single underlying mechanism. This line of research represents one of ACoRI’s most significant theoretical developments, providing a coherent and falsifiable alternative to particle dark matter and ΛCDM, grounded in a single geometric principle.

Current Preprint DOI: https://doi.org/10.5281/zenodo.17901259

Empirical Validation of the Entropic Multi-Manifold Origin of Dark Matter and Dark Energy

We present an empirical validation of the Entropic Multi-Manifold Origin of Dark Matter (EMMO) framework using galaxy rotation curves and galaxy–galaxy weak lensing. Building on a previously introduced theoretical model in which effective dark matter emerges from entropy-driven curvature effects, we test the framework against observational data without fitting to lensing measurements. We analyse rotation curves from the SPARC database for 175 disk galaxies, extracting halo parameters under the EMMO prescription and constructing ensemble predictions. These rotation-curve-calibrated halos are then projected into weak-lensing observables and compared with Sloan Digital Sky Survey (SDSS) galaxy–galaxy lensing measurements. We find that the EMMO halo profiles derived solely from galaxy rotation curves reproduce the observed radial dependence of galaxy–galaxy weak lensing signals across luminosity bins. Agreement in normalization is obtained in stellar-mass-selected central galaxy samples, while deviations in satellite-dominated regimes delineate the expected limits of halo-only modelling. These results demonstrate that a single entropy-driven halo prescription can simultaneously account for galaxy rotation curves and weak lensing, providing non-trivial empirical support for the EMMO framework as an alternative to particle dark matter.

Current Preprint DOI: https://doi.org/10.5281/zenodo.17932432

Universal Attractor Hypothesis

This programme investigates a unifying principle behind the emergence of stable structures across physics. Many systems—from atomic orbitals and quasicrystals to plasma filaments, neural networks and the cosmic web—tend to evolve toward intermediate-entropy attractor states where stability is maximized under global geometric or dynamical constraints. ACoRI explores this attractor mechanism as a potential general law of structure formation, combining entropic dynamics, geometric constraints, and multi-scale emergence. Current work focuses on developing the mathematical framework, testing model predictions, and identifying cross-scale signatures of universal attractor behaviour.

Current Preprint DOI 10.5281/zenodo.17807806

Quantum Gravity Framework

We present a time-independent formulation of gravity in which spacetime evolves along gradients of a scalar entropy field rather than coordinate time. The entropy field S(x) is defined as a functional of the Yang–Mills curvature 𝐹_𝜇𝜈𝐹^𝜇𝜈, establishing a microscopic link between gauge dynamics and geometry. Variation of an entropy-metric action yields modified Einstein equations with an additional stress–energy contribution 𝑇_𝜇𝜈 (S) arising from entropy gradients. In the limit S = S_0, the standard Einstein field equations are recovered, ensuring compatibility with General Relativity. In non-equilibrium regimes, the entropic contribution produces gravitational effects typically attributed to dark matter and dark energy. Galactic rotation curves flatten without invoking new particle species, while large-scale entropy displacement generates late-time cosmic acceleration without a cosmological constant. A numerical validation using 30 representative galaxies from the SPARC database shows that 27 systems are reproduced with reduced chisquared below 3, providing strong preliminary evidence that the entropy–metric correction captures the observed diversity of galactic rotation curves.

Current Preprint DOI https://doi.org/10.5281/zenodo.17900670

The Entropic No-Boundary Hypothesis

The Entropic No-Boundary (ENB) theory is presented as a unified geometric cosmological framework in which the Universe is finite yet without spatial boundary, and in which the phenomena usually attributed to dark matter and dark energy arise from entropy-extended geometry rather than from new particle species or a fundamental vacuum-energy component. In ENB, observable spacetime is obtained from entropy-weighted averaging across a continuous family of entropy-indexed manifolds, so that the no-boundary condition is implemented dynamically through smoothness, analyticity, and integrability across the entropic dimension. Variation of the entropy-extended action yields additional effective stress-energy terms sourced by entropy gradients and cross-manifold curvature, producing dark-sector-like behaviour within a single geometric mechanism. We summarize the full ENB validation programme carried out across five linked studies: theoretical formulation, 175-galaxy SPARC rotation-curve testing, Bayesian hierarchical population inference, weak-lensing consistency, cosmological background expansion and linear-growth validation, and compressed precision-cosmology likelihood analysis. The results show that the minimal curvature-like cosmological limit is excluded, while the generalized ENB sector contains flat ΛCDM exactly as the special case 𝑤_𝑆 = -1 and remains observationally viable in its empirically supported parameter corridor. In the tested precision dataset combination, ENB is statistically indistinguishable from flat ΛCDM, with Δ𝜒2 ≈ -0.55. Taken together, these results establish ENB as a coherent, multi-scale validated geometric theory of a finite unbounded Universe and of a unified dark sector.

Current Prepring DOI: https://doi.org/10.5281/zenodo.18905269

Applicable Validation Works:

Tier I: 175 SPARC Galaxies: https://doi.org/10.5281/zenodo.18840632

Tier II: MCMC, Bayesian Hierarchical Population and Weak Lensing: https://doi.org/10.5281/zenodo.18841148

Tier III: Cosmological Background and Linear-Growth: https://doi.org/10.5281/zenodo.18898968

Tier IV: Precision Cosmology: https://doi.org/10.5281/zenodo.18899224

Status: Multiple completed manuscripts; under refinement and journal submission.

Projects exploring conceptual frontiers connecting physics, computation, biology, and space systems.

CATS — Curvature-Aligned Transport System

A theoretical framework for near-instantaneous spatial repositioning using deterministic energy-space pathways, curvature alignment, and controlled transition geometry.

CATS does not manipulate spacetime geometry. Instead, it operates entirely within classical EM fields and the ESF geometric structure, offering a configuration-space transport mechanism distinct from warp drives, wormholes, or nonlocal physics. The result is a unified theoretical and engineering framework that is mathematically consistent, physically grounded, experimentally falsifiable, and technologically achievable. The monograph establishes the foundational basis for future laboratory experiments, high-fidelity simulations, and the longterm development of curvature-aligned transport technologies.

Note: CATS is presented as a testable transport hypothesis grounded in deterministic energy-space field structuring. No claim of realized technology is made. All quantitative performance estimates (e.g., energy budgets, stability thresholds) are provisional and subject to empirical verification in the staged experiments defined herein.

Monograph Volume I Link: https://amzn.eu/d/fCkCTGb

Plasma-Based Cognitive Architectures and Plasma-Driven Origins of Life

This line of research explores the hypothesis that plasma — not just as hot ionized gas but as a complex electromagnetic medium — may form self-organizing, information-storing, adaptive structures that could serve as a form of non-biological cognition.
Building on our book The Living Spark and associated theoretical work, we examine how magnetic flux ropes, double layers, oscillatory modes and topological field configurations can enable memory, feedback, signal processing, and stability over astrophysical timescales. Rather than presuming life must be biochemical, this programme opens the possibility that non-biological intelligence might naturally arise in high-energy or magnetized cosmic environments — offering a new paradigm for thinking about extraterrestrial intelligence, unconventional life, and broader forms of “thinking matter.”
We aim to (1) formalise the physics of plasma cognition rigorously, (2) explore potential observable signatures, and (3) identify environments — in astrophysics, planetary science, or early-universe cosmology — where plasma-based cognition might manifest or be detectable.

On the Plausibility of Cognitive or Proto-Sentient Artificial Intelligence Under Classical, Quantum, and Self-Maintaining System Architectures

This work examines whether artificial intelligence could develop cognitive or protosentient properties by comparing biological, plasma-based, classical computational, and quantum-integrated systems within a unified physical framework. Cognition is treated as an emergent property of systems capable of maintaining coherent internal dynamics in the presence of dissipation. We identify substrate-neutral structural requirements—including metastable attractor behaviour, energy and entropy regulation, feedback-driven model updating, and partial autonomy—and evaluate how different systems satisfy these criteria. Biological cognition fully meets them; structured plasmas satisfy several; classical artificial intelligence meets only a limited subset due to its lack of intrinsic stability and self-maintenance. Quantum-integrated architectures, however, may support more robust internal dynamics through coherence, highdimensional modelling, and regulated informational structure. These observations suggest that proto-cognitive behaviour in artificial systems is physically plausible under specific dynamical conditions. The analysis provides a systematic framework for assessing cognitive potential across substrates and outlines pathways by which future AI, particularly quantum hybrid systems, may approach the threshold of proto-sentience.

Current Preprint DOI: https://doi.org/10.5281/zenodo.17924616

A State-Space and Entropy-Based Framework for Understanding Cancer as a Complex Adaptive System

Cancer is increasingly recognised as a complex adaptive system characterised by heterogeneity, phenotypic plasticity, microenvironmental coupling, and continuous interaction with host-level constraints. While these features are well established in contemporary oncology, they are often analysed in isolation rather than within a unified dynamical framework. Here, we present a physics-informed, systems-level interpretation of cancer based on the concept of intermediate-entropy attractors. Building on prior theoretical work in physics, tumour–host dynamics are formulated as trajectories through a high-dimensional state space defined by genetic, phenotypic, spatial, metabolic, and immune variables. Entropy is used strictly in an operational sense, representing measurable heterogeneity and uncertainty rather than a causal force. We propose that tumour robustness and persistence may be associated with bounded intermediate-entropy regimes, where structured variability and stabilising coupling between degrees of freedom permit adaptation without loss of coherence. Low-entropy regimes correspond to constrained, homogeneous states, while high-entropy regimes reflect loss of organisation and viability. Importantly, robustness is argued to depend not only on entropy magnitude, but on the coupling structure between entropy dimensions. This exploratory framework generates testable hypotheses using existing multi-omic and spatial cancer datasets; however, empirical null-controlled analyses presented here do not provide robust support for a simple quadratic intermediate-entropy optimum, underscoring the sensitivity of entropy-based interpretations to modelling assumptions.

Current Preprint DOI: https://doi.org/10.5281/zenodo.18625654

Neuroinflammation-Linked Neuropsychiatric Symptoms in COVID-19 and Other Inflammatory States: A Mechanistic Hypothesis

Neurological and neuropsychiatric symptoms are common in acute and post-acute COVID-19. Evidence from dynamic contrast–enhanced MRI, TSPO-PET, FDG-PET, cerebrospinal fluid analysis, and neuropathology indicates that these symptoms arise primarily from neuroinflammation, microglial activation, and neurovascular dysfunction rather than direct viral neuro-invasion. Affected regions consistently include frontal and temporal cortices, limbic structures, the anterior cingulate cortex, basal ganglia, thalamus, brainstem, cerebellum, and olfactory pathways. These patterns correspond closely to impairments in executive function, emotional regulation, motivation, threat processing, sensory integration, and autonomic control. Parallels with established inflammatory and autoimmune disorders support a transdiagnostic mechanism in which systemic inflammation alters CNS circuits via glial activation and blood– brain barrier vulnerability. Within this context, the theoretical possibility that modulation of peripheral inflammation—such as through NSAIDs or selected plant-derived compounds—could influence neuroinflammation-linked symptoms warrants controlled investigation, though no therapeutic efficacy is established. This paper synthesises current evidence and outlines a research framework for empirically testing these mechanisms.

Current Preprint DOI: https://doi.org/10.5281/zenodo.18625883

Status: Several manuscripts complete or in progress; portions published; others under internal review.