Core uses mathematical and computational models to test whether increasingly mature relationships can arise from previously earned structure. Equations shown here fall into two categories: relationships recovered within bounded ancestry tests, and working mathematical structures used to define or analyze the models.
Similarity to an established physical equation does not by itself establish physical equivalence. Numerical constants of nature are not claimed unless they have been independently derived and tested.
The relativity ancestry produced a limiting causal speed, rest-state invariance, energy-like and momentum-like quantities, and a zero-rest branch. The resulting relationship has the structural form of relativistic dispersion.
Here E*, p*, m*, and c* are model quantities. The asterisk is intentional: these are not automatically identified with measured physical energy, momentum, mass, or the empirical speed of light.
The statistical ancestry connected microscopic multiplicity to macroscopic organization and recovered entropy-like, temperature-like, equilibrium, and distribution behavior.
For systems restricted to a dynamically accessible sector, the corresponding bounded form becomes:
These relations emerged within the thermodynamic/statistical ancestry. Their structural resemblance to standard statistical mechanics is the comparison of interest; empirical identification requires a separate quantitative test.
A persistent signed source quantity eventually supported sign-sensitive response, field-like propagation, induction, magnetic-like structure, transverse waves, gauge-like redundancy, and field-energy transport.
The electromagnetic-like ancestry ultimately produced a mutually connected field structure with source, circulation, induction, and displacement-like terms.
In the source-free model regime, the coupled field relations support transverse wave-like propagation with characteristic speed c*.
The field representation admitted potential-like quantities whose mathematical description could change without changing the corresponding field-like observables.
This was also found to be structurally compatible with the local phase freedom developed in the quantum ancestry.
The electromagnetic and quantum ancestry branches supported a localized zero-rest excitation with discrete exchange and frequency-dependent energy-like behavior.
The symbols remain model quantities. This result identifies a photon-like structural bridge inside the model; it does not establish that the simulated excitation is a physical photon.
The gravity ancestry connected localized content to geometry-like response and then geometry to motion. In the weak-field branch, effective three-dimensional flux spreading generated an inverse-square-like scaling.
Bound trajectories subsequently produced a Kepler-like orbital scaling:
Later gates extended the ancestry into redshift-like behavior, signal deflection, periapsis-precession-like effects, propagation delay, geometry waves, radiation reaction, nonlinear geometry, trapping, and rotational/frame-dragging-like structure.
Wave Rider does not require a model object to move locally faster than its limiting causal speed. The compression branch instead investigates whether the effective relational path between origin and destination can become shorter than the corresponding uncompressed path.
A value greater than one represents a shorter effective relational path in the model. Large values observed in earlier toy networks are therefore compression factors, not measured spacecraft velocities.
The quantum ancestry developed interference-like probability and a quadratic mapping between an amplitude-like model quantity and observable probability.
Subsequent gates explored noncommuting-observable-like structure, Bell-type nonclassical correlations, exchange behavior, spin-like rotational topology, local field-like excitation, and decoherence-like classicalization.
Core2 is intentionally being rebuilt from minimal intrinsic properties and local relationships. The mature equations above are not automatically granted to the Real Space branch.
Mathematical relationships will be added here only after the corresponding Core2 structures earn them. If Core2 independently converges on relationships resembling the earlier ancestry, those results can then be compared without retroactively changing the starting rules.
Structural resemblance is not the final test. A stronger physical claim requires freezing the relevant model before comparison and testing its numerical predictions against established equations, measured constants, laboratory results, or astronomical observations.
The equations collected on this page document mathematical relationships used or recovered within the Core research program. Some resemble equations in established physics because those structural correspondences are precisely what the ancestry tests investigate.
The current research does not establish that starred model quantities are identical to physical quantities in nature, nor that proportional relationships automatically contain the measured constants required by established theories.