Mehrdad Pajuhaan

This note interprets C as a physical generator space while retaining standard quantum, variational, Gaussian, Maxwell, and infrared Dirac mathematics. It links a Gaussian state on C, its Hubbard–Stratonovich lift into R³, and a locked one-loop electron, treating electron mass as an emergent infrared quantity rather than a bare input.

This overview presents particles and fields as effective descriptions of locked complex relations rather than primitive objects. It assigns phase to clocking, winding, and electromagnetic holonomy, and positive scale to distance and gravitational deficit, then summarizes proposed links to the fine-structure constant, electron mass, and a three-loop baryonic sector.

This paper formulates a candidate rest-frame closure for electron mass using a locked Gaussian ring across separate generator and propagation spaces. Two independent scalar and vector closure paths yield stationary radii and mass expressions built from the Planck scale, α, and dimensionless geometry; their numerical outputs are compared with the CODATA electron rest energy.

Within Relator kinematics, this note combines the Rω = c lock, E = ℏω, and a rotationally symmetric Gaussian energy profile on C. It reports a state-independent energy–time action and an averaged scale of ℏ/2, presenting this as a geometric realization of saturated energy–time uncertainty consistent with Gaussian position–momentum packets.

This Letter introduces a conservative nonlinear modification of single-particle Schrödinger dynamics that represents the Rω = c lock through amplitude–phase coupling. From an effective Lagrangian it derives a real phase potential while preserving norm and standard continuity; numerical simulations report that negative coupling suppresses Gaussian wave-packet dispersion over the tested interval.

This paper proposes that entanglement emerges from the Relator condition Rω = c in a two-space construction separating internal generator space C from ordinary propagation space R³. It describes interactions as creating a shared internal-frequency component and resonant coupling in C-space, intended as a geometric account of entanglement and the classical–quantum divide.

This paper introduces Quantum Bifurcation Theory, in which measurement is modeled as an interaction-induced geometric bifurcation constrained by Rω = c. It proposes a joint account of interference and entanglement without explicit collapse or hidden variables, and reports recovery of interference patterns, Bell correlations, Tsirelson’s bound, and no-signaling.

The paper proposes a local phase–scale transformation that unifies electromagnetic U(1) and gravitational positive-scale gauge branches. From invariant clock and ruler relations plus a Gaussian information cost, it derives a field equation, Newtonian two-body attraction, a lapse–metric relation, and an exact Schwarzschild static vacuum within the stated construction.

Within a conditional Relator construction, the preprint models gravity and electromagnetism as distinct infrared readouts of a shared Gaussian–Coulomb edge kernel on C, with fields represented in R³. It reports recovery of Newton and Coulomb potentials and an Einstein–Maxwell–Dirac reading, subject to explicit refinement, locality, positivity, and normalization assumptions.

This preprint recasts the Relator lock Rω = c and its complex–spatial frequency decomposition within covariant general relativity. It proposes an internal complex fiber populated by an energy-dot ensemble whose maximum-entropy state is Gaussian, then shows how special relativity, gravitational redshift, and the massless sector arise as limiting cases.

This Letter studies a Planck-cutoff QED–Dirac–Maxwell boundary problem in which an Eguchi–Hanson Maxwell action fixes an exponential factor. Balancing fixed-charge and collar-stiffness terms determines a stationary radius and an electron-mass estimate; the abstract reports reduced-branch and one-loop-audited values without using the observed electron mass as input.

The full preprint derives an electron-mass formula from massless QED coupled semiclassically to Euclidean Einstein gravity on Eguchi–Hanson space. A spin structure, Gaussian source profile, boundary location, radial response, and one binary homogeneity axiom define the construction; radial stationarity yields a one-loop estimate compared with the observed mass only as an audit.

This note recasts the broader Alpha/Relator route as a conditional Dirac–QED finite-part closure for the fine-structure constant using standard Dirac/QED ingredients plus five explicit nonstandard assumptions. With no measured α or continuous fit parameter inserted, a reduced audit matches CODATA closely; an error-bounded transverse-photon resolvent evaluation remains necessary for full certification.

This paper proposes a conditional shell-geometric mechanism that selects the fine-structure coupling from an Rω = c lock, pinned electron branch, scalar slowdown law, vector shell geometry, and a universal logarithmic coefficient. It reports a value near the accepted benchmark and derives a related pure-photonic electron g−2 series as a cross-check.

This note formulates the Relator electron as a stationary-action problem on C ⊕ R³ and connects the result to Dirac and special-relativistic infrared physics. Its variational locks are said to determine electron mass without an inserted mass parameter; phase gauging supplies charge and Maxwell coupling, while a Pauli term accommodates g−2.

This paper derives a closed charged-lepton mass-ladder law in which the electron, muon, and tau are treated as three shell realizations of one Gaussian Relator core. Shell-dependent source terms pass through a determinant-normalized Schur/Feshbach construction before producing mass logarithms; it reports electron-anchored muon and tau ratios without fitting those masses.

This paper presents a finite electromagnetic-sector Relator calculation of charged-lepton g−2, treating the anomaly as the magnetic image of self-field-induced internal-clock slowdown rather than an independent Pauli term. A universal shell branch is combined with lepton-mass-dependent source-covariance terms, and the resulting coefficients are compared externally with pure-photonic QED benchmarks.

This paper extends the charged-lepton Relator construction to normally ordered neutrino masses using a ring–collar geometry fixed by Rω = c. With coefficients obtained from analytic series and one-dimensional integrals, it reports mass ratios and a mass-squared-splitting ratio, then compares them with global-fit values while stating that no neutrino data enter the construction.

This Letter defines a recastable Relator-Z₅ charged-vector benchmark for LHC searches, centered on a 10.7707 TeV spin-1, unit-charge state and a heavier partner near 22 TeV. It identifies interference in the high-MT charged-current Drell–Yan tail as the main observable, conditional on unresolved geometric overlap and interference parameters.

The preprint replaces a scalar Z₃ triplet junction gate with a bounded projective Hesse construction on CP². Under stated shell-admission and spectral-matching assumptions, it gives conditional formulas for a proton-candidate/electron mass ratio and charge spacing, plus a reduced geometric proton g-factor estimate, while withholding a full baryonic magnetic derivation.

The preprint extends the Relator closure to a Z₄-locked four-loop bouquet, which it claims selects an electroweak-scale parent and a parameter-free W–Z–H mass triad. It associates topology with dominant couplings and decay channels, and predicts a heavier Z₅ rung that could yield new resonance scales at sufficiently energetic collisions.

The preprint models a neutron as a lock between a Z₃-stabilized proton junction and a one-loop lepton. Using the Relator phase budget, Gaussian collar, measured neutron g-factor, and PDG/CODATA inputs, it formulates an invariant “attempt × gate” decay rate and reports a mean lifetime of 877.83 s.

This Letter extends the one-loop Relator construction to a Z₃-locked three-loop bouquet as a proton candidate. Without introducing QCD microphysics or fitted couplings, it derives a closed proton–electron mass-ratio estimate while explicitly acknowledging omitted composite microstructure; the reported value exceeds the CODATA ratio by about 405 ppm.

The preprint asks whether entropy can arise from the algebra of a one-dimensional complex generator space. Assuming luminal “energy dots,” symmetry, additivity, and a fixed information-update rate, it argues that Shannon entropy and a circular Gaussian distribution follow, interpreting entropy as a statistical expression of the underlying complex structure.

This Letter reports a numerical conjecture relating the Planck length, electron and Planck masses, and a cosmic radius derived from the Universe’s age. The proposed scaling links microscopic and cosmological quantities, but the abstract explicitly states that it lacks an established microscopic derivation and does not yet constitute a complete physical theory.