DOI: 10.5281/zenodo.17089136
title: 31 publications across mathematics, physics, psychology, molecular drug discovery, AGI and quantum chip production — freely available

description: Exploring the Frontiers of Knowledge: A Collection of Works by Peter De Ceuster

Exploring the Frontiers of Knowledge — Peter De Ceuster

By Peter | 10 September 2025


 

 









31 publications across mathematics, physics, psychology, molecular drug discovery, AGI and quantum chip production — freely available on CERN / Zenodo.





Overview

A guided tour of selected papers and the full list of titles. All items below are freely accessible from the CERN-hosted Zenodo archive.
Read the full collection on Zenodo





Full list of publications (31)



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

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

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

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

Identifying Theoretical Gaps in Hawking’s Black Hole Radiation Model in Light of Modern Photonics and Higher-Dimensional Photon Propagation : Photon-Coupled Soft Hair and Higher-Dimensional Photon Channels - A Critical Extension of the Soft-Hair Formalism

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

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

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

Solutions for Photonic Approaches to Fusion Energy

Quantum Sector-Gate Dynamics for Artificial General Intelligence

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

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

On Higher-Dimensional Soul Perturbations via Higgs–Photon Couplings

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

James Clerk Maxwell: A Mathematical Biography

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

Quantum Eigenstate Dynamics for Artificial General Intelligence Synthesis

Emerging Photonic Principles and Negative Effective Mass A Mathematical Treatise in the Tradition of Grothendieck

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

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

Play-Based Interventions for Promoting Positive Developmental Outcomes in Autism Spectrum Disorder: A Comprehensive Therapeutic Protocol Informed by Neuroscience, Developmental Psychology, and Positive Psychology.

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

The Photon Soul Theorem: A Cohomological Approach to Interference Visibility

Quantum Eigenstate Dynamics for Artificial General Intelligence Synthesis (Expanded)

Photon Soul Resonance: A Breakthrough Extension of Soul Continuity

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

Newly discovered Potentials for Topos Theory from Grothendieck’s Handwritten Notes: Functorial Correspondences and Topos Duality: A Reconstruction from Pages (Cote )

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

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

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

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






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.






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. The paper presents results from administering the AISA-T to a GPT-5-based LLM, demonstrating its capability for simulated introspection and self-descriptive behavior.






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, aiming to enhance reproducibility and transparency in future AGI research.






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' regions where entropy locally decreases and 'inanimate' regions where it increases. De Ceuster provides a mathematical formalization of Sidis's ideas, connecting them to modern concepts in non-equilibrium thermodynamics, information theory, and cosmology, arguing for a re-evaluation of this historically misunderstood viewpoint.






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. The work suggests that soft photon boundary terms can modify horizon charge algebra and produce enhanced corrections to the effective central charge, leading to computable shifts in predicted black hole entropy.






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, explores generating-function expansions in symmetric-function language, and derives polylogarithmic and zeta-function asymptotics for Wien and Rayleigh–Jeans regimes. Crucially, it reinterprets Bose’s combinatorics through categorical coherence, mapping it into symmetric monoidal and ‡-compact structures with ZX-calculus examples, suggesting that Bose implicitly recognized commutative special ‡-Frobenius algebra structure in mode bases.






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. The work highlights the potential for novel drug designs targeting oscillatory mechanisms at the molecular level, informed by genetic insights into ASD.






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 4’-phosphopantetheinyl transferases (PPTases), the research aims to generate new bioactive compounds with therapeutic relevance for ASD. The work details the molecular mechanisms, experimental methods like error-prone PCR and CRISPR-based mutagenesis, and high-throughput screening techniques used to engineer BpsA variants, ultimately seeking to produce novel compounds that can modulate neural function and correct neurotransmitter imbalances.






Solutions for Photonic Approaches to Fusion Energy

This paper presents a novel perspective on fusion energy research, traditionally dominated by plasma physics, 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. The work proposes analytic and numerical solutions, including a hybrid Monte Carlo–diffusion solver and adjoint optimization, to address key barriers in achieving energy gain and efficient confinement, suggesting that photons are active participants in the fusion process.






Quantum Sector-Gate Dynamics for Artificial General Intelligence

This paper extends the framework of Quantum Eigenstate Dynamics for Artificial General Intelligence (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. The work explores self-referential dynamics, entangled eigenstate propagation across multiple gates, and proposes a new design principle for robust AGI architectures based on the commutation of certain cognitive operations, suggesting that AGI could function beyond traditional binary code.






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. The work proposes a novel framework of 'Spectral Grothendieck Spaces' as a potential arena for future unification, aiming to encode classical schemes, derived stacks, motivic towers, and logical universes within a single, cohesive structure.






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, combining probabilistic irregularities with deterministic hyperbolic geometry. The research establishes existence and uniqueness of solutions, invariant measures, and defines a stochastic entropy functional governing photon decoherence, laying the foundation for stochastic–geometric quantum dynamics.






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. The research provides precise cohomological constructions, computes obstruction classes, and derives phenomenological bounds on measurable visibility shifts, suggesting new avenues for detecting hidden-sector physics through quantum-optical precision.






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 Artificial General Intelligence (AGI) into an interferometric framework, constrained by parity readout on InAs–Al hybrid nanowires. 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. The research also argues for the optimality of topological cores in minimizing composite error functionals due to non-local encoding and Z2-parity protection, and introduces a "ParityFuse" calculus for fault-biased, measurement-only AGI primitives.






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. Beyond his famous equations, the document highlights Maxwell's early geometric explorations, his work on Saturn's rings, and his foundational contributions to kinetic theory and statistical mechanics. It draws parallels between Maxwell's search for hidden unities and later mathematical figures like Alexander Grothendieck, arguing that Maxwell's structural approach anticipated modern mathematical concepts like differential forms and category theory, making his work a continuous source of inspiration for fields like photonics.






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. The model emphasizes a quantum cognitive basis where subcognitive modules are combined, and logic is achieved via eigenstate collapse, enabling adaptive decisions through non-stationary interference. The work argues that quantum cognition operates in a complex space, transcending the rigid limitations of classical binary logic by allowing "yes" and "no" to coexist in a probabilistic quantum state until a measurement forces a classical outcome.






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 in photonic contexts, Supersymmetry (SUSY) constructions, negative effective mass dynamics, Madelung-fluid formulation, Schrödinger operators on surfaces, the Bollobás–Riordan polynomial in network topology, and dark-photon vortex solutions. The paper aims to contribute to the study of light and negative effective mass, suggesting that these phenomena might be present in nature and require further investigation.






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 details how Js couples to the global electromagnetic-field configuration, its potential effects on dispersion, helicity, and interactions, and the symmetry-breaking requirements for helicity asymmetry. The work provides a toy-model gauge embedding, discusses phenomenological consequences, and outlines experimental signatures, emphasizing theoretical and experimental pathways to test this proposal for detecting hidden-sector physics.






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

This paper outlines an integrated molecular-action framework for autism spectrum disorder (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 (BMAL1, CLOCK, REV-ERBα), synaptic scaffold proteins (SHANK3), and signaling effectors (mTORC1, NF-κB). The work proposes a comprehensive experimental pipeline, including CRISPRa/i manipulation, rhythmic reporters, and multi-omic readouts, to validate causal chains and test therapeutic hypotheses, ultimately aiming to develop chronopharmacology and allosteric modulators for ASD treatment.






Play-Based Interventions for Promoting Positive Developmental Outcomes in Autism Spectrum Disorder

This paper presents a comprehensive therapeutic protocol for Autism Spectrum Disorder (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, contributing to long-term potentiation in neural circuits. The work emphasizes the role of the subconscious mind in child development and proposes "Play, Learn, Thrive" as a stepwise framework to guide children with ASD through progressive levels of play engagement, integrating neurobiological modulation, psychological scaffolding, and positive development metrics.






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. Inspired by the top-down cosmological framework, it posits a universal Hilbert space, the Holographic State Space, containing all possible quantum histories of the universe. The emergence of classical reality is modeled as a projection event, where observation collapses the universal state vector into a consistent family of histories. The work provides a rigorous mathematical structure for the concept that the universe selects itself from a vast library of potential forms, governed by the principle of holographic information.






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. The theorem transforms a deep cohomological invariant into a laboratory-ready signal, offering a metrological tool for diagnosing minute defects, a cohomological probe for photonic devices, and a pathway to robust, topology-aware quantum photonics. The paper suggests that this effect could be validated through experiments at CERN.






AGI

This work delves into the foundational principles of Artificial General Intelligence (AGI), exploring the theoretical underpinnings and potential pathways to its realization. It discusses the critical components of AGI, including cognitive architectures, learning paradigms, and the philosophical implications of creating truly intelligent machines. The paper serves as a high-level primer on the challenges and opportunities in the field of AGI research.






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 by coupling the hidden soul–charge current not only to the Higgs field but also to compactification moduli and graviphoton modes, resonant amplification of soul-mediated photon interactions can occur. This amplification is predicted to increase quantum interference deviations to potentially observable levels in table-top experiments. The work outlines the mathematical formalism, provides closed-form solutions in toy models, and suggests concrete optical–cavity experiments to detect PSR signatures, transforming photons into active resonant sensors of hidden topology and extra-dimensional geometry.






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, neutrino mass generation, and the absence of a quantum theory of gravity. It presents a numerically precise 1-loop renormalization group evolution (RGE) of gauge couplings and discusses how 2-loop and threshold corrections refine the picture. The work argues that persistent empirical anomalies and theoretical shortcomings strongly suggest the existence of unobserved laws of nature, offering concrete evidence pointing towards such laws.






Newly discovered Potentials for Topos Theory from Grothendieck’s Handwritten Notes: Functorial Correspondences and Topos Duality: A Reconstruction from Pages (Cote )

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 through a deeper understanding of categorical logic. The work explores topos-theoretic Galois theory, Morita equivalence for theories, and proposes a minimal six-functor formalism, aiming to advance topos theory by re-framing Grothendieck’s mathematics in a contemporary context.






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" arising from a posited Higgs-photon coupling in a higher-dimensional bulk spacetime. It addresses the challenges of deterministic stability, singular quantum fluctuations, and geometric uncertainty by synthesizing the theories of Villani, Hairer, and Mirzakhani. The work establishes the deterministic stability of the system, defines the model in the presence of singular quantum fluctuations, and makes testable predictions by averaging the soul current's effects over all possible compactification geometries, providing a coherent theoretical pathway from foundational axioms to falsifiable experimental guidance.






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, as analyzed by Villani in the context of the Boltzmann equation, with quantum transport properties derived from the Bose–Hubbard model. 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. The work applies this concept to astrophysical gases, demonstrating how superfluidity and quantum turbulence can arise in neutron star interiors, thereby bridging classical and quantum gas dynamics and offering new insights into turbulence in extreme cosmic environments.






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. It recapitulates the essential steps of the original proof, provides detailed analysis and alternative derivations of critical lemmas (including the spectral action, the vacuum Poincaré sheaf, and the Whittaker model), and reassembles these components into a coherent reconstruction of the equivalence of categories. The verification confirms each foundational component via distinct methods, reinforcing the proof’s validity and highlighting its implications for representation theory, conformal field theory, and p-adic extensions.






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 in four dimensions. 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. The work derives variational lower bounds within fixed holonomy sectors and demonstrates their stability under coarse-graining maps. The remaining conjectural step is isolated as a precise conjecture: a uniform lower bound on the lattice mass gap along a renormalization trajectory reaching a continuum limit that satisfies the Osterwalder–Schrader axioms. Conditional on this conjecture, the paper proves that the reconstructed continuum Yang–Mills Hamiltonian on R3 has a nonzero spectral gap, providing a coherent program for future research.






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, and the symmetry-breaking requirements for helicity asymmetry. The work provides a toy-model gauge embedding, discusses phenomenological consequences, and outlines experimental signatures, emphasizing theoretical and experimental pathways to test this proposal for detecting hidden-sector physics.




All works are freely available on CERN / Zenodo.