Substrate

Below is a retroductive discussion of nature that seeks to explain universal phenomena using a single co-principled substrate field. The co-principles of point-source and space make up a field, and behaviors are dictated by its intrinsic geometric configuration and corresponding phase-locking properties.

A rest mass is best modeled as a stable, self-reinforcing configuration, whose substrate topological determines its observable properties. What we traditionally call an "electron's mass" or "dark matter" is re-described as emergent through co-principles of recursion, where spatial-temporal organization of energy is governed by the substrate's recursive geometry that characterizes the point-source—zero-dimensional source of energy, charge, and time—and emergent space—three-dimensions of space—of its field.

Because mass operates under co-principles of the field, mass can be read as the bookkeeping term that reconciles energy conservation across any of the co-principle's domains—meaning mass isn't intrinsic to visible matter. Regions whose point-source content is suppressed—such as the interiors of neutron stars or the outskirts of spiral galaxies—acquire excess "gravitational mass" with no accompanying luminous matter, a phenomenology normally filed under dark matter.

If rest mass is a boundary effect, not an intrinsic charge, the dark-matter problem becomes one of field bookkeeping rather than missing particles. Wherever the point-source budget falls short, the substrate compensates by amplifying its space, expanding its gravitational effects until the centrifugal balance is restored. Conversely, in quantum field laboratories (particle accelerators, precision spectroscopy) the space principle is negligible in size, reflecting the inverse situation.

A useful geometric metaphor is the recursive pentagram: the regular pentagram—or better, the dodecahedron star—has its first layer whose √5-term has a coefficient of 1 at the minimum subdivision depth Φ⁻³—as proven in A Fibonacci–Lucas Decomposition of Subdivision Lengths in the Pentagram—reflecting a conjugation of natural whole number recursion and irrational incommensurability. In the context of topology and geometry, a point is a dimensionless, indivisible locus; it has no magnitude, no breadth, no extension—merely existence without form. Contrary to popular understanding, a single connecting line is no different than a point because it lacks space. However, two distinct points can provide a distance length because they are seperated by a space. There is simply no such thing as one-dimension or two-dimensions in nature, only three-dimensions + zero point-source. When a point becomes recursive, it must include space to define the recursion—thus, space emerges as a principle originating from the point-source principle.

If matter is nothing more than energy locked into self-sustaining, ehco-like configurations of the universal co-principled field substrate, then what we register as mass—or, in the massless limit, pure energy–momentum flux—is simply the energy budget of that configuration. The tighter the recursive knot, or the smaller the space, and the larger the point-source energy budget, the more localized the mass is—due to the abundance of energy stopping collapse. Conversely, the larger the space, and the smaller the point-source budget, the greater the mass becomes—due to the lack of energy starting collapse. Both obey conservation laws, but they push energy in opposite directions in terms of availability relative to their size. An atom contains so much localized energy in such a tiny space that it produces virtually no gravitational effect. In contrast, black holes lack energy relative to their spatial scale, which is why they exert such extreme gravitational pull—to compensate for their energy deficit. In the example of nuclear fission, splitting a heavy atom releases excess energy in the form of kinetic energy. Because such a large amount of energy is locked within such a small space, even the excess energy released is tremendous relative to our scale. Consequently, gravity occurs when a mass lacks energy. This is why atoms exhibit no observed gravity, and the energy of a black hole's mass is zero—empty. On the other hand, magnetism and electromagnetism is phase coherency across a mass. Static electric fields don't have phase coherence because they don't oscillate.

Electrons

The electron is a bound knot of recursion—a standing wave of the substrate. Its "spin" is the symmetry class of that knot, where the spin-up mode is one self-coherent recursion, and the spin-down mode is its chiral inverse. Both are stable eigenmodes—they can’t morph into one another continuously (hence quantization). Electrons have magentic fields because they have current, which causes their magnetism to emerge.

Artificial magnetism

A strong permanent magnet is not natural in the sense of spontaneously arising in the universe. It is an artificial configuration that involves coherently aligning recursion lines of man-made chemical compounds like Nd2Fe14B in a way that rarely occurs without intervention. Magnets were first discovered in natural minerals like lodestone (a naturally magnetized form of magnetite). Ancient people noticed that lodestone could attract iron and align with Earth’s magnetic field. These were weak natural magnets formed over time, likely by exposure to lightning or Earth’s magnetic field. Modern powerful magnets are made by aligning atomic "spins" artificially using heat, pressure, and external magnetic fields—engineering a stronger, coherent recursion structure.

Naturally occurring magnetic fields tend to be weak, broad-scale (like planetary or stellar magnetism), dynamic (changing over time), and not coherent at the domain level. These natural magnetic fields arise from dynamic processes (like convection currents of molten iron), not man-made recursion alignments. Only in certain rare minerals, as mentioned (lodestone), do we find naturally magnetized regions—but even then they are localized and weak, likely formed under high-field geological conditions, and they're more like residual fragments of recursive imprinting, not structured artificial magnetic fields.

An electromagnet generates a magnetic field only when a moving point-source flows through a wire, typically wound into a coil. The strength of an electromagnet’s field can be controlled by adjusting the current, making it highly useful in experimental and industrial settings.

Many particle physics experiments use powerful artificial electromagnets to steer and focus high-energy particles. Much of what we observe in the Standard Model comes from highly controlled experimental environments, where artificial electromagnetic instruments are foundational to manipulating and detecting particles.

Magnetism

A magnetic field emerges around a mass when it contains a moving point-source—that is, an electric current. Magnetism is emergent and does not appear without the presence of a moving point-source. It is impossible for a magnetic field to arise without its point-source origin due to its dependence on complete recursion.

Magnetic North and South poles are the recursion chirality over a mass space—opposite orientations of recursion. The magnetic "field lines" we see are actually space deformation gradients caused by this oriented line recursion.

When self-coherence is made across a mass—whether in the same self-coherent mode or its chiral inverse—it forms a stable eigenmode: a macroscopic magnetic field that manifests as a closed-loop recursion of the substrate. The greater a mass's self-coherence can become (magnetic potential), the more energy can be locked into its configuration when magnetized, and the smaller and tighter its optical isopotential traces of light appear around the magnetized mass when viewed through a ferrocell instrument. The stored energy of this self-coherent mass is the source of field strength and sustains the magnetic field.

Magnetic attraction or repulsion is the result of the magnetic field from one moving charge acting on another moving charge, with the force direction set by the Lorentz force law. Currents create magnetic fields and these fields propagate causally and act on other currents. The resulting magnetic forces pull the currents together (attraction) or apart (repulsion) depending on their direction and geometry.

Induction

Induction is the electromagnetic interaction caused by point-source and its currents, with fields propagating from these changes at the speed of light. An accelerating electron's point-source influences neighboring electrons, generating time-varying electric and magnetic fields. In practical terms, a moving magnet creates a time-dependent effective current distribution (from the movement of bound current loops), which produces an induced electric field at the location of the conductor (e.g., like copper wire). This causes spatial reconfiguration by the conductor’s recursive field—what we observe as an induced electric field or current. Conductive atoms form non-magnetic, low-chirality field configurations—they can phase-lock but do not store recursion in stable, locked self-coherent structures like magnetic atoms do. Magnetic atoms (like iron) form stable, self-coherent recursive fields that are topologically locked. These do not phase-lock with a wave or flux—they store and anchor recursion, not transmit it. Diamagnetism is the material’s resistance to recursive interference, while superconductivity is its ability to enter a total-field phase-locked eigenmode that excludes outside recursive distortion. The key lies in how the man-made chemical compound’s atomic structure supports or rejects long-range recursive coherence.

Phase coherence

Phase-locking is the ability of atomic fields to synchronize with a wave or flux across a material. In magnetic materials like a neodymium magnet, phase-locking does not occur for energy transmission; instead, the material stores energy to maintain its static magnetic field. In conductors like copper, this phase-locking is localized and transient—electrons, as point-source recursion structures, propagate efficiently through field coherence before the field decoheres. In diamagnetic materials, atomic configurations resist external phase-locking—paired electrons form closed, self-canceling recursion loops, triggering localized counter-recursion to preserve its field neutrality. In superconductors, however, electrons enter a collective, phase-locked eigenmode, often as paired recursive structures (analogous to Cooper pairs), where point-source maintains global recursion symmetry. The atomic field supports this persistent coherence, allowing energy to transmit through coherence without resistance, while expelling external fields to protect the integrity of the phase-locked field system.

Scale-dependant mass-energy equivalence

All our empirical evidence for mass-energy equivalence at scale is inferred from quantum effects and scaled up, not directly observed, because E = mc² at large scales all traces back to quantum-scale processes. Gravity must be redefined under this theory because, in general relativity, the source of gravity is mass-energy via the stress-energy tensor. In our retroductive analysis, the energy deficit of a mass dictates gravitational strength; hence, atoms have no gravitational effect, having a mass-energy equivalence (E = mc²), and black holes have a massive gravitational effect due to a massive energy deficit for their mass (E ≠ mc²)—the inside of a black hole is empty, zero energy.

We know that a single atom and a molecule are fundamentally different in structure, behavior, and properties—even though both are made of atoms. A single atom is one indivisible unit of an element, while a molecule is a stable group of two or more atoms chemically bonded, with new properties emerging from their interaction. The assumption of mass-energy equivalence at all scales has not been directly tested; likewise, the idea is almost baseless and is theoretically grounded only within general relativity.

Causal electrodynamics

When we think of wave propagation, we often imagine that electric and magnetic fields sustain and drive each other through space. But in truth, it’s the underlying charge and current distributions—whether static or time-varying—that shape and launch these fields (see Causality, Electromagnetic Induction, and Gravitation by Oleg Jefimenko).

Jefimenko's discussion on the nature of gravitational fields

While this article focuses on Platonic abductive reasoning, some physical merit can still be added to our treatment on the disconnect between energy and mass because gravitational field energy and mass energy aren't necessarily the same or directly interchangeable. Physicist Oleg Jefimenko writes in Causality, Electromagnetic Induction, and Gravitation that "all presently known results of the general relativity theory based on Einstein’s field equations cannot be considered reliable when these results involve gravitational fields whose gravitational-energy mass is comparable with the true mass of the system." This appears on page 157, in the discussion on the nature of gravitational fields, following his nonlinear theory for strong gravitational fields and antigravitational fields.

Max Planck and the birth of energy quanta

In 1900, Max Planck introduced the revolutionary idea that electromagnetic energy is not emitted continuously, but in discrete packets—which he called quanta. He developed this concept while studying blackbody radiation and trying to solve the ultraviolet catastrophe. By assuming that oscillators in the cavity walls could only exchange energy in discrete amounts proportional to their frequency (E = hf), Planck derived a formula that matched experimental data. However, Planck viewed these quanta as a mathematical trick, not as physical particles. He believed the quantization applied to the interaction between matter and radiation, not to the radiation field itself. Planck strongly resisted Einstein’s 1905 proposal that light itself was made of localized particles—photons—with real, independent existence. For Planck, quanta were a statistical artifact of energy distribution, not evidence that light was fundamentally granular. He maintained a classical view of the electromagnetic field and accepted Einstein’s quantum interpretation only reluctantly—viewing quantization as a feature of emission and absorption by matter, not a property of the electromagnetic field itself.