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Conceptual Summary

Non-relativistic quantum mechanics is reformulated by expressing the evolution of a system as a superposition of contributions from all possible space-time paths connecting initial and final configurations. The central problem concerns the relationship between classical action principles and quantum probability amplitudes, and how quantum evolution can be represented without taking differential equations as primitive. The framework introduces a construction in which each path contributes a complex amplitude determined by the classical action, and the total amplitude arises from summing over all such paths. This replaces the notion of a single trajectory with a distribution over histories and provides a space-time description that is structurally distinct from conventional formulations. Quantum evolution is thereby encoded directly in the action functional through phase accumulation rather than through differential operators. The resulting structure establishes equivalence with the Schrödinger formulation under appropriate limiting procedures, while maintaining the probabilistic interpretation through amplitude superposition. The framework connects classical and quantum descriptions by treating classical trajectories as limiting cases within a broader interference structure.

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Conceptual Summary

A higher-dimensional cosmological construction is formulated to address the S8 tension through a unified description of dark energy and dark matter. The framework situates a temporal scalar field, termed the chronon, within a Randall–Sundrum brane–bulk geometry, where the radion zero mode governs late-time cosmic acceleration and a tower of Kaluza–Klein modes provides a clusterable dark matter sector. The central structural move consists of linking both components of the dark sector to a single geometric origin, producing a scale-dependent modification to gravitational growth encoded in an effective coupling function. Observable consequences arise from this modification, including deviations in structure formation and a predicted oscillatory signature in void–galaxy correlations. The formulation introduces a minimal parameterization of growth modification that connects higher-dimensional spectral properties to measurable quantities. The resulting structure organizes the theory around a small set of parameters controlling amplitude, scale dependence, and temporal evolution, enabling direct comparison with large-scale structure, lensing, and clustering observations.

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Conceptual Summary

A unified description of fundamental interactions is formulated by treating time as a physical field that carries both energy and geometric structure. The central problem addressed is the separation of gravitation, electromagnetism, and quantum phenomena into distinct theoretical frameworks. The manuscript introduces a temporal–density formulation in which these domains arise from a single underlying medium governed by an invariant relation linking temporal coupling, propagation speed, and linear density. Within this structure, curvature, field dynamics, and quantum coherence are interpreted as different expressions of temporal variation rather than independent physical mechanisms. The framework proposes that proper time is not a passive coordinate but an active field whose local variations define observable physics. A triad of constants {α, c, λ} is constrained by the invariant relation αcλ = 1, establishing a unified scaling between temporal flow, spatial propagation, and mass–energy density. This relation serves as the organizing principle from which classical and quantum behaviors are derived, allowing known physical laws to appear as limiting cases within a continuous temporal formulation.

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Conceptual Summary

A general-relativistic reconstruction of the low-redshift luminosity–distance relation is formulated to examine whether the observed curvature of the Type Ia supernova Hubble diagram can be reproduced without invoking cosmological expansion. The central problem concerns the interpretation of redshift as a mapping between observed quantities and spacetime structure. The framework introduces a lapse-based modification that alters the operational relationship between redshift and distance while preserving the Einstein field equations and underlying geometry. A scale-free reconstruction based on Pantheon(+) low-redshift data demonstrates that the curvature of the Hubble diagram can be reproduced using a single additive offset that absorbs absolute calibration. A separation between kinematics and dynamics is established by retaining standard gravitational field equations while modifying only the observational mapping. The resulting construction treats redshift as influenced by a smooth lapse function along null geodesics, allowing the curvature of the luminosity–distance relation to be reproduced without introducing additional stress–energy components. A quasi-static extension introduces time dependence in the lapse, yielding a redshift-drift signal that provides a direct observational discriminator.

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Conceptual Summary

A bounded arithmetic sequence derived from elliptic curve trace values is embedded into a smooth continuum framework on three-dimensional space. The central problem concerns translating discrete, prime-indexed data with irregular multiscale structure into a differentiable representation that preserves both boundedness and variability. The construction defines a smooth field t(x) on R³ through mollification centered at spatial representations of primes, enabling the integration of arithmetic structure into variable-coefficient elliptic partial differential equations. A spatial embedding of discrete coefficients provides a geometric representation of arithmetic data, while a mollification scheme distributes each value locally to produce a continuous field. The resulting framework establishes a direct correspondence between discrete arithmetic modulation and analytic structures, allowing multiscale variability to persist within a controlled continuum setting.

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Conceptual Summary

A unified theoretical framework is formulated in which informational structure is treated as the primary substrate underlying physical law. The central problem addressed is the absence of a single derivational structure capable of producing fundamental constants, particle properties, and cosmological parameters without adjustable degrees of freedom. The framework introduces a scalar informational field I(x) and a dimensionless constant αinfo = 1/(8π^3 ln π), fixed through a Ward-closure condition ε = (2π)⁻³. This deformation parameter propagates across gravitational, electroweak, fermionic, and cosmological sectors, generating quantitative relations without continuous free parameters. Informational geometry defined by Liouville invariance, Jeffreys prior, and Born linearity serves as the organizing structure from which physical observables emerge. Physical laws are expressed as effective descriptions of this geometry, with a single invariant controlling cross-sector behavior. The construction links informational measures to observable quantities through a unified deformation framework, providing a consistent pathway from principle to numerical prediction.

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Conceptual Summary

A unified description of physical interactions is formulated in response to the separation of modern physics into distinct theoretical frameworks with independent axioms and parameters. The central problem concerns the absence of a single structure capable of reproducing quantum, electromagnetic, gravitational, and cosmological behavior within a common ontology. The framework introduces the Unified Curvature Field (UCF), in which all interactions arise from a single asymmetric curvature field governed by two constants, the curvature coupling λ and the polarity asymmetry ε. A continuous scaling law λeff(ξ), defined over a coherence-scale variable ξ, regulates behavior across physical regimes. Matter and radiation are described as configurations of polarity fields, and phenomena typically treated probabilistically are represented through deterministic curvature dynamics. A variational structure defines the field equations and establishes a scale-dependent coupling that connects micro and macro regimes. The formulation organizes physical behavior as different operational regimes of a single curvature system, with transitions governed by a continuous flow rather than discrete theoretical boundaries.

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Conceptual Summary

A cosmological framework is formulated to examine whether late-time structure formation and gravitational observables can be reproduced without introducing non-baryonic dark matter. The central problem concerns the extent to which observed large-scale structure, lensing signals, and clustering statistics require a distinct matter component versus modifications to gravitational dynamics. The Modified Matter Dynamics with Dynamic Mass Function (MMA-DMF) model replaces dark matter clustering with a scale- and time-dependent modification of gravitational strength acting on baryonic matter. Validation is performed across multiple observational probes spanning redshifts 0 ≤ z ≤ 4, including redshift-space distortions, weak lensing, cosmic microwave background lensing, Lyman-α forest power spectra, and baryon acoustic oscillation measurements. Statistical agreement is evaluated through a combined likelihood analysis over 147 degrees of freedom, with reported global fit χ²/dof ≈ 1.019. A baryons-only cosmology is constructed in which gravitational enhancement substitutes for dark matter’s dynamical role while preserving standard background evolution. The framework separates expansion history from perturbation dynamics through the introduction of an auxiliary background component and a modified growth equation. The resulting structure allows observational distances to remain consistent with standard cosmology while altering the mechanism of structure formation.

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Conceptual Summary

The manuscript formulates a conceptual approach to the cosmological constant problem, which concerns the discrepancy between large theoretical estimates of vacuum energy and the small value inferred from cosmological observations. The central structural move introduces a dust-time foliation of spacetime using Brown–Kuchař dust fields, combined with a constrained energy-density sector. Within this construction, constant contributions to vacuum energy are reorganized so that they do not appear as independent sources in cosmological dynamics, while the standard gravitational degrees of freedom are preserved. The framework is explicitly developed at a classical and illustrative level. A relational notion of time is established through dust fields, and this time parameter is used to define both local and semi-global constraints on energy densities. These constraints are constructed to act algebraically and through spatial averaging on each dust-time slice, producing a mechanism in which constant energy shifts are absorbed into a time-dependent function rather than contributing directly to gravitational dynamics.

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Conceptual Summary

The manuscript addresses the measurement problem by introducing a stochastic modification of spacetime geometry that links quantum decoherence to metric fluctuations. The central issue concerns the incompatibility between quantum superposition and the thermodynamic structure of spacetime, particularly in gravitational collapse models that rely on white noise and produce unphysical heating rates. The framework, termed Holographic Zeno Gravity, replaces white-noise gravitational fluctuations with a colored noise process applied directly to the spacetime metric. This modification yields a finite spectral structure across frequencies while maintaining measurable decoherence effects for macroscopic systems. Continuous interaction between matter configurations and the fluctuating metric produces an effective monitoring mechanism that suppresses macroscopic superpositions while leaving microscopic systems largely unaffected. The formulation narrows toward a stochastic geometric description in which proper time fluctuations drive phase evolution and decoherence. The resulting structure is governed by a single phenomenological parameter constrained by experimental bounds, and produces scaling relations that connect mass, spatial separation, and decoherence rate within a unified framework.

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Conceptual Summary

Nuclear structure, decay, fission, and fusion are formulated as consequences of a geometric description of spacetime in which curvature dynamics determine physical behavior. The manuscript addresses the problem that conventional nuclear models rely on probabilistic transitions and extensive parameterization to describe observables such as decay rates, binding energies, and reaction processes. A deterministic alternative is introduced in which atomic nuclei are represented as localized curvature eigenmodes embedded in a trembling spacetime metric. Stability corresponds to sustained suppression of intrinsic curvature, while decay and reactions arise from causal relaxation and redistribution of that curvature along proper-time trajectories. A single global calibration anchors the framework, after which nuclear observables across multiple domains are derived from curvature-based functionals. Binding, decay, fission, and fusion are treated within a unified geometric structure in which all processes emerge from curvature suppression, saturation, overlap, and reconfiguration. This formulation replaces stochastic descriptions with deterministic relations tied to spacetime geometry and proper-time evolution.