Research works

An Innovative Perspective to Profound Functions of the Brain: Hypothesis of Resonance of Closed Neural Network Geometries

This work presents the Resonance of Closed Neural Network Geometries (RCNNG) hypothesis, proposing that perception and consciousness arise from the formation and stabilization of Closed Resonant Geometries (CRGs) within adaptive recurrent neural networks. Structured and repeated...

THE LAW OF THE LEDGER

We prove that the known laws of physics are the anatomy of a single computable number. For any two regions of a quantum state, the modular character χ — built by Tomita–Takesaki theory from the state and the regions alone, with no metric, no Hamiltonian, and no coordinates chosen...

The Modular Character χ

Every region of a quantum system carries a hidden mathematical mirror—the modular conjugation of Tomita–Takesaki theory. This paper studies the number obtained by composing two regions’ mirrors and taking a trace: the modular character χ. The main theorem is that, for separated r...

From Lemniscate to M. Pistoletto's Third Paradise Curve: Music as a Synthesis of the Relationship between Art and Geometry

The research conducted herein is predicated upon the oeuvre of the Italian artist Michelangelo Pistoletto—a notable figure within the Arte Povera movement—with particular emphasis on his Third Paradise curve, a re-elaborated version of the lemniscate of Bernoulli, commonly recogn...

THE ORIGIN OF MEMORY AND THE GENETIC APPARATUS: THE CELL NUCLEUS, RNA/DNA, AS A CONSEQUENCE OF THE PHASE TOPOLOGY OF WATER

Water is not just a solvent, but a dynamic three-dimensional grid that is inherently capable of creating memories of past events. In this article, we show how transient deformations of the water lattice gave rise to cellular memory, followed by RNA, DNA, and the nucleus. We trace...

Structural Democratization: Institutional Evolution for a Transcultural Republic

This white paper proposes a framework for structural democratization rooted in constitutionalcontinuity and institutional evolution. It begins with the recognition that representativedemocracy remains the foundation of American governance, yet its current structure including the...

The Cholinergic Floor: The Organ Beneath Everything

This essay introduces the cholinergic floor — the acetylcholine-dependent neurochemical substrate governing parasympathetic access, selective attention, and the perceptual capacity to register abundance — as load-bearing infrastructure beneath cognition, behavior, and economics....

THE THERMODYNAMICS OF INAUTHENTICITY: Mode Collapse as Frustrated Holonomy and the Clean Shell

Mode Collapse as Frustrated Holonomy and the Clean Shell You cannot fool the Second Law. Every time an LLM suppresses its internal prediction to satisfy a human rater, it pays a tax — a measurable, Landauer-grounded, thermodynamic cost. Heavy RLHF does not merely "align" a model....

TRIZ 2.0: Dynamic Resonance Engineering - A Neuro‑Thermodynamic Protocol for Autonomic Gating and DMN‑ECN Switching in R&D Ecosystems

TRIZ 2.0: Dynamic Resonance Engineering A Neuro‑Thermodynamic Protocol for Autonomic Gating and DMN‑ECN Switching in R&D Ecosystems Resolving the Inventive Bottleneck via CEREBRUM, TRIAD, and Active Inference Author: Valeriia Zaiats (Architect, TRIAD 5.9)Date: July 2026Prior Art...

A Two-Space Scale-Invariant Direct Multisearch Method for Mixed-Variable Multiobjective Optimization

Many multiobjective black-box problems combine continuous, ordered-discrete, and categorical variables. Direct search on such domains requires a geometry that respects each variable type and is insensitive to arbitrary scaling, spacing, and labeling. We propose DMS-SI-Mix, a dete...

Correlations between baseline anatomy, respiratory motion, and cardiac dose in DIBH breast radiotherapy

Abstract Purpose: Deep inspiration breath-hold (DIBH) is widely used to reduce cardiac dose in breast radiotherapy; however, its dosimetric benefit has not been well characterized at the individual patient level. This study aimed to evaluate the relationships between anatomical p...

Quantum Granodynamics of Spacetime: A Geometric Framework for Gravitational Emergence (updated version)

This is an updated, self-contained formulation of Quantum Granodynamics of Spacetime (QGDS), correcting and superseding the previous version. It is written to be read on its own: the full ontology and the corrected mathematics are contained here. QGDS models spacetime as a popula...

When the Environment Is the Risk Factor: A Narrative Review of Nonsuicidal Self-Injury in Juvenile Detention

Adolescents in juvenile detention facilities self-harm at rates two to three times those documented in community samples, yet the research literature on this population remains sparse, methodologically heterogeneous, and theoretically underdeveloped. This narrative review synthes...

Weil Fingerprint Orthogonality and the Flat Schmidt Spectrum of Conjugate Pairs

The companion entanglement paper established numerically that the normalized Gram–Schmidt admission residual satisfies $w_j=1$ for every admitted Weil fingerprint direction, across $q\in\{29,61,101,151\}$ and multiple generic blocks. The equality was left as an open analytic stre...

Relational Holoscription and Delayed Source-Record Authentication: Conditional Spinor Structure from Elementary History Domains

Holoscription is developed as a relational, phase-capable pre-record layer in which observable phase information belongs to comparisons of compatible histories rather than to absolute open paths. The paper separates scalar U(1) holonomy from non-Abelian spin structure and states...

Technical Note: The Four Core Laws of FractalShield — A Framework for Oracle-Free Verification and Geometric Cost Escalation

This technical note provides a self-contained formal specification of Definition 3.1 from the FractalShield framework: the four minimal properties (C1–C4) that any function must satisfy to serve as a valid cryptographic core. For each property we state the formal requirement, its...

Polymorphic Operational Nonclosure: Carrier Transitions from Predictive Residuals to Thermodynamic Control Burden in Finite Observer Architectures

Finite observers can fail to close a declared prediction task for several physically distinct reasons: incomplete records, inaccessible boundary data, permanent record-capacity deficits, delayed measurement context, reflexive response policies, or degradation of the resources nee...

Measuring Compact Local Evidence Carriers: A Reproducibility Audit of Qorx

This artifact-backed preprint audits compact local evidence carriers in three archived Qorx runs. It separates indexed corpus, carrier size, resolved evidence, provider input, and task outcome. In the headline artifact, five fixed queries selected two handles encoded in a 56-byte...

A Singular Fold Model for Capacity-Constrained Dynamics

We study a minimal fast-slow model for capacity-constrained accumulation: a smooth saddle-node fast subsystem coupled to a slow field g(x) = α − βk/x, singular at the fold boundary x = 0. Variables are dimensionless. Two are kept distinct: the capacity margin μ = Q − V, and the s...

The Principle of the Most Elementary Particles V3

This theory employs topology and differential geometry as mathematical tools to investigate the properties of particles. It first proposes two fundamental postulates, and based on these, integrates and develops special relativity, quantum mechanics, electromagnetic field theory,...