Artificial General Intelligence

Evaluating Large Language Model Meta-Cognition via the Advanced AI Self-Awareness Test (AISA-T)

Introduces the AISA-T, a novel test for AI/AGI systems to evaluate meta-awareness and context-sensitive reasoning. Presents results from administering the test to a GPT-5-based LLM, demonstrating capabilities for simulated introspection.

Theoretical Physics & Mathematics

The Photon Soul Theorem: A Cohomological Approach to Interference Visibility

Introduces the "photon soul effect," showing that topological obstructions in a photon’s field structure can reduce interference contrast. The theorem transforms a deep cohomological invariant into a laboratory-ready signal for quantum photonics.

Molecular Drug Discovery

Directed Evolution of the BpsA Carrier Protein Domain for Enhanced Activation by Non-Cognate 4’-Phosphopantetheinyl Transferases

Explores a novel approach to Autism Spectrum Disorder (ASD) drug discovery through protein evolution, aiming to generate new bioactive compounds that can modulate neural function and correct neurotransmitter imbalances.

Mathematics

On a Newfound Panorama in Geometry and Category Theory: A Tribute to Grothendieck

Revisits Grothendieck’s foundational contributions to topos theory and schemes through a modern lens, exploring extensions via ∞-categories, derived algebraic geometry, and homotopy type theory.

Physics & Photonics

  • After the Higgs: Missed Opportunities in Gauge Vacuum Diagnostics and the Photonic Sector

    This paper explores the implications of the Higgs boson discovery, focusing on potential missed opportunities in understanding the gauge vacuum and its interaction with the photonic sector. It delves into advanced concepts of gauge theory and particle physics, suggesting new avenues for research in the post-Higgs era.

  • Identifying Theoretical Gaps in Hawking’s Black Hole Radiation Model in Light of Modern Photonics and Higher-Dimensional Photon Propagation

    This paper critically re-examines Stephen Hawking’s black hole radiation model, highlighting a theoretical gap related to photon propagation in higher-dimensional spacetimes. It proposes an extension to the soft-hair formalism, incorporating electromagnetic degrees of freedom and their higher-dimensional channels.

  • Bose’s Photonic Mathematics Revisited: Entropic Optimization, Polylogarithmic Asymptotics, and Categorical Coherence from Symmetric Functions to ZX-Calculus

    This paper re-examines S. N. Bose’s foundational work on photon statistics, offering a deeper and reframed perspective. It provides a full Lagrange-multiplier optimization of entropy and reinterprets Bose’s combinatorics through categorical coherence, mapping it into symmetric monoidal and ‡-compact structures with ZX-calculus examples.

  • Solutions for Photonic Approaches to Fusion Energy

    This paper presents a novel perspective on fusion energy research by focusing on the role of photons. It develops a mathematical framework to analyze fusion problems through photon transport in dense plasmas, radiative instabilities in laser-driven systems, and optimization of photonic structures for confinement.

  • On Higher-Dimensional Soul Perturbations via Higgs–Photon Couplings

    This paper extends the photon soul theorem to higher-dimensional geometries, proposing that the electromagnetic field can acquire novel topological couplings to the Higgs sector. It demonstrates that in D > 4 bulk or derived-stack contexts, nontrivial morphisms can induce Higgs–photon soul deformations that leave calculable imprints on low-energy interference phenomena.

  • Regularity Structures for Interacting Photon Fields

    We adapt Mr Martin Hairer’s well written theory of regularity structures to a class of stochastic Maxwell-type PDEs modeling interacting photon fields with nonlinear coupling and additive space-time noise.

  • G-Theory→Maxwell Duality: Lie-N Compactification, a Nonsingular Bounce, and Topological Photon Signatures

    As the photon travels, we can anticipate the surroundings of the photon. In this work, we present further evidence related to an unobserved law of nature by working with our Maxwell extensions.

  • Photon Cohomology and Higher Gerbes: Topological Invariants of Photonic Sectors

    We introduce Photon Cohomology, a differential cohomology theory tailored to classify photonic bundle data comprising ordinary U(1)-connections, higher gerbe potentials and multi-form couplings that arise in exotic photonic channels and engineered photonic media.

  • A Geometric Photon Mass-Gap Conjecture: Spectral Gaps for Photonic Operators

    We formulate a precise Geometric Photon Mass-Gap Conjecture asserting that Laplace-type operators modelling photonic dynamics on compact manifolds with photonic coupling admit a strictly positive spectral gap above zero under explicit geometric and bundle-theoretic hypotheses.

  • Photon Soul Continuity: An Unobserved Extension of Maxwell’s Equations

    This paper proposes a minimal extension of Maxwell’s equations to incorporate a hidden “soul” current (Js) originating from a higher-dimensional Higgs–photon coupling. It details how Js couples to the global electromagnetic-field configuration, its potential effects on dispersion, helicity, and interactions.

  • Emerging Photonic Principles and Negative Effective Mass

    This mathematical treatise explores emerging photonic principles and the concept of negative effective mass, distinct from negative mass. It presents mathematical formulations for mirror symmetry, SUSY constructions, Madelung-fluid formulation, and dark-photon vortex solutions.

  • Photon Soul Continuity - Unobserved Extension of Maxwell’s Equations: Pathways

    This paper proposes a minimal extension of Maxwell’s equations to incorporate a hidden "soul" current (Js) originating from a higher-dimensional Higgs–photon coupling. It outlines experimental signatures and emphasizes theoretical and experimental pathways to test this proposal.

  • The Holographic State Space: A Mathematical Formalism for the Cosmic Storehouse: Proto-theory

    This paper introduces a mathematical formalism for a "cosmic storehouse"—the primordial state of potentiality from which all observable forms emerge. It posits a universal Hilbert space, the Holographic State Space, containing all possible quantum histories of the universe.

  • The Photon Soul Theorem: A Cohomological Approach to Interference Visibility

    This experimental work introduces the "photon soul effect," demonstrating that topological obstructions in a photon’s field structure can lead to reduced interference contrast. It models single-photon quantum field amplitudes as a sheaf on an étale site and identifies an obstruction class whose nontriviality causes a measurable drop in interferometric visibility.

  • Photon Soul Resonance: A Breakthrough Extension of Soul Continuity

    This paper presents a significant extension of the Photon Soul Continuity framework by introducing the principle of Photon Soul Resonance (PSR). It proposes that resonant amplification of soul-mediated photon interactions can occur, increasing quantum interference deviations to potentially observable levels.

  • Beyond the Standard Model: Analytic Approach for the detection related to Unobserved Laws of Nature

    This paper provides a mathematical exposition of the Standard Model (SM) of particle physics, analyzing its limitations such as the hierarchy problem and the absence of a quantum theory of gravity. It argues that persistent empirical anomalies and theoretical shortcomings strongly suggest the existence of unobserved laws of nature.

  • A Unified Framework for Photon-Soul Continuity: From Deterministic Stability to Stochastic Renormalization and Geometric Averaging

    This paper presents a unified mathematical framework for an extension to Maxwell's equations that introduces a "soul current." It synthesizes the theories of Villani, Hairer, and Mirzakhani to address challenges of deterministic stability, singular quantum fluctuations, and geometric uncertainty.

  • Applying Villani to understand Cosmic Gas: Kinetics for Classical and Quantum Gas Dynamics: On the Emergence of Quantum Turbulence in Cosmic Media

    This paper unifies kinetic properties of classical gases with quantum transport properties. It introduces a "quantum-corrected Boltzmann equation" that incorporates bosonic statistics into the collision operator, leading to a generalized H-theorem and entropy production functional.

  • Yang‒Mills Existence and Mass Gap in Four Dimensions: Important hints and clues

    This paper presents a partial solution towards the Clay Millennium Prize Problem of Yang–Mills existence and mass gap. It rigorously constructs the Hamiltonian in temporal gauge, establishes reflection positivity, and proves a positive spectral gap in the strong-coupling regime on finite lattices.

Artificial General Intelligence (AGI)

  • Evaluating Large Language Model Meta-Cognition via the Advanced A I Self-Awareness Test (AISA-T)

    This work introduces the AISA-T, a novel intelligence test designed for both AI and AGI systems. It evaluates meta-awareness, inner traceability, and context-sensitive reasoning by having the AI answer questions and rate its own performance.

  • A Follow-up Work to AISA-T: Elucidating the Human Evaluation Rubric for AGI Self-Awareness

    This paper serves as a crucial addendum to the AISA-T study, detailing a comprehensive rubric for human evaluation of AGI responses. It formalizes the methodology for assessing AI self-awareness across dimensions like Depth, Coherence, and Architectural Accuracy.

  • Quantum Sector-Gate Dynamics for Artificial General Intelligence

    This paper extends the framework of Quantum Eigenstate Dynamics for AGI Synthesis by introducing a sector-gate formalism. It posits that the total Hilbert space of an AGI can be decomposed into interacting sectoral subspaces, with cognitive processes governed by unitary gate operators that drive eigenstate transitions.

  • Interferometric Sector-Gate Quantum Dynamics for AGI: Parity-Driven Tunneling First and the Case for a Topological Core

    This paper synthesizes Sector-Gate and Eigenstate Dynamics for AGI into an interferometric framework. It proposes a "Tunneling-First Principle," suggesting that optimal learning capacity and error exponent improvement are achieved by optimizing engineered tunnel networks before large-scale sector expansion.

  • Interferometric Sector–Gate Nervous Systems: Orchestrating AGI via ParityFuse Quantum Primitives and Deterministic Java Injection

    We present a mathematically rigorous architecture that integrates measurement-first parity interferometry (“ParityFuse”) with a provable runtime orchestration layer (a capability-constrained Java injection agent) to form an n8n-like nervous system for an AGI substrate encoded in sectoral eigenstate dynamics.

  • Quantum Eigenstate Dynamics for Artificial General Intelligence Synthesis

    This paper proposes a model for Artificial General Intelligence (AGI) based on quantum eigenstate dynamics. It suggests constructing AGI states as superpositions of quantum eigenstates, allowing for simultaneous resolution of binary logic through eigenvalue collapse.

  • Quantum Eigenstate Dynamics for Artificial General Intelligence Synthesis (Expanded)

    This paper proposes a model for Artificial General Intelligence (AGI) based on quantum eigenstate dynamics. It suggests constructing AGI states as superpositions of quantum eigenstates, allowing for simultaneous resolution of binary logic through eigenvalue collapse. (Expanded version)

Mathematics

  • The Animate and the Inanimate in Pure Mathematics: A Modern Reappraisal of William James Sidis’s Underrated Viewpoint

    This paper re-examines William James Sidis’s 1925 work, which proposed a division of the universe into 'animate' and 'inanimate' regions based on local entropy. De Ceuster provides a mathematical formalization of Sidis’s ideas, connecting them to modern concepts in non-equilibrium thermodynamics, information theory, and cosmology.

  • On a Newfound Panorama in Geometry and Category Theory: A Tribute to Grothendieck

    This paper pays homage to Alexander Grothendieck, revisiting his foundational contributions to topos theory, motives, and schemes through the lens of modern mathematics. It explores how concepts like ∞-categories, derived algebraic geometry, and homotopy type theory extend and reframe Grothendieck’s unifying vision.

  • A new field: Stochastic–Dynamical Interactions: A Hairer–Mirzakhani Framework for Photon Dynamics

    This paper proposes a new field of study that unites stochastic partial differential equations (SPDEs) with hyperbolic flows on moduli spaces of Riemann surfaces, building on the works of Hairer and Mirzakhani. It introduces stochastic Teichmüller flows to model photon dynamics.

  • James Clerk Maxwell: A Mathematical Biography

    This paper presents a mathematical biography of James Clerk Maxwell, emphasizing his intellectual trajectory and the role of geometry, analysis, and structural abstraction in his scientific imagination. It draws parallels between Maxwell's search for hidden unities and later mathematical figures like Alexander Grothendieck.

  • A Geometric Langlands Correspondence for Photonic Gauge Sectors

    We propose a photonic adaptation of the Geometric Langlands program: a conjectural equivalence between categories associated to moduli of G-bundles with photonic boundary/coupling data and a spectral category built from Langlands-dual local systems augmented by photonic insertions.

  • Topoi for Photons: A Categorical Formulation of Electromagnetic Duality

    We propose a categorical formulation of electromagnetic (Maxwell) duality by identifying a class of Grothendieck topoi whose internal cohomological data encode electric and magnetic sectors and admit a canonical duality isomorphism.

  • An Information-Geometric Program for AM-GM Stability: Log-Sobolev Bounds and Variance Control

    This work proposes and develops an information-geometric program to establish a quantitative stability bound for the Arithmetic Mean – Geometric Mean (AM-GM) inequality.

  • Toward the Analytic Resolution of the Variance-AM-GM Inequality: The Role of Taylor Expansion and Asymptotic Analysis

    This work provides the direct analytic proof and refinement of the Variance-AM-GM Inequality Conjecture. The best possible universal constant is established as Cn = 1/2.

  • A Variance–AM–GM Inequality Conjecture: A Call to the Mathematical Community

    This note proposes a new inequality linking the classical arithmetic and geometric means with the variance of positive real variables.

  • Kinematics of the Sol–Soror Binary: The Gravitational Bond and the Twin Sister’s Cycle

    We present a theoretical astrophysics study of a hypothetical, distant binary companion to the Sun—Soror—and perform a detailed kinematic analysis of the putative Sol–Soror system.

  • Mapping the Mind: Techniques for Structuring and Interpreting Grothendieck’s Evolving Mathematical Thought in His Notes

    This paper presents a methodological framework for the systematic analysis and interpretation of complex, often unstructured handwritten mathematical notes, using Alexander Grothendieck’s personal manuscripts as a primary case study.

  • Geometric Averaging and Deterministic Limits for Stochastically Renormalized Field Equations

    We present a general averaging theorem showing that a family of stochastically renormalized field equations converges to a deterministic effective PDE obtained by geometric averaging under scale-separation and ergodicity hypotheses.

  • Functorial Renormalization: A Categorical Framework for Scale Transformations

    We propose a categorical formulation of renormalization in which scale changes are encoded as functors between categories that represent physical models at distinct resolution scales.

  • Newly discovered Potentials for Topos Theory from Grothendieck’s Handwritten Notes: Functorial Correspondences and Topos Duality

    This paper reconstructs and formalizes concepts from Alexander Grothendieck’s handwritten notes on functorial correspondences and topos duality. It translates his sketches into modern bicategorical diagrams and ∞-categorical language, bridging logic and geometry.

  • Illuminating the Breakthrough: A Dual Verification of the Geometric Langlands Conjecture Proof

    This paper presents an independent, dual verification of the recently completed proof of the Geometric Langlands Conjecture (GLC) for reductive groups. The verification confirms each foundational component via distinct methods, reinforcing the proof’s validity.

Neuroscience, Psychology & Medicine

  • Integrating Circadian Rhythm and Neurobiology in Precision Medicine: A Novel Approach for Treating Severe Autism Through the Exploration of Time Cells and Genetic Mechanisms

    This paper proposes a precision medicine framework for treating severe autism by integrating circadian biology and neurobiology. It explores the critical role of circadian rhythms and time cells in neurodevelopment and synaptic plasticity and how their disruption contributes to ASD pathophysiology.

  • Directed Evolution of the BpsA Carrier Protein Domain for Enhanced Activation by Non-Cognate 4’-Phosphopantetheinyl Transferases Implications for ASD Drug Discovery

    This paper explores a novel approach to Autism Spectrum Disorder (ASD) drug discovery through the directed evolution of the BpsA carrier protein domain. By enhancing its activation by non-cognate PPTases, the research aims to generate new bioactive compounds with therapeutic relevance for ASD.

  • Molecular-Action Pathways for Autism Drug Discovery: Organoids, Circadian Dynamics, and Genetic Engineering

    This paper outlines an integrated molecular-action framework for ASD drug discovery, combining human patient-derived cerebral organoids, circadian biology, and targeted genetic and chemical interventions. It details explicit biochemical sequences for key molecular nodes like clock transcription factors and synaptic scaffold proteins.

  • Play-Based Interventions for Promoting Positive Developmental Outcomes in Autism Spectrum Disorder: A Comprehensive Therapeutic Protocol

    This paper presents a comprehensive therapeutic protocol for ASD that leverages play-based interventions, informed by neuroscience, developmental psychology, and positive psychology. It explores how play stimulates dopaminergic pathways, enhances synaptic plasticity, and modulates neurotrophic factors.