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: Completed manuscript; submitted and in peer review.

Yang–Mills Mass Gap (Constructive 4D Approach)

A 4-dimensional constructive Hamiltonian structure yielding a positive lower-bounded excitation spectrum, addressing the existence of a non-zero mass gap.

Current Preprint DOI: https://doi.org/10.5281/zenodo.18041131

Status: Completed manuscript; submitted and in peer review.

Hodge Conjecture: Analytic–Spectral Reformulation

Recasting the Hodge Conjecture as a spectral partitioning problem involving energy-minimising harmonic representatives and curvature-aligned eigenmodes.

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

Status: Completed manuscript v1.1; pending journal submission.

Riemann Hypothesis: Hamiltonian Spectral Framework

Developing a self-adjoint quantum-style operator whose eigenvalues recover the non-trivial zeros of ζ(s), using a combination of spectral theory, energy-space analysis, and dynamical encoding.

Early Preprint DOI: https://doi.org/10.31219/osf.io/h2dte_v2

Status: Manuscript in revision.

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: Manuscript in revision.

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.

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. Energyspace gravity naturally explains gravitational wave dispersion, black hole horizon corrections, and deviations in the CMB power spectrum without invoking dark energy. 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.

Early Preprint DOI: https://doi.org/10.31219/osf.io/ycmtq_v3

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.

Early Preprint DOI: https://doi.org/10.5281/zenodo.17834399

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

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.

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.

Plausibility of Cognitive or Proto-Sentient AI

Weexamine 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.

Magneto-Seismic Early Warning (Airborne Detection)

A model for detecting pre-seismic magneto-electric anomalies from the air using AI-filtered signature analysis and plasma coupling effects.

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