Primitive V/h Architecture
Year: 2026
Type: preprint
Abstract: PRIMITIVE V/H ARCHITECTURE — TRANSPOSITION OF SUBATOMIC PARTICLES INTO THE EQUILIBRIUM STRUCTURE OF THE RIEMANN HYPOTHESIS This work presents an extension of the Primitive V/H Architecture, originally organized around the equilibrium structure of the Riemann Hypothesis, to the structural organization of subatomic particles, composite particles, exotic states, collective states, and the transition between the quantum and macroscopic domains. The construction begins with the intersection V∩H=CENTER,V \cap H = \mathrm{CENTER}, which defines the central reference of the architecture. From this CENTER, the structure is organized through symmetry, fixed point, equilibrium, levels, dynamics, convergence, and states. The fundamental symmetry is expressed by s↦1−s,s \mapsto 1-s, whose fixed point is β=12.\beta=\frac{1}{2}. The displacement from the equilibrium position is defined as d=β−12,d=\beta-\frac{1}{2}, so that the equilibrium condition is d=0.d=0. Within the architecture, the critical line is therefore associated with the equilibrium coordinate 1/21/2. The work then transposes this structure to the organization of subatomic particles. Quarks, leptons, bosons, baryons, mesons, tetraquarks, pentaquarks, gluonic states, exotic states, and collective states are interpreted as different occupations of levels within the same structural architecture. The diversity of physical states is consequently represented through successive levels rather than through the creation of independent fundamental centers. The representation ρn=12+iγn\rho_n=\frac{1}{2}+i\gamma_n is retained as the structural expression connecting the equilibrium coordinate 1/21/2 with the successive levels represented by γn\gamma_n. Within the proposed architecture, the real component corresponds to the equilibrium position, while the γ\gamma-coordinate organizes the succession of levels. A central structural proposition of the work is therefore: 1 CENTER→1 AXIS→1 SPIRALITY→N LEVELS→N STATES.1\ \mathrm{CENTER} \rightarrow 1\ \mathrm{AXIS} \rightarrow 1\ \mathrm{SPIRALITY} \rightarrow N\ \mathrm{LEVELS} \rightarrow N\ \mathrm{STATES}. The article incorporates, within this framework, the structures discussed in relation to the doubly charmed baryon Ξcc+\Xi_{cc}^{+}, toponium, glueball X(2370)X(2370), baryon junctions, exotic states, and quark-gluon plasma. These states are treated within the same CENTER, the same equilibrium axis, and the same spiral organization. The resulting unified structural sequence is: CENTER→SYMMETRY→FIXED POINT→EQUILIBRIUM→12→CRITICAL LINE→LEVELS→STATES→DYNAMICS→CONVERGENCE.\mathrm{CENTER} \rightarrow \mathrm{SYMMETRY} \rightarrow \mathrm{FIXED\ POINT} \rightarrow \mathrm{EQUILIBRIUM} \rightarrow \frac{1}{2} \rightarrow \mathrm{CRITICAL\ LINE} \rightarrow \mathrm{LEVELS} \rightarrow \mathrm{STATES} \rightarrow \mathrm{DYNAMICS} \rightarrow \mathrm{CONVERGENCE}. The work subsequently extends the same architecture to the problem of the relationship between the quantum and macroscopic domains and to the relation between quantum structure and gravity. The central transition is formulated as MICRO→TRANSDUCTION→MACRO.\mathrm{MICRO} \rightarrow \mathrm{TRANSDUCTION} \rightarrow \mathrm{MACRO}. Within this extension, transduction is placed between microscopic quantum states and macroscopic structure. The proposed sequence is: QUANTUM→MATTER→DYNAMICS→TRANSDUCTION→FORM→GEOMETRY→SPACETIME→GRAVITY.\mathrm{QUANTUM} \rightarrow \mathrm{MATTER} \rightarrow \mathrm{DYNAMICS} \rightarrow \mathrm{TRANSDUCTION} \rightarrow \mathrm{FORM} \rightarrow \mathrm{GEOMETRY} \rightarrow \mathrm{SPACETIME} \rightarrow \mathrm{GRAVITY}. The work further expresses the transductive process through four successive levels: Q→C→F→G→Γ,Q\rightarrow C\rightarrow F\rightarrow G\rightarrow\Gamma, representing: QUANTUM→COLLECTIVE→FORM→GEOMETRY→GRAVITY.\mathrm{QUANTUM} \rightarrow \mathrm{COLLECTIVE} \rightarrow \mathrm{FORM} \rightarrow \mathrm{GEOMETRY} \rightarrow \mathrm{GRAVITY}. The resulting formulation places quantum states, matter, dynamics, collective organization, form, geometry, spacetime, and gravity within a single structural chain. The distinction between microscopic and macroscopic domains is consequently represented as different regimes or levels of the same architecture. The final unified form proposed in the work is: CENTER→SYMMETRY→FIXED POINT→EQUILIBRIUM→12→LEVELS→STATES→DYNAMICS→TRANSDUCTION→COLLECTIVITY→FORM→GEOMETRY→SPACETIME→GRAVITY\boxed{ \mathrm{CENTER} \rightarrow \mathrm{SYMMETRY} \rightarrow \mathrm{FIXED\ POINT} \rightarrow \mathrm{EQUILIBRIUM} \rightarrow \frac{1}{2} \rightarrow \mathrm{LEVELS} \rightarrow \mathrm{STATES} \rightarrow \mathrm{DYNAMICS} \rightarrow \mathrm{TRANSDUCTION} \rightarrow \mathrm{COLLECTIVITY} \rightarrow \mathrm{FORM} \rightarrow \mathrm{GEOMETRY} \rightarrow \mathrm{SPACETIME} \rightarrow \mathrm{GRAVITY} } The work therefore presents the Primitive V/H Architecture as a single structural framework in which one CENTER, one equilibrium axis, and one spiral organization can accommodate successive levels and states, from the organization of non-trivial zeta zeros to subatomic states and to the proposed transductive passage from quantum structure to macroscopic geometry and gravity. Keywords: Primitive V/H Architecture; Riemann Hypothesis; Critical Line; Equilibrium 1/2; Subatomic Particles; Quarks; Gluons; Glueball; Toponium; Baryon Junction; Spirality; Quantum Structure; Macroscopic Structure; Transduction; Geometry; Gravity.
Author: Vicente da Silva, Cláudio
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214534659
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