Academic
Correspondence
Academic Correspondence | Research Dialogues
Theoretical Framework
Our research synthesizes Grothendieck's mathematical frameworks with contemporary photonic theory, exploring negative effective mass phenomena through computational topology , symmetry and quantum field theory. Various other mathematical techniques are covered. This interdisciplinary approach enables novel insights into photon behavior in metamaterials. The medicine side our research focus on directed evolution and drug development to aid the condition of the autistic patient.
New Research Release: The Holographic State Space
In my recent work I introduce a universal Hilbert space, termed the Holographic State Space, envisioned as a “cosmic storehouse” that encompasses all possible quantum histories of the universe as basis states. Observable, classical reality is portrayed as emerging via a projection event, where a late‑time boundary condition (akin to an observation) “collapses” the universal state vector into a consistent set of histories.
We are inviting input: We appeal to the audience—namely, fellow researchers, theorists, or students—to help solve the relationship between negative effective mass and the Higgs field.
Newly discovered Potentials for Topos Theory from Grothendieck's Handwritten Notes: Functorial Correspondences and Topos Duality: A Reconstruction from Pages (Cote 115)
This abstract delivers a remark related to Topos Duality. We base ourselves on Alexander Grothendieck’s handwritten manuscript [from 1982] 103 Functorial "correspondences".
View Publication →G-Theory → Maxwell Duality: Lie-N Compactification, a Nonsingular Bounce, and Topological Photon Signatures : Prospects for evidence of an unobserved extended Maxwell law
As the photon travels, we can anticipate the surroundings of the photon. In this work, we present further evidence related to an un- observed law of nature by working with our Maxwell extensions.
View Publication →Integrating Circadian Rhythm and Neurobiology in Precision Medicine: A Novel Approach for Treating Severe Autism Through the Exploration of Time Cells and Genetic Mechanisms
. A precision medicine framework that incorporates circadian bi- ology could enable the rational design of novel drugs targeting oscil- latory mechanisms at the molecular level.
View Publication →Interferometric Sector–Gate Nervous Systems: Orchestrating AGI via Parity Fuse Quantum Primitives and Deterministic Java Injection - From Java Injection to Quantum Eigenstates: Engineering an n8n-Style Nervous System for AGI
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.
View Publication →Play-Based Interventions for Promoting Positive Developmental Outcomes in Autism Spectrum Disorder: A Comprehensive Therapeutic Protocol Informed by Neuroscience, Developmental Psychology, and Positive Psychology.
A deeper understanding in relation with psychoanalytics, and a protocol from a molecular and neurobiological perspective, is possible and since engagement in play stimulates dopaminergic path- ways, enhances synaptic plasticity, and modulates neurotrophic fac- tors such as brain-derived neurotrophic factor (BDNF) we find use in a more modern approach
View Publication →Emerging Photonic Principles and Negative Effective Mass
The sun has a twin sister star, and there is much related to gravity we do not under- stand today. However, deeper questions related to the standard model remain. Questions related to dark matter, and mass. We will focus in this work on mass. We suspect there are discoveries to be made related to negative effective mass (not negative mass).
View Publication →Directed Evolution of the BpsA Carrier Protein Domain for Enhanced Activation by Non-Cognate 4'-Phosphopantetheinyl Transferases Implications for ASD Drug Discovery
In this article, we will explore the options we have, engineering such a new drug, we will focus mostly around molecular action and directed evolution technique, while delivering proper analysis regarding our BpsA variants.
View Publication →Solutions for Photonic Approaches to Fusion Energy
This paper develops a mathematical framework for analyzing fusion energy problems from a photonic perspective.
View Publication →Applying Villani to understand Cosmic Gas: Kinetics for Classical and Quantum Gas Dynamics: On the Emergence of Quantum Turbulence in Cosmic Media
It is possible to unify certain kinetic properties of classical gases, as developed in Villani’s analysis of the Boltzmann equation, with quantum transport properties derived from the Bose–Hubbard model.
View Publication →A New Field: Stochastic–Dynamical Interactions: A Hairer–Mirzakhani Framework for Photon Dynamics
We propose a new field of study—basing ourselves on Hairer–Mirzakhani—uniting stochastic partial differential equations (SPDEs) with hyperbolic flows on moduli spaces of Riemann surfaces.
View Publication →James Clerk Maxwell: A Mathematical Biography
James Clerk Maxwell (1831–1879) is often remembered as the unifier of electricity, mag netism and light. Yet, beyond the fame of “Maxwell’s Equations,” his intellectual trajectory reads as a deeply mathematical biography, in which geometry, analysis, and structural ab straction guided his scientific imagination.
View Publication →In this experimental work, we use techniques derived from algebraic geometry and spectral sequences to show that certain topological obstructions in a photon’s field structure can lead to reduced interference contrast.
The Photon Soul Theorem: A Cohomological Approach to Interference Visibility
View Publication →Quantum Eigenstate Dynamics for Artificial General Intelligence Synthesis
The central idea is to propose a model for Artificial General Intelligence (AGI).The author suggests constructing AGI states as superpositions of quantum eigenstates.
View Publication →Illuminating the Breakthrough: A Dual Verification of the Geometric Langlands Conjecture Proof
i wrote a (double)proof in support of the evidence. Hopefully this will draw more attention to the proof.
View Publication →Grothendieck's Mathematical Techniques and their Potential Applications in Photonics
Unobserved Photonic States in Higher Dimensions: A Bridge Between Mirzakhani Geometry, Langlands Program, and Supersymmetry
View Publication →A Novel Approach to Precision Medicine for Autism: Integrating CRISPR-Cas9 Technology, Brain Organoids, and Circadian Rhythm Insights
Directed-evolution centered precision medicine for the autistic patient.
View Publication →Illuminating the Breakthrough: A Dual Verification of the Geometric Langlands Conjecture Proof
we recapitulate the essential steps of the original proof, focusing on the construction of the Langlands functor
View Publication →On Higher-Dimensional Soul Perturbations via Higgs–Photon Couplings
We propose an extension of the photon soul theorem to higher-dimensional geometries where the electromagnetic field acquires novel topological couplings to the Higgs sector.
View Publication →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
This paper will reexamine Hawking’s framework by incorporating photonic propagation models drawn from modern optical physics, extended to higher-dimensional scenarios.
View Publication →A Unified Framework for Photon-Soul Continuity: From Deterministic Stability to Stochastic Renormalization and Geometric Averaging
This framework addresses the three central challenges inherent to the theory: establishing the deterministic stability of the system, rigorously defining the model in the presence of singular quantum fluctuations, and making testable predictions despite unknown extra dimensional geometries.
View Publication →The Holographic State Space: A Mathematical Formalism for the Cosmic Storehouse: Proto-theory
We posit the existence of a universal Hilbert space, termed the Holographic State Space
View Publication →Photon Soul Theorem
in this experimental work, we use techniques derived from algebraic geometry and spectral sequences to show that certain topological obstructions in a photon’s field structure can lead to reduced interference contrast (photon soul effect)
View Publication →Photon Soul Continuity: An Unobserved Extension of Maxwell's Equations
We formulate the law, derive its consequences, and outline experimental signatures.
View Publication →Photon Soul Resonance: A Breakthrough Extension of Soul Continuity
We present a dramatic extension of the Photon Soul Continuity framework, introducing the principle of Photon Soul Resonance (PSR).
View Publication →Evaluating Large Language Model Meta-Cognition via the Advanced AGI-AI Self-Awareness Test (AISA-T)
In this work we propose AISA-T, a new intelligence test for both AI and AGI systems.
View Publication →Photon Soul Continuity - Unobserved Extension of Maxwell's Equations: Pathways
This extended manuscript includes the original formulation and a detailed discussion of the physical interpretation
View Publication →Beyond the Standard Model: Analytic Approach for the detection related to Unobserved Laws of Nature
This paper provides a mathematical exposition of the SM’s structure, followed by an analysis of its limitations---hierarchy problems, neutrino mass generation, CP-violation insufficiency, lack of a quantum theory of gravity, and gauge coupling unification failure.
View Publication →After the Higgs: Missed Opportunities in Gauge Vacuum Diagnostics and the Photonic Sector
We argue that the post-2012 focus of the high-energy physics community—while historically productive—systematically underweighted the gauge-vacuum diagnostics that the Brout–Englert–Higgs (BEH) mechanism makes uniquely accessible.
View Publication →Yang–Mills Existence and Mass Gap in Four Dimensions: Important hints and clues
Solving this problem, comes with a notorious reward of one million dollars. We present a partial completed proof for the four-dimensional Yang–Mills existence and mass gap problem.
View Publication →Bose's Photonic Mathematics Revisited: Entropic Optimization, Polylogarithmic Asymptotics, and Categorical Coherence from Symmetric Functions to ZX-Calculus
Is it possible to deepen and reframe S. N. Bose’s 1924 photonic breakthrough?
View Publication →The Animate and the Inanimate in Pure Mathematics: A Modern Reappraisal of William James Sidis's Underrated Viewpoint
This paper provides a purely mathematical formulation of Sidis’s idea
View Publication →A Follow-up Work to AISA–T: Elucidating the Human Evaluation Rubric for AGI Self-Awareness
This follow-up work proposes a comprehensive rubric designed to standardize the human evaluation process for AGI-level responses.
View Publication →Quantum Sector-Gate Dynamics for Artificial General Intelligence
We extend the framework of Quantum Eigenstate Dynamics for Artificial General Intelligence Synthesis by introducing a sector-gate formalism.
View Publication →Interferometric Sector-Gate Quantum Dynamics for AGI: Parity-Driven Tunneling First and the Case for a Topological Core
We synthesize the Sector-Gate and Eigenstate Dynamics programs for Artificial General Intelligence (AGI) into a single interferometric framework that is emphhardware-constrained by parity readout on InAs–Al hybrid nanowires.
View Publication →- © Peter De Ceuster 2024-2026