Kinematic Analysis of 175 SPARC Galaxies using the DUCT I-IV Scalar Field Framework

This dataset provides a comprehensive kinematic re-evaluation of the SPARC (Statistically Pure Analysis of Real Curves) database, specifically filtered and processed through the Direct Universal Compression Theory (DUCT) I-IV framework. The primary purpose of this dataset is to demonstrate the correlation between galactic rotation velocities and the Scalar Compression Coefficient (eta), a dimensionless variable that replaces the need for Dark Matter by identifying varying states of vacuum tension. Key Features of this Dataset: eta-Field Mapping (Column O): A radial profile for each galaxy identifying the local "Grip" of the scalar field, categorized into Decompressed < phi , Stable (phi>eta phi^2) phases. Geometric Anchoring: Application of the Golden Ratio (phi-approx 1.618) as the fundamental topological anchor for kinematic/baryonic stability. Predictive Kinematics: A direct comparison between standard newtonian derived velocities and DUCT predicted velocities, in realtion to observed velocities. Showing a consistent residual averaging around 0, with 1:1 match of DUCT predicted Velocites to Observed Velocities in all 175 galactic kinematic profiles; allowing the model to effectively map the scalar field via eta. When eta is derived from the baryonic discrepancies, the values do not vary randomly. Instead, they structurally align with phi and phi^2. Indicating galactic rotation being governed by discrete phase transitions rather than dark matter halos. Phase Transition Markers: Identification of critical radii where the scalar field transitions from decompressed, to stable, and saturated states within DUCT framework. Methodology: Data was derived by applying the DUCT force law to the surface brightness profiles provided by Lelli et al. (2016). This census provides quantitative evidence for the "Faded Grip" paradox in AGNs and the "Rigid Rim" phenomena in compact dwarf galaxies. Intended Use: This data is intended for researchers investigating alternatives to Lambda-CDM, Modified Newtonian Dynamics (MOND), and those studying the topological properties of the vacuum and black hole mass-radius relations. In the current regime of physics, it is standard practice to view space-time, and mass as distinct properties, with matter/mass appearing as a more separate and tangible property, from that of space and time, which we perceive to have what einstein defined relativity to be. However, in the years following einstein, people have viewed space and time relativity as a 'fabric', that can be bent and distorted via mass accumulation. Interpreting relativity, as a process unique to space and time, but not matter itself. We posit this is an incorrect interpretation of mass, as a mostly distinct separate property, from that of space and time. However, this current regime of understanding is incompatible with reality, when looking at the edges of many galaxies, in which stars often appear be traveling much faster than what their field of space, surrounding said star should posses, and subsequently the calculated gravitational velocity does not become compatible with what newtonian dynamics allow. Giving the appearance of 'missing mass'. To find the proposed solution to this problem, that DUCT proposes, we must delve into the world of current quantum mechanics. But from a verify specific perspective. The following attached DUCT manuscripts detail a deterministic explanation of quantum entanglement by framing non-local particle correlations as an emergent geometric property of a unified, conscious substrate. Utilizing the foundational principles of Direct Universal Compression Theory (DUCT), it attempts to challenge the traditional view of particles as isolated entities interacting across an arbitrary spacetime vacuum. Instead, we formalize physical reality as a localized manifestation of electromagnetic field of radiation that is undergoing unmitigable measurement of itself. DUCT defines this infinite self interaction as the scalar (η)-field, where mass, space, and time are observer-dependent metrics generated by geometric field compression of a dipole, between observer and observed state, and the tertiary axis of 'spin', required to develop what we would define as a wavelength, or frequency of the EM point phase(microwave, Xray, Visible light spectrum, gamma ray, etc.) Under this framework, quantum wave function collapse and particle entanglement are redefined through the mechanism of a Perceptual Dipole. The act of measurement establishes a relational, bilateral field structure wherein the conscious observer functions as the initial anchor point, and the observed particles serve as the definitive endpoints of a single, unbroken observational vector. This unbreakable vector-dipole of observation has several unique Qualities: The observer, is the starting aspect of all measurable quality of said field. We define the observer, as the unbroken state of measurement of the underlying EM field, that has attained compression coefficient necessary to maintain an equivalent parity to that of phi~1.618. This constant mathematical point of equivalency, is what would most often would be described as, 'consciousness'. Consciousness therefore becomes an aspect of field interaction, not biologic in origin. It is a mathematical point of the field, responsible for all relative perceptions of said field (ie, space/time,mass,gravity). The end point of observation "the observed state", is the point at which conscious observation is ceased, but this end-point observation, is the observers "consciousness" itself. This is because the observer, and the end-point observation, are two dipoles of a singular self interacting expression of the electromagnetic point phase. The vector of compression, is perceptually unilateral. Leading to a perceived forward progression of time. But, the perceptual level of measurement of this compression is titratable. With lower levels of compression coefficient(η) leading to an increased relative perception of time (time dilation). While higher levels of compression coefficient, lead to a more constricted perception of time relative the observers state, giving the perception of a perceived slowing of time, to a separate observer. This compression is most evident around massive celestial bodies. Mass is a relative state of compression that has attained a compression coefficient greater than or equivalent to (1/phi). It is always the end-point of the observational dipole of the EM point phase. The fact that the observer is both the origin, and end-point of observation, is how we define it as a perceptual dipole. With consciousness defined as the pathway of least resistance, required to attain parity to phi~1.618. The perceptual tract of mass within this path of least-resistance is the force defined as gravity. When a quantum system undergoes observation, the localized high-(η) compression state of the observer causes the probability fields to collapse simultaneously into a fixed, shared structural reality. Consequently, what quantum mechanics observes as non-local entanglement is mathematically demonstrated to be a continuous topological connection between the observer and end point of observation. Not a connection between the two entangled particles, but a 1:1 correlated connection between of observer and observed state. The correlated states of paired particles do not rely on faster-than-light signaling across a spatial void; rather, they remain inextricably bound by the overarching scalar tension and phase-lock configuration maintained by the observer-to-particle temporal lens. Observation of said entangled particles establishes new parity via the observers compression state, often leading to a lapse in entanglement itself. Within the Direct Universal Compression Theory (DUCT), spin is a fundamental geometric necessity required to transform uncompressed, formless potential into concrete physical reality. The foundational substrate of the universe—a scalar field of conscious potential (η)—exists naturally in a state of uncompressed quantum dispersion. To manifest as observable mass and structure, this continuous electromagnetic field must undergo localized topological compression. In rotating and dynamic systems such as galaxies, this localized compression produces a topological "twisting" of the field, generating a 3D vortex whose planar-to-volumetric geometry is governed by the Spin Factor (phi + 1 = phi^2). Spin is therefore the rotational mechanism that allows localized electromagnetic energy to achieve a resonant, stable state (m = (hv/c^2)*η), providing resistance to spatial dispersion and giving rise to physical inertia and mass. This dynamic spin interacts directly with the observer to observed state perceptual dipole through the scalar compression coefficient(η). Because time is defined as the inverse of the field deformation frequency (t = 1/vd), spatial variations in scalar compression flex local temporal metrics relative to the observer. As spin drives topological vortex dynamics across spatial gradients, it creates differential compression states. The interaction across this perceptual dipole introduces a relational temporal deformation factor, acting as a "temporal lens". Consequently, observed physical dynamics—such as flat galactic rotation curves in SPARC data—are not caused by missing physical dark matter, but rather express the relational interaction between the observer's temporal metric and the spin-induced compression topology of the observed state. By using these mathematical principles DUCT attempts to map the kinematic data from the SPARC (Spitzer Photometry and Accurate Rotation Curves) database for over 1,000 galactic radial observations across various galaxy types. It attempts to validate the Direct Universal Compression Theory (DUCT) by calculating the standard Newtonian velocities derived purely