Research works

Fermionic Matter and Chirality from Projective Dirac Admissibility

The preceding gauge–gravity synthesis of the Cosmochrony programme showed that gravity and Yang–Mills dynamics arise from the $a_2$ and $a_4$ Seeley–DeWitt responses of the same admissible spectral functional. The present paper extends this principle to the fermionic sector. Ferm...

Beyond PAM: digital photography and RGB color analysis as a cost-effective method for coral bleaching assessment

<title>Abstract</title> Coral reefs are experiencing increased frequency and severity of thermal stress events, underscoring the urgent need for rapid and scalable methods to assess coral bleaching susceptibility. Quantifying bleaching responses typically relies on pulse-amplitud...

Automated synthetic cell-based screening for designed proteins with emergent functions

Abstract Designing minimal biological systems with emergent functions such as spatiotemporal self-organization is a central goal of bottom-up synthetic biology. While computational optimization and design show promises to accelerate functional protein engineering through Design-B...

EXISTENTIAL STRUCTURAL GEOMETRY OF INFORMATION (RDG-EULER) MO-ADEL

Existential Structural Geometry of InformationThe Recursive Deductive Generation (RDG–Euler) Framework Mo-AdelA Formal Mathematical, Informational, and Observer-CentricAlternative to the Theory of EverythingPreliminary Draft v1.1Mohamed Adel Mohamed Abdelnabi Mahmoud HamamIndepen...

Dirichlet Form and Reconstruction of Macroscopic Geometry

Can macroscopic geometry be derived from a finite stochastic mechanism rather than assumed in advance? This article develops a rigorous route from reversible microscopic jump dynamics to an intrinsic metric, measure, differential operator, and curvature. The starting point is del...

Adhesion investigation of waterborne and solventborne epoxy coatings on oil-contaminated and surface-corroded steel substrates

Epoxy coatings are widely used to protect steel structures; however, industrial substrates often retain residual corrosion products and organic contaminants after surface preparation. Waterborne (WB) epoxy coatings are generally considered less surface-tolerant than solventborne...

Born–Infeld Parity Forces an Equatorial Admissible Fibre: Analytical Derivation of the [1:½:½] Eigenvalue Ratio in Sym²(Vρ)

Papers O28–O29 of the Cosmochrony spectral admissibility sub-programme established that the per-pair covariance $\mathcal{C}_c$ in $\operatorname{Sym}^2(V_\rho)$ has rank $r_{\mathrm{eff}} = 3$ with invariant eigenvalue structure $[\lambda_1: \lambda_2: \lambda_3] = [1: \tfrac{1}...

Semiclassical Consistency of the Weil Representation on Heis3(Z/qZ): Quantitative Sinc Embedding, Generator Convergence, and Aliasing Control

We prove that the rescaled Weil generators ${\hat{X}_q}$ and ${\hat{P}_q}$ of the discrete Heisenberg group ${\mathrm{Heis}_3}({\mathbb{Z}/q\mathbb{Z}})$ converge strongly to the position operator $x$ and the momentum operator $-i\partial_x$ as $q \to \infty$, in the sense of Hyp...

Fourier Structure of the Pre-Saturation Admissible Pipeline: What the Three-Coordinate Projection Does and Does Not Measure

The numerical pipeline of the spectral admissibility programme stores, for each conjugate Weil pair $(c, q-c)$, two distinct objects: a full Gram–Schmidt basis of ${\mathbb{C}}^q$ reaching rank $q$ at saturation, and a three-coordinate array of projections onto the first three se...

Proof of the Lifting Hypothesis [H-lift]: Kinetic-Sector Identification via Generator Suppression

The companion paper Q5b introduces Hypothesis [H-lift]: the operator ${L_\Pi} = -A\partial_k^2$ produced by Q5a as the Mosco limit of the admissibility forms ${\mathcal{E}_q}$ is the image, under the Schr\"odinger representation $\pi_1$ at unit central character, of the kinetic s...

Sub-Principal Symbol of the Effective Operator and Casimir Rigidity of the Central Direction

Paper Q7 reduced the open problem Q5b-O2 of to a single computable criterion: whether the sub-principal symbol of the effective operator ${L_{\mathrm{eff}}}$ in the central direction ${\widetilde{Z}} = [{\widetilde{X}}, {\widetilde{Y}}]$ of ${\mathrm{Heis}_{3}(\mathbb{R})}$ carri...

Weight Stabilisation of the Admissible Dirichlet Form: Proof of Hypothesis [H-w] from Spectral Universality

We close open problem Q5a-O3 of the Cosmochrony spectral admissibility programme by proving Hypothesis [H-w]: the admissibility weights $a_q(s)$, which enter the filtered Dirichlet form ${\mathcal{E}_q}$, converge to a positive constant $A > 0$ uniformly in the generator $s \in S...

Asymptotic su(2)-Isotropy of the Effective Quadratic Form and the Identification AH = 2

Papers Q7 Q9 of the Cosmochrony spectral geometry programme establish that the effective operator $L_{\mathrm{eff}}$ on $\mathbb{R}_\tau \times {\operatorname{Heis}}_3(\mathbb{R})$ has a principal symbol $\sigma_2(L_{\mathrm{eff}})|_{H_{\mathrm{eff}}} = A_H(k_X^2+k_Y^2) + A_Z k_Z...

Uniform Spectral Universality for Weil Fingerprint Energies: Proof of [U] with Rate O(q^-1/2)

The Q10 paper of the Cosmochrony programme reduces the proof of isotropy $A_H = 2$ to the O-series spectral universality hypothesis [U]: $\max_c |\sigma_c(n) - \sigma_*(n)| \leq \varepsilon(q)\sigma_*(n) \to 0$ uniformly over the fitting window $n \leq n_*(q)$. The present paper...

Three Admissible Directions and Three Spatial Dimensions: A Structural Bridge Candidate between Heff ≃ C³ and the Horizontal Geometry of Heis3(R)

Two independent sub-programmes of the Cosmochrony framework independently produce the integer three as a structural output. Paper Q5b derives a four-dimensional effective Lorentzian geometry from the homogeneous dimension ${D_{\mathrm{hom}}} = 4$ of ${\mathrm{Heis}_3}(\mathbb{Z}/...

The Topological Invariance Principle: Exact Spatial Flatness and the Spin–Torsion Link: an Open Problem in Einstein–Cartan Cosmology

Standard cosmology treats the observed spatial flatness of the Universe (Ω_K ≃ 0) as an observational coincidence, to be explained dynamically by inflation. We adopt a different stance and state it as a postulate: spatial flatness is exact, Ω_K ≡ 0, as a topological property of s...

Carrier Identification via the Veronese Collapse: Effective Dimension of the Admissible Covariance in End(Heff)

Paper O28 established that the per-pair covariance ${\mathcal{C}_c}$ in ${\operatorname{End}}({H_{\mathrm{eff}}})$ has rank ${r_{\mathrm{eff}}} = 3$ with invariant eigenvalue structure $[1: \tfrac{1}{2}: \tfrac{1}{2}]$. The present paper gives the structural explanation of this r...

Asymptotic Calibration of the BFS Window and Effective Dimension of the Admissible Trajectory

The O25 programme identified the ratio $n_1(q)/q$ as the central open asymptotic variable controlling the finite-size drift of $\bar{\delta}_{\mathrm{pair}}(q)$, and O26–O27 identified the effective dimension $r_{\mathrm{eff}} = d_\rho^2$ of the per-pair covariance operator in $\...

Analytical performance of a multi-target open real-time PCR assay for simultaneous detection of tuberculosis, non-tuberculous mycobacteria, and drug resistance in a high-burden setting

ABSTRACT Timely diagnosis of tuberculosis (TB) and drug resistance is crucial for effective disease control. Multiplex open molecular platforms capable of simultaneously detecting Mycobacterium tuberculosis complex (MTBc), non-tuberculous mycobacteria (NTM), and resistance to fir...

Beyond Molecular Dispersion: A Molecular-Cone Architecture of Cobalt Phthalocyanine on CNTs for Selective CO2 Electroreduction to Methanol

Abstract Molecularly dispersed cobalt phthalocyanine (CoPc) on carbon nanotubes can be used as an efficient catalyst for electrochemical CO2-to-methanol conversion. However, increasing the CoPc loading to enhance the current density typically induces aggregation, which compromise...