Physical Sciences

Abstract: Physical states and objective observation conditions jointly determine experimental records. Starting from the physical--observation dual-axis (PODA) structure of Physobser Theory, we construct a common dynamics for the parent connection, response projector, matter fields, and spacetime geometry. In the stated chiral and stable-vacuum realization, an internal five-dimensional space splits into three- and two-dimensional blocks; color and electroweak breaking yield the three gauge interactions, while all stresses source the same gravitational field. The common Dirac spectrum relates gravitational and gauge kinetics through \( k_{\rm sp}g_{\rm sp}^2=2\Omega^2 \). Compatible elimination preserves the parent solutions and their physical source responses. The monograph's sequential return becomes an explicit five-dimensional channel: populations, coherence, and time composition determine when a finite return belongs to the continuous dynamics used here. Eliminating the common coupling and running time then gives a direct relation between two return probabilities and three inverse gauge couplings. Fermion anomalies, thresholds, the strong-CP phase, proton partial lifetimes, and vacuum constraints are treated in the same realization. Positive normal-mode reductions retain the leading low-energy spectral relations, but the purely exponential covariance has a high-energy positivity obstruction and is not identified with a complete positive parent quantum theory. The result is a common classical and controlled low-energy quantum realization with explicit source, response, and matching relations. The four physical interactions remain distinct from the geometric direction types XX, XS, and SS.

Abstract: A two-field configuration cannot generally be reduced to a single scalar while preserving its dynamics, because discarding its internal relative structure omits positive internal stress and thereby artificially lowers the stress represented in the reduced description. In a specified two-field model, three gradient and two contact channels fix the compression generator \(2I_3\oplus3I_2\) and internal virial \(2E_s+3E_a\). The resulting energy carrier yields a sharp entropy-virial bound, attained by smooth fields and strengthened at fixed positive core density. Restricted weak-field GR profile tests use 153 SPARC galaxies, withholding 659 outer observations in 131. With matched stellar, distance and inclination priors, the fixed-shape core lowers median outer loss from 24.46 for the adopted baryonic source to 3.89: an 84.1% reduction (paired-bootstrap 95% interval 75.9-90.8%). It wins 101/131 comparisons, or 100/130 excluding one infeasible baseline. Under independent galaxy signs and equal win probabilities, the five-test Holm-adjusted \(p=7.00\times10^-10\) has two-sided Gaussian equivalent \(Z=6.17\). Navarro-Frenk-White retains lower median outer loss, 1.97, and wins 87/131 comparisons against the core (\(Z=3.52\), separate three-test correction). All comparisons use the same GR law. The fitted cores have zero excess internal stress; these retrospective tests do not uniquely identify entropy geometry. Common baryonic gravity preserves the model's unexcited mixed sector; internal stress supports the field, while tracers respond to gravity. Physical validation requires shared-parameter equilibria in the combined baryonic and field potential, calibrated uncertainties and independent evaluation.

Abstract: Standard formulations of General Relativity treat the gravitational coupling constant, G/c⁴, as a fundamental and invariant property of spacetime. This theoretical paper proposes an alternative framework where macroscopic gravity is an emergent statistical variance—a volumetric dilution—of the bare 1D spatial tension inherent to quantum chromodynamic (QCD) flux tubes. By defining a holographic phase space of discrete angular orientations for confined nucleons, we reveal a mathematical duality, demonstrating that G/c⁴ is synonymous with the residual isotropic noise of this quantum ensemble. Furthermore, we demonstrate that subjecting a macroscopic continuum—such as the degenerate matter of a rapidly rotating neutron star or a terrestrial experimental lattice—to extreme kinematic rotation introduces a localized spatial gradient of proper time. This proper acceleration immerses the nucleons in an anisotropic non-inertial vacuum. By mapping this vacuum anisotropy through a Finslerian geometric framework, we demonstrate how this kinematic bias restricts the holographic phase space and breaks the isotropic cancellation of a fraction of the bare strong-force tension, coupling it directly to the macroscopic metric tensor. This derivation provides a formal, first-principles basis for anomalous scaling in rotating continuum materials. It predicts a falsifiable, non-linear thermodynamic backreaction (“quantum drag”) during angular acceleration against the entropic inertia of the QCD vacuum. By acting as a reactive quantum drag during terrestrial spin-up and a thermodynamic flywheel during stellar spin-down, this mechanism offers a novel, first-principles resolution to anomalous pulsar braking indices (n<3). By analytically constraining this macroscopic field using observational data from the Crab Pulsar, this framework bounds the phenomenon to physically realistic limits, establishing parameters for terrestrial laboratory verification.

Abstract: We develop a history-amplitude construction for the residual Weyl freedom of anchored causally stratified Lorentzian systems with prescribed Ricci-source data, fixed anchors, discrete causal succession without fundamental simultaneity, and admissibility conditions requiring histories to realize rather than redefine the transition. Dendrographic Holographic Theory (DHT) provides a concrete realization.Once the Ricci sector is fixed, the remaining pointwise curvature freedom in four dimensions is the electric--magnetic Weyl sector, with five electric and five magnetic components. For a canonical quadratic Fermi representative and centered round tube, a boundary-completed Einstein--Hilbert plus Gibbons--Hawking--York calculation yields the local Weyl-jet potential, including distinct electric and magnetic terms and an electric-Weyl coupling to source anisotropy. We equip the ten-dimensional Weyl fiber with a positive configuration-space geometry and introduce an independent jet-refinement principle as a dynamical postulate. On the canonical flat fiber, locality, unitarity, composition consistency, and leading second-order dependence on this geometry select the Gaussian short-time kernel and define the history integral by time-sliced refinement rather than an assumed infinite-dimensional Lebesgue measure.For prescribed source anisotropy independent of the Weyl history and \( \kappa>0 \), the ambient dynamics separates into five forced electric harmonic oscillators and five magnetic inverted oscillators, with an explicit principal function, propagator, and Van Vleck determinant. Within regular realizability sectors, the branch-conditioned construction restricts to self-consistent metric--geodesic branches and imposes endpoint conditions by finite-dimensional coarea, yielding endpoint kernels, proper-duration-resolved operators, arrival classes, and a decoherence functional with sufficient phase-mixing criteria.In DHT, exact relational anchors, their succession, and the informational Ricci source are fixed independently of the auxiliary Lorentzian realization. The informational source gives the completed electric-Weyl--anisotropy coefficient \( 4\pi/135 \). Different admissible branches of one exact relational transition may carry different proper durations. Hence \( \tau\not\equiv T_\gamma \): relational succession remains distinct from geometrical arrival duration.

Abstract: Based on an extended scalar field framework, this work investigates the connection between geometric level displacements and metric deformations through scale perturbations under point massinteractions. A perturbative mechanism modifying the vacuum state is proposed to model the anisotropy between the temporal and spatial sectors. This approach reveals an internal compatibility condition that reproduces the metric reciprocity relation and yields an emergent localized point mass. In the long-distance regime, the resulting metric deformation is consistent with General Relativity predictions in the weak-field limit. Furthermore, the local deformation remains strictly finite and free of singularities throughout the spacetime domain, establishing a regular emergent gravitational background derived from vacuum collapse.

Abstract: This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein’s research regarding general relativity and attempt to link general relativity to quantum laws.

Abstract: Can geometry, electromagnetic propagation, and electromagnetic backreaction be derivatives of one function before a metric or a matter action is introduced? We exhibit a local affirmative construction. The only dynamical field in the parent action is an \( SL(3,\mathbb C) \) connection, and a degree-one homogeneous adjoint-invariant phase \( \Phi(X) \) of curvature wedge products supplies its constitutive response \( B_I=2\Phi_{,IJ}F^J \). Curvature-derived spectral projectors define an analytic parent phase near an ordered 3+4+1 response. Its exact, consistently embedded neutral sector admits an algebraic stationary representation that enforces the simplicity constraints on the full gravitational response at finite electromagnetic amplitude within the regular local neutral branch. The resulting triplet reconstructs the geometry; the central derivative gives Maxwell propagation in that geometry; and the gravitational derivative gives its Maxwell source, controlled by the same parent coefficient. On the specified Lorentzian real branch, the neutral equations are exactly the Einstein–Maxwell–\( \Lambda \) electrovacuum equations, not an amplitude truncation or an inference from quadratic matching. We prove the local invariant completion, compute its ordered connection two-jet, and give explicit curvature and coupling conventions. The construction realizes one classical ordered branch of a single phase; its domain is the regular analytic neighborhood of that branch.

Abstract: To determine the covariant four-momentum of a physical system in curved spacetime, we introduce an energy-momentum field, whose four-potential and tensor are included in the Lagrangian density. From the principle of least action, we derive an equation for the metric, equations for the energy-momentum field, and the four-dimensional Euler-Lagrange equation. The equations of particle motion are derived in two ways: through the covariant derivative of the right-hand side of the equation for the metric, and by varying the action function with respect to the four-coordinates. These equations are equal when the invariant mass density of the particles is constant. The four-potential of the energy-momentum field makes it possible to find the four-momentum density and four-momentum of the system. The corresponding equations are derived by varying the action function under a four-shift of all particles of the system by a constant four-vector. The four-momentum density and the four-momentum of the system must satisfy these equations for the system's symmetry associated with such the four-shift to hold.

Abstract: This work considers the hypothesis that the cosmological vacuum may retain a residual relational capacity, here described as vacuum porosity, and that cosmic expansion may involve a continuous redistribution of the response associated with this condition. At the macroscopic level, this response is represented by a residual scalar stress S. Here, S denotes residual vacuum stress, not thermodynamic entropy. Any connection between the two would need to be established separately. In a homogeneous and isotropic equilibrium regime, the corresponding vacuum-like contribution is written in the form \( Σ_{μν} = - Sg_{μν} \). When this term is included in the source sector of Einstein’s field equation, \( G_{μν} = \frac{8πG}{c^4} (T_{μν} + Σ_{μν}) \) substitution of the isotropic vacuum-stress tensor gives \( G_{μν} + \frac{8πG}{c^4} Sg_{μν} = \frac{8πG}{c^4} T_{μν} \). Direct comparison with Einstein’s equation containing the cosmological term, \( G_{μν} + Λg_{μν} = \frac{8πG}{c^4} T_{μν} \) therefore yields \( Λ = \frac{8πG}{c^4} S \). The tensorial correspondence is exact once this vacuum-like isotropic form is assumed. The physical proposal is to interpret S as a residual stress associated with the redistribution of a relationally non-saturated vacuum during cosmic expansion, while leaving the Einstein tensor and the geometrical structure of general relativity unchanged. The present work is limited to the macroscopic tensorial description and physical interpretation of the residual stress.

Abstract: The quantum anomalous Hall effect is ordinarily written on the Brillouin torus of a fixed Hamiltonian. Here the occupied Chern band is held fixed while the state that forms the observation record is allowed to vary independently. Two projectors carry the two roles: an occupied-band projector PX(k) and an observation-response projector R(k, s). On every fixed observation section the construction reduces exactly to the standard theory, σxy = CXe 2 /h. When the observation state contains a periodic coordinate φ, the response bundle can carry a mixed first Chern number ν_iφ on \( S^1_{k_i}\times S^1_{\varphi} \) without changing the physical Chern number. Once the response connection enters the phase-transport law, one closed observation cycle transports Q_i = eν_iφ per equivalent transverse response channel. The integer collapses to ν_iφ = ±1 whenever the mixed response line bundle is topologically primitive; orientation fixes the sign. An elementary nontrivial response cycle therefore carries exactly one charge quantum per channel, while higher integers describe composite topological sectors. A two-level projector realizes the primitive class. The parameter-free relations Q/e = 1, I/(ef) = 1, and eV_H/(hf) = 1 follow, distinct from ordinary Thouless and Brouwer pumping. The experimental question is whether such a quantized, orientation-odd residue survives while the physical QAH Hamiltonian remains fixed.

Abstract: Planck units are fundamental constants of physics. Time, velocity, mass, and gravitational force can be expressed in terms of Planck units. Planck time constitutes the fundamental unit of the numerical order of events unfolding in time-invariant space. There is neither a physical past nor a physical future. Time as duration is an emergent physical quantity that arises only in the process of measurement. Every physical object is an energetic structure of space itself. Gravity is mediated by variations in the energy density of space.

Abstract: We present the Lucron Model, a physical framework in which fundamental reality is a network of identical units called Lucrons. Each Lucron possesses intrinsic minimal properties---length, time, mass, charge, and action---that are the smallest non-zero values in every metric. The apparent absence of intrinsic properties at ordinary scales is an effect of scale, not a metaphysical absence. We show that a single-scale Lucron with scale \( \ell_L \) and coupling \( g_* \), together with the permutation symmetry \( S_3 \) of the bound-state ``candado,'' reproduces the following without fine-tuning: (i) the Planck scale, \( G = \ell_L^2 \); (ii) gauge unification with \( \alpha_{\rm GUT} = g_*^2/(4\pi) \approx 1/24 \); (iii) the Weinberg angle \( \sin^2\theta_W = 3/8 \) at the GUT scale; (iv) the electroweak hierarchy \( v/m_P = e^{-2\pi^2/g_*^2} \); (v) the electron hierarchy \( m_e/v = e^{-7/g_*^2} \); (vi) the Koide formula with \( \theta = 2/9 \) rad; (vii) the Cabibbo angle \( \sin\theta_C = \sqrt{m_d/m_s} \); (viii) the PMNS angles \( \theta_{23} \approx 45° \) and \( \theta_{13} \approx 8.5° \); (ix) the cosmological constant \( \Lambda \ell_P^2 = N^{-2/3} \approx 10^{-122} \) for \( N \sim 10^{183} \). We also identify where the model fails quantitatively: the CKM angle \( \theta_{23} \) (factor \( 1.4 \)), the CP phase \( \delta_{\rm CP} \) (factor \( 2.4 \)), and the PMNS angle \( \theta_{12} \) (factor \( 1.25 \)). These failures point to unresolved geometric details of the candado. We further show that the volume law \( V = v_0 \sum_i 1/c_i \) reproduces \( \Lambda \)CDM at the cosmological level, yielding \( \chi^2 = 12.8 \) against DESI DR2 BAO, identical to \( \Lambda \)CDM. With two fundamental parameters \( (\ell_L, g_*) \) and one symmetry (\( S_3 \)), the model accounts for approximately twenty dimensionless constants, a significant reduction over the Standard Model's nineteen free parameters.

Abstract: A lattice of locally coupled quantum oscillators is proposed as a candidate microscopic substrate for emergent spacetime. Each oscillator is treated as an elementary substrate unit (ESU): a minimal quantum degree of freedom whose local dynamics, correlations, and collective organization may underlie higher-level physical structure. For the minimal fixed cubic-lattice realization, the exact collective-mode dispersion relation is derived and shown to approach relativistic propagation at long wavelength, with limiting speed c_eff = a√(K/M). The leading lattice correction is anisotropic and quadratic in momentum, providing both a direct Lorentz-violation signature and an intrinsic ultraviolet cutoff. For a Planck-scale lattice spacing, the corresponding Lorentz-violation scale is E_LV ≈ ħc/ℓ_P ≈ 1.22×10^19 GeV, roughly eight orders of magnitude above the conservative quadratic-order lower bound inferred from GRB 090510 for the bosonic collective sector constructed here. Comparison with strings and matrix models, spin networks, causal sets, causal dynamical triangulations, and quantum graphity shows that the oscillator substrate trades background independence at this stage for calculability, explicit microscopic dynamics, and quantitative falsifiability. The framework further treats possible chains, loops, defects, networks, fields, and particles as structures to be generated—or excluded—by the substrate dynamics rather than inserted independently. Thus the model supplies a concrete first-stage substrate hypothesis and a dynamical selection principle. The calculation establishes kinematic continuum-like emergence on a fixed lattice; dynamical connectivity, a universal causal structure, a massless spin-2 gravitational sector with the required gauge structure, and viable chiral matter remain decisive tests of the broader hypothesis.

Abstract: We compute the complete relative entropy of a faithful quantum family controlled by spatial translations and Lorentz boosts. The prescribed contrast has a minimal three-dimensional positive Hessian realisation. Finite comparisons determine every minimal single-chart embedding up to an affine transformation and fix the potential's first jet, leaving its normal Hessian free. No positive single-chart realisation on a globally convex domain exists in any finite dimension for the entire control plane, whereas every bounded rapidity strip admits one. An exact dephasing channel preserves the energy-momentum law while reducing the contrast to classical rapidity distinguishability. Calibrating a preparation Hamiltonian gives sharp work-susceptibility and finite-work control-area bounds. Within the specified four-parameter preparation family, intrinsic Bogoliubov-Kubo-Mori (BKM) length bounds entropy change; paths outside that family need not obey this bound, even at the same observable law. A genuine Born lift preserves the commutator form with an exact area remainder independent of normal-potential freedom. These results separate finite-contrast rigidity, calibrated energy response, and geometric compatibility without identifying statistical transport with physical dynamics.

Abstract: We propose a field-quantum framework in which discrete field quanta constitute space (A), attract their neighbours (P1), each carry a two-component complex amplitude whose normalised states carry the Hopf fibration \(S^1\to S^3\to\mathrm{CP}^1\) (P2), and every coherent excitation is one configuration whose energy, orientation and integer counts—action \(\hbar\) per cycle—are attributes of the whole (P3), from which one-quantum wholeness follows as a theorem. The continuum limit is a Lorentz-invariant nonlinear Klein–Gordon theory, and the numerical checks below use lattice simulations of this action. Rest mass is the vacuum-subtracted deformation energy, \(mc^2=\int(T^{00}-T^{00}_{\rm vac})\,d^3x\), verified by 3D decomposition; a boosted soliton recovers \(E=\gamma mc^2\). Velocity and gravitational time dilation issue from one internal light clock: a moving clock's internal signal slants at unchanged transverse size; a static clock's spacing and update rate are each scaled by \(\lambda_g\) (shorter steps, slower steps). The two combine into \(\omega=\omega_0\sqrt{1-v_{\rm eff}^2/c^2}\) (\(v_{\rm eff}=v\) for a moving clock, \(v_{\rm esc}\) for a static one; one rule applied level by level, the factors multiplying when both act), with the conserved product law \(E_\infty=S\,m_{\rm loc}\) verified to 0.65%. The coordinate light speed \(c\lambda_g^2\) gives the $1.751''$ light deflection and the Shapiro delay by Fermat's principle, and the composition law \(\lambda_g=e^{\Phi/c^2}\) yields \(\beta=1\) and the perihelion advance. A finite-energy topological closure principle selects stable structures: a winding line cannot end in vacuum, so it must close. The electron is a localized winding of the orientation field whose charge is the turning sense of its tilt about the vacuum axis—the Gauss charge of the contact-face connection, one half-unit for odd Hopf winding by the Finkelstein--Rubinstein sign—and whose winding is its shape; spin \(\tfrac12\) is the angular momentum of the charge turning through the winding (\(L=-HQ\), at no rotational cost), the magnetic moment the winding current's field. Gravity is the medium's compression response to deformation energy; electromagnetism lives on the contact faces between quanta: with the identification of neighbouring internal frames promoted to a dynamical connection (P1b), Gauss's law is a theorem, Amp\`ere's law is the connection's own dynamics, the Coulomb law with both signs is a lattice result, and light is the connection's free wave—tmassless, two transverse polarisations, helicity \(\pm1\). A wavelength-sized source in this medium radiates an energy per cycle strictly proportional to \(\omega\), so the size of the unit is not obtained. Quantum measurement, interference and entanglement are read through the one-configuration postulate (P3), from which all-or-nothing delivery, the Born weights, the Malus law and the Bell correlations (\(S_{\rm CHSH}=2\sqrt2\)) follow as theorems and numerics, with the origin of the unit itself left open. The fine-structure constant is \(\alpha_e=\kappa_E\tilde\hbar/16\pi\), a product of two lattice numbers left as input; the Sakharov coefficient and absolute particle masses remain open.

Abstract: An observation record depends on the physical state being measured and on the conditions through which that state becomes a record. We consider a classical relativistic realization in which the latter are described by a continuous observation field. The metric, observation field, and matter are varied in a single action, restricted to an independent metric, a positive-definite observation kinetic metric, and minimal two-derivative coupling. A constant observation field at a stationary point of its potential defines an exact general-relativistic sector: its vacuum stress shifts the cosmological constant, and compatible initial data preserve the sector under evolution. Away from it, kinetic, gradient, and potential terms contribute stress-energy and determine the geometry together with matter. The coupled equations admit a common characteristic cone and an exact spatially homogeneous, time-dependent solution. Response comparison along a history is governed by a generally noncommuting connection. These results lead to two complementary experimental questions: whether independently calibrated transport predicts coherent records, and whether the stress-energy of a prepared observation field produces the predicted clock-frequency difference. We derive the weak-field integral relating that stress-energy to a differential clock reading. Near a stationary background, the additional gravitational source is quadratic in the perturbation; opposite perturbations must therefore be combined evenly, with an unperturbed reference and an amplitude scan, to retain the leading signal. An amplitude estimator including systematic effects and a source-sensitivity estimate specify the experimental requirements. The resulting tests depend on independently established field preparation, energy normalization, boundary conditions, and the formation law that turns a field solution into a record.

Abstract: Building on the published finite-resolution, background-independent framework for local semiclassical gravity, this work examines its phenomenological consequences across cosmology and particle physics. The underlying construction is formulated on a causal diamond equipped with a boundary-completed algebra, reflecting the non-factorization of the diffeomorphism-invariant Hilbert space. This algebra supplies the edge data needed for a local Wheeler--DeWitt description and is shared by the operational state and semiclassical reference family, whose relative entropy defines the local response. The entropic boundary capacity, with its topological term set by the Euler curvature charge, fixes an effective channel multiplicity \( N\approx1.23\times10^{11} \). Calibrating the coherent tensor response to Newton's constant then gives the matching scale \( M_s\approx3.02\times10^{13}\,{\rm GeV} \). In the equilibrium KMS regime, the leading relative-entropy Hessian separates into tensor, vector, and scalar response blocks, which a quasi-local heat-kernel expansion connects to the effective theory at the matching scale. The finite--continuum bridge uses the noncommutative-geometric algebra \( \mathcal A_F\simeq\mathbb C\oplus\mathbb H\oplus M_3(\mathbb C) \) with a common trace convention to map finite responses to Standard-Model observables. Once the boundary capacity, Newton calibration, and finite internal structure are fixed, the primary projections require no sector-specific continuous retuning. In cosmology, finite-resolution saturation identifies the scalaron pole with the matching scale, \( M_R=M_s \), and fixes the curvature stiffness \( \lambda_{R^2}=N_{\rm eff}/12 \). The isotropic boundary response gives the coherence duration \( \mathcal N_*=18\pi \), yielding \( n_s\approx0.9646\ \)and \( r\approx0.0038 \). All continuous dimensional scales cancel from the primordial scalar amplitude, leaving the finite-capacity relation \( A_s=81\pi/N \). Extensions of the same response give exploratory late-time targets for vacuum energy, structure growth, and the acceleration scale. In particle physics, single-pixel scalar saturation provides linked electroweak consistency tests, while the vector Hessian fixes correlated gauge responses. At the matching scale the construction gives \( \alpha_s^{-1}=12\pi, \alpha_{\rm em}^{-1}=36\pi \), and \( \sin^2\theta_W=7/18 \). The same finite geometry carries a Lie-theoretical filtration \( G\to\mathfrak g\to T \), whose successive accessibility levels organize the charged-lepton mass hierarchy, while canonical anticommutation relations provide the fermionic operator structure supporting the quark Yukawa hierarchy. Finally, finite-mesh simulations test the main analytical mechanisms numerically across the boundary, cosmological, gauge, and flavor sectors, including the modular filtration that selects the threefold generation carrier. The resulting cross-sector consistency makes the construction constrained and fragile in a useful sense: changing a shared input affects several sectors at once.

Abstract:

Spacetime is conventionally treated as a four-dimensional background within which matter and gravitational phenomena occur. Space-Clock Field Theory (SCFT-A) advances a field-first alternative: the Lorentzian metric is the gravitational field, and physical space is the clock-orthogonal spatial state of that field, rather than an independent background container in which gravity resides. A dynamical scalar clock \(T\) selects the physical foliation and distinguishes cosmological clock-field time \(T\) from matter proper time \(t\), the invariant time measured along material worldlines. Along homogeneous clock-comoving trajectories, the two physical times satisfy \(dT=Q\,dt\), so that \(\mathcal N_T\equiv dt/dT=Q^{-1}\) and \(H_T=H/Q\). Because \(T\) carries stress, conjugate momentum, conserved charge, and gravitational backreaction, this distinction changes relational observables and cannot be removed by a coordinate transformation. The theory's central reciprocal statement is: As physical space expands, cosmological time contracts or moves slower; as physical space contracts, cosmological time expands or moves faster. The expanding branch obeys the on-shell response \(d\mathcal N_T/dH<0\).

Abstract: We investigate whether gravity-like dynamics can emerge from transformations of finite relational records rather than from matter evolving in a pre-existing spacetime. In Dendrographic Holographic Theory (DHT), finite ordered dendrograms define exact relational states, causal growth trajectories, and representation-specific probability distributions. We analyzed Path, Embedding, Views, and Branch-Monna entropies in incoming and forward ensembles. Their terminal-referenced entropy variables were well described by Newtonian inverse-square and Schwarzschild-like radial profiles, with broad but non-universal held-out predictive support and an overall predictive advantage for the Schwarzschild-like form. Independent four-dimensional reconstructions produced Lorentzian target-local geometries whose Einstein tensors showed robust held-out proportionality to entropy-derived source tensors, revealing a recurring trajectory-local GR-like organization without establishing the Einstein equations of physical spacetime. We then formulate a trajectory-supported differential completion in exact Z = (τ,ϕ) coordinates. Exact induced transitions are timelike under an explicit flat anchored reference metric. Representation-specific probability laws remain defined only on supported exact DHT states or ordered state pairs, whose finite Shannon entropies provide exact anchors for smooth auxiliary two-endpoint scalar fields. Level-balanced relational derivatives define a premetric informational tensor and an action-derived source tensor. Under a single-effective-gradient reduction, this source reduces to the kinetic entropy source used in the numerical tensor reconstruction, providing an explicit connection between the empirical and theoretical constructions. An auxiliary local metric action of Einstein--Hilbert form defines an Einstein-like Euler--Lagrange tensor. Within this chosen geometrical construction, a constructive curvature-jet argument establishes nonempty anchored metric segments on the elementary regular transition domain, with \( G_{\mu\nu} = \kappa_qT_{\mu\nu}^{(q)} \) holding along the corresponding DHT trajectories. This construction does not constitute a derivation of the Einstein field equations from DHT. Generic continuum points supply only the transverse differential data required for curvature and are not additional DHT states. The Views and Branch-Monna sectors retain their exact quantum-like state and event-level interpretations without introducing probability laws on non-exact continuum points.

Abstract: This work, building upon T.N. Lockyer's Vector Particle Physics (1992), presents a simplified geometric model for the proton and neutron, enabling the calculation of the proton-to-electron mass ratio (\(m_p / m_e\)) with no freely adjustable parameter fitted to the experimental nucleon mass and a remarkable accuracy of seven significant digits (\(m_p / m_e \approx 1836.1521964\), relative error $-2.6 \times 10^{-7}$) compared to the CODATA value of 1836.15267343. The neutron-to-electron mass ratio (\(m_n / m_e \approx 1838.68982960\), error \(3.35 \times 10^{-6}\)) yields six significant digits.The purpose of this work is not to challenge the existence of quarks or the validity of Quantum Chromodynamics (QCD), which remains the established theory describing the strong interaction and has been extensively validated experimentally. Rather, the article examines whether Lockyer's geometric model provides an alternative or complementary description of nucleon mass and internal structure. In particular, the model appears to suggest that the internal structure attributed to the proton and neutron under ordinary conditions may not be identical to the effective structure revealed in high-energy scattering processes. This possible distinction is presented as a question for further investigation rather than as an established physical result.