Wave Relativity

Author disclosure. Wave Relativity is the work of the same author who maintains this site and authored the structural admissibility framework. The framework is applied here on the same template, with the same legs, as every other entry in the survey. The contrast case for the framework's strongest verdict shape is also the entry where the conflict-of-interest is most visible. Readers should verify the verdict against the book chapters and the papers listed in the sources section.

Claimed bucket: Physical theory at the substrate, with effective scaffolding named at the layers where empirical inputs remain.

Supported bucket: Physical theory at the substrate, with the structural backbone closed at tree level and the loop-level precision residue named openly in the monograph and in the journal submissions. Open items live at the layer where they are open, not buried.

Steelman

Wave Relativity derives the classical and semiclassical content of physics from one principle. Physical reality is self-consistent, so the equations for physically-real potentials take the form of self-consistency equations. Applied once per regime, three structural requirements (frame-independence, index matching, self-sourcing) produce electromagnetism with special relativity, general relativity, and matter-wave quantum mechanics in curved spacetime. The three potentials ($g_{\mu \nu }$, $A^{\mu }$, $\psi$) then assemble as separately-describable aspects of one underlying structure $\mathrm{\Psi }$, and the apparent incompatibility of QM and GR dissolves at the assembly level because the matter wave and the metric are derived as aspect-projections of a single field rather than as objects from two separate theories that need to be unified.

The strongest version of the claim is that the master equation for $\mathrm{\Psi }$ is the substrate equation. From the substrate equation, by self-consistency at the regime where the matter sector is well-defined, the Standard Model gauge group, the fermion spectrum, the three-generation count, electroweak masses, and the chirality structure are recovered at tree level, with the precision residue (loop-level Yukawa matching, precise CP-phase value, neutrino mass matrix specifics) named in Chapter 30 as the work that remains. The cosmological-tension companion programme (dark matter from the spin-resolved PIDM closure curve and the Hubble residual) is written up in the paper currently under review at Nuclear Physics B.

Components-in-regimes decomposition

Component	Regime	Category claimed	Category supported
$A^{\mu }$ as physically real	EM, after Aharonov-Bohm	Physical theory	Physical theory
Maxwell equations + SR	EM, classical	Physical theory	Physical theory
$g_{\mu \nu }$ field equations	Gravity, classical	Physical theory	Physical theory
$\psi$ as physically-real matter wave	QM, post-Davisson-Germer	Physical theory	Physical theory
Matter wave in curved spacetime	QM + GR, regime where both apply	Physical theory	Physical theory
Master equation for $\mathrm{\Psi }$	Substrate	Physical theory	Physical theory
$g_{\mu \nu }={\mathcal{G}}_{\mu \nu }[\mathrm{\Psi }]$ from sub-Planck self-consistency	Below ${\ell }_P$	Physical theory	Physical theory
Standard Model gauge group from $\mathrm{\Psi }$'s internal directions	Tree-level SM	Physical theory	Physical theory
Three generations, mixing, masses	Tree-level SM	Physical theory	Physical theory
Loop-level precision (Yukawa specifics, CP phase, neutrino specifics)	Loop SM	Open	Open (named)

Three-leg verdict at claimed category

Leg A. Are the primitives at the right level? Pass. The empirical anchors are named and small in number. Aharonov-Bohm motivates $A^{\mu }$ as physically real (Ch. 1). Newton's law of gravity is the empirical anchor for gravity (Ch. 7). Davisson-Germer plus Stern-Gerlach, neutron interferometry under $4\pi$ rotation, and Pauli exclusion motivate $\psi$ as a physically-real matter wave carrying intrinsic spin-half (Ch. 11 §11.6). Non-observation of pervasive micro-black-hole structure at sub-Planck scales anchors $\mathrm{\Psi }$ as the hidden variable of the separable $(\psi ,g_{\mu \nu })$ description (Ch. 14 §14.4, Ch. 20 §§20.1–20.3). The three self-consistency requirements (frame-independence, index matching, self-sourcing) are structural demands on any equation for a real potential, not stipulations. The numerical values of $c$, $G$, $\hslash$ are experimental inputs. No primitive is operationally defined at a layer where derivation is claimed.

Leg B1. Does the work operate at the QM+GR level? Pass via dissolution. The sub-Planck "what is QM-in-curved-spacetime" question presupposes that the matter wave and the metric are independent objects to be reconciled. Wave Relativity derives that they are aspect-projections of a single field $\mathrm{\Psi }$, and the projections that define them fail together at ${\ell }_P$. The question stops applying past the derived boundary. The closure mode is the strongest of the three modes the framework recognises (reaches ground / honest deferral / dissolution); dissolution is the mode where the structure shows that the presupposed question was malformed past a derived scale.

Leg B2. Is the work correctly positioned relative to established physics? Pass at tree level, with the loop-level residue named. The Standard Model gauge group ($SU(3)\times SU(2)\times U(1)$) is derived from $\mathrm{\Psi }$'s Lorentz-scalar internal directions, where the overall phase produces $U(1)$, the ${\mathbb{C}}_{xyz}^3$ factor produces $SU(3)$, and the ${\mathbb{C}}_W^2$ conversion fiber on the L-projection produces $SU(2{)}_L$ (Ch. 23 §23.2). Parity violation is read from the L-only attachment of $W_{\mu }^a$, not posited (Ch. 24). The three-generation count emerges from the family-sector structure (Ch. 29 §29.5b). Electroweak masses arrive through the composite chiral background, with the load-bearing Pöschl-Teller branch overlaps producing $\kappa =3\sqrt{5}/5$ (Ch. 28 §28.6a). Hypercharge ratios follow from chiral-anomaly cancellation on the matter-mode trace (Ch. 26 §26.5). Tree-level SM recovery is closed at the Ch. 30 checkpoint, where the master-integral residue, the gauge-cancellation theorem, the UV-finiteness theorem, and the hierarchy theorem are stated and proved. The loop-level precision residue (Yukawa-matrix matching to per-mille precision, CP-phase specifics, neutrino mass-matrix specifics) is the named open work, stated as such in the monograph and in the journal submissions, not concealed.

Closure mode summary

Reaches ground at the substrate layer (Leg A). Dissolves the QM-in-curved-spacetime question past ${\ell }_P$ (Leg B1). Reaches ground at the tree-level SM (Leg B2) with honest deferral at the loop level. All three legs close in a recognised mode.

Sources

• Wave Relativity, monograph (Zenodo concept DOI 10.5281/zenodo.19663818). Chapters cited above: 1, 2, 7, 11 §11.6, 14 §14.4, 20 §§20.1–20.3, 21, 23 §23.2, 24, 26 §§26.5–26.6, 28 §28.6a, 29 §§29.5b, 29.7, 30. Appendix B carries the worked derivations; Appendix A carries open items.
• "Massless neutrino and dark matter proposition," paper extracted from Ch. 26 §26.6 and Ch. 29 §29.7. Under review at Nuclear Physics B. Companion programme: the spin-resolved PIDM closure curve at $m_s\sim {10}^{12}$ GeV, Conditional CDM Proposition.
• "Quantum Yang-Mills and the mass gap," paper extracted from the gauge-cancellation and UV-finiteness theorems in Ch. 30. Under review at the Journal of Mathematical Physics.
• Aharonov, Y. & Bohm, D. (1959). "Significance of electromagnetic potentials in the quantum theory." Physical Review 115, 485. The anchor for $A^{\mu }$ as physically real.
• Davisson, C. & Germer, L.H. (1927). "Diffraction of electrons by a crystal of nickel." Physical Review 30, 705. The anchor for $\psi$ as a physically-real matter wave.

Cross-references

• Framework for the full ontology and the three legs.
• QM + GR instantiation for the QG-specific application of the framework that this entry exemplifies the contrast case for.
• String Theory and Loop Quantum Gravity (Phase 3 draft) for the contrast verdict where Physical theory is claimed and the structure supports at best Theory proposal.
• Survey index for the full table.