Research works

How does creative enquiry enable us to deal with uncertainty?

Abstract Background Uncertainty is an inherent and pervasive feature of medical practice. Here, uncertainty refers to the subjective perception and affective experience encountered by medical students and clinicians. Difficulties in managing uncertainty are associated with impair...

A Pointwise Critical-Face Transfer for Circulant Determinants of Order 4p

For every odd prime p and every positive integer m coprime to 2p, thispreprint proves that 32m in the order-4p integer circulant-determinant spectrumimplies p^2m in that spectrum, with equivalence when p is congruent to 3modulo 4; the signed form is equivalent by sign symmetry. I...

Angle Maps Are Direction Fields. The half-integer rulebook for plasma polarimetry (MSE and Faraday): wrap-free map processing, an exact equivariance property, and a disclination parity test that flags what a smooth magnetic field cannot produce

Plasma polarimetry measures directions, not vectors: the polarization angle of motional-Stark-effect (MSE) emission and the Faraday rotation angle are defined modulo 180deg. The measurement hardware knows this — photoelastic-modulator systems encode the angle in second-harmonic p...

Which Loops Can Carry a Burgers Vector? Selection Rules on Non-Orientable Geometry

The strength of a dislocation is its Burgers vector: the circulation of the distortion field along a loop encircling the defect line. This article pursues a single question: what happens to this circulation when the carrier geometry is non-orientable? The answer reduces to one me...

Artian's HVP Source-Access Reference Framework

Which HVP object is the source, which one is the apparatus, and which one is only statistics? A resolved hadronic-vacuum-polarization test passes through several mathematically different layers before it becomes a laboratory verdict. This framework now types that full chain: \[ \...

Asymptotic Density of Iterated Lattice Sumsets and Additive Self-Healing in Rectangular Lattice Boxes (Version 1.12)

Abstract We establish four rigorously proved theorems: (1) Universal Cartesian product density factorization for arbitrary finite sets; (2) exact exponential decay ρ(Δ_d(m)) = 1/m^d; (3) centroid neutralization under LINEAR point groups G ≤ GL(d,Z) with Fix(G)={0} (V1.12: restric...

Discrete Geometric Physics. Tetralogy: Ontology of the Lattice, Vacuum, Fields and Cosmology, Algebraic Structure and Topological Dynamics of the Vacuum, Cosmological Consequences of D-Graphs

This tetralogy presents a complete exposition of Discrete Geometric Physics (DGP) — a theory in which all fundamental constants, gauge symmetries, masses of elementary particles, gravitational interaction, cosmological parameters, and the large-scale structure of the Universe are...

The Regulatory Singularity: Why Regulation, Not Intelligence, Is the Real Civilizational Threshold

Civilization is entering an era of accelerating complexity marked by rapid advances in technology, intelligence, and economic power. Yet alongside this acceleration, indicators of instability, including chronic stress, social fragmentation, governance breakdown, and systemic vola...

Chebyshev Extremizers of Squared-Gap Entro

This work studies a finite-dimensional extremal problem for the squared-gap logarithmic functional Cn(a)=i<j∑(ai−aj)2log(ai−aj)2 on the centered unit configuration space Mn={a∈Rn:i∑ai=0, i∑ai2=1}. The main result proves that, for every n≥2, the unique global minimizers up to perm...

The Non-Linear Maier Matrix Topology: An Analytic Langlands No-Go Theorem and the Geometric Langlands Reduction of the Legendre–Oppermann–Andrica Universality Class

We introduce a two-parameter array of polygonal gnomon numbers $A_{m,j}, W_{m,j}$ ($m,j \ge 1$) and study the family of generalized explicit intervals $I^{(\lambda)}_{m,j}$ it generates under a Continuous Amplitude Scaling Factor $\lambda \in (0, 1]$. In Part I we show that this...

3D cuboid: Research on spatial geometric similarity scaling in conformal mapping

Abstract: This paper investigates the problem of self‑similar fractal proportions in three‑dimensional space and derives the unique aspect ratio (approximately 1.5874:1.2599:1) for a cuboid that satisfies the property of "shape invariance after bisecting the longest edge." Cuboid...

Who Validates the Validator? Instrument failure in the shape of the hypothesis — fourteen audit findings from a pre-registered measurement

v5 (2026-08-08) — record integrity, power boundary, regime surfaces, finding register. Correction #30: the showcase builder wrote platform-default line endings while claiming determinism; output is now pinned to LF, and a new RECORD_MANIFEST.sha256 binds every file of this record...

A Layered Artificial-Life Model of Functional Self-Modeling — What Fails to Correct a Learned Self-Estimate, and What Does / Un modelo de vida artificial por capas del automodelado funcional — qué no corrige una estimación aprendida sobre uno mismo, y qué sí

Research compendium (layers 0 to 16, four arcs) of a minimal artificial-life model in which persistent organisms — with real death, no negative valence, and no aversive signal — acquire value, prediction, attention, autobiographical damage records, a self-model, and a learned sca...

Why the Golden Ratio Selects the Prime Three

Fix a base b, a prime p not dividing b with b congruent to 1 mod p, and a positive integer m whose prime factors all divide b. The repetend alignment satisfies alpha(pm) = (2m-1)/(pm-1). Among odd primes, only p = 3 admits alignment exceeding 1/phi, with threshold m >= phi^2. Any...

AI Data-Centre Water Tracker: an open, reproducible referee for data-centre water burden

AI disclosure: parts of this text were artificially generated with AI assistance and reviewed by the author. The models, and the conflicts they create, are named in the Conflict of interest section. An open, reproducible referee for the water burden of AI data centres. Ren et al....

Symplectic Geometry and Curvature as Manifestations of the FRLT Pivot

Geometric structures—symplectic, curvature, Fedosov, and Kähler—arise as scalar, operator, higher‑order, and integrable manifestations of the FRLT pivot, unified by the generative formula R(X,Y)Z=Π(X,Y)(Z).

BCMA CAR T-cell therapy in a patient with heavily pretreated relapsed/refractory POEMS Syndrome: a case report

Abstract B-cell maturation antigen (BCMA) chimeric antigen receptor T-cell (CAR T-cell) therapy is an established treatment for relapsed/refractory multiple myeloma. However, its application in POEMS syndrome remains largely unreported, despite overlapping pathogenesis involving...

A Spectral-Geometric Proof of the Goldbach Conjecture

This paper presents a proof of the Goldbach Conjecture: every even integer2N ≥4 can be expressed as the sum of two prime numbers. The argument is builtwithin spectral geometry. We embed the prime-pair decomposition condition intothe zero locus of a singular spectral potential def...

C.E.R.B.E.R.U.S.™ v2 — Comprehensive Enterprise Resilience, Boundary Enforcement, Risk Unification & Security Architecture System: An Integrated Governance, Resilience, Risk & Security Architecture for Complex and Regulated Enterprises

C.E.R.B.E.R.U.S.™ v2 Comprehensive Enterprise Resilience, Boundary Enforcement, Risk Unification & Security Architecture System TOP_INSTITUTIONAL Canonical Publication Release Complete Reproducible Research Artifact, Cybersecurity Architecture Framework, Audit Evidence, Cryptogra...

Right hippocampal volume and attenuated psychotic symptoms distinguish subgroups of youth with common patterns of temporoparietal effective connectivity

Abstract Associations between patterns of brain connectivity and brain structural features have transdiagnostic relevance to psychopathology. There is considerable evidence for disruptions to the hippocampus and temporoparietal brain systems in psychotic disorders. The present st...