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This work advances a relational physics that begins not with spacetime but with a fibred continuum \((\mathcal C_d)\) of primordial quantum singularities \((\mathfrak B_{\vec r})\) animated by a quantum holo-state, Holo-State \(|\overset{\circ}{\mathbf{\Psi}}\rangle\), \[ \mathcal{C}_d := \left\{ \mathfrak{B}_{\vec{r}},\ \hat{\Omega}_{\vec{r}},\ \mathfrak{F}_{\vec{x}} \right\}_{\vec{x} \in \mathcal{C}_d}. \] Reality is scaffolded by a triadic distance and time \emph{relational phase-geometry bundle} \((\pi:\mathfrak F\to\mathcal X_q)\) with fibres \((\mathfrak F_x=\mathcal F_x^{\mathrm{dist}}\times\mathcal F_x^{\mathrm{time}})\), so separation and duration are read from the triad of \emph{correlational}, \emph{spectral}, and \emph{vacuum-response} measures (and their temporal counterparts) rather than imposed as primitive background. At the foundation stands the tetralemma—the \emph{Fourfold Algebra of Symmetry}, \((\mathbf{\overset{\circ}{\Lambda}})\), (Symmetry, Antisymmetry, Parasymmetry, Holosymmetry)—treated as a generative grammar whose concrete vocabulary is the full algebra of observables, deliberately prior to geometric assumptions. The quantum holo-state \(\omega^{\overset{\circ}{\mathbf\Psi}}\) is the global, holosymmetric state on the algebra that, via the Gelfand--Naimark--Segal (GNS) construction, converts valuations into \emph{operational expectation values} and forges the inner products that knit local fibres into an emergent Hilbert arena, \(\mathcal H_{\mathrm{em}}\) and \(\mathcal H_{\mathrm{phys}}\), and its relational geometry. This forging proceeds through the fourfold inter-modal correlator \(\hat{G}_\Lambda(\mathfrak{B}_x, \mathfrak{B}_{x'})[\psi_1^*, \psi_2]\), which couples the tetralemmatic modes and supplies the state-conditioned structure required for parallel transport \[ \langle \psi_1 | \psi_2 \rangle_{\mathcal{H}_{\mathrm{mod}}^{(\mathfrak{B}_x)}} := \lim_{x' \to x} \langle \overset{\circ}{\mathbf{\Psi}} | \hat{G}_\Lambda(\mathfrak{B}_x, \mathfrak{B}_{x'})[\psi_1^*, \psi_2] | \overset{\circ}{\mathbf{\Psi}} \rangle \] and comparison across the continuum: \begin{equation*} \hat G_\Lambda(\mathfrak B_x,\mathfrak B_{x'})[\psi_1^*,\psi_2] := \hat{\mathcal F}_\alpha^\dagger(x)\, \mathcal U(x\!\leftarrow\!x';\gamma)\, \hat{\mathcal F}_\beta(x') \;\in\;\mathcal B(\mathcal H_{\mathrm{em}}), \end{equation*} where \(\mathcal U(x\!\leftarrow\!x';\gamma)\) is the gauge–covariant transporter along the path \(\gamma\), and \(\mathcal B(\mathcal H_{\mathrm{em}})\) is the Banach *-algebra (indeed C\(^*\)-algebra) of bounded operators on the emergent Hilbert space \(\mathcal H_{\mathrm{em}}\), with implicit summation over the modal indices \(\alpha,\beta\) understood. Two novel fundamental fields, \(\hat{\mathcal{F}}_\alpha^\dagger(x)\) and \(\hat{\mathcal{F}}_\beta(x')\), have been proposed to inhabit this structure. The \emph{Gaiamiti} \(\hat{\mathbf{\Phi}}_x\) shapes chronogeometry and carries the radiative content associated with the graviton; the \emph{Tantrakyma} \(\hat{\mathbf{\Theta}}_x\) organises excitations and internal symmetries, seeding particle spectra and interactions. Their interaction correlators, varied as a single operational action, yield the \emph{Chronogeometric Einstein Equations}—a covariant, state-conditioned field system that explicitly unifies general relativity with quantum mechanics, taking the form \begin{align*} \underbrace{\bar{\Sigma}_{\mu\nu}(x)}_{\text{General Relativity}} &= \underbrace{\big\langle \overset{\circ}{\mathbf{\Psi}} \big| \hat{\Sigma}_{\mu\nu}(x) \big| \overset{\circ}{\mathbf{\Psi}} \big\rangle}_{\text{Quantum Mechanics}} = \big\langle \overset{\circ}{\mathbf{\Psi}} \big| \big(\hat{g}_{\mu\nu}(x) + \hat{t}_{\mu\nu}(x)\big) \big| \overset{\circ}{\mathbf{\Psi}} \big\rangle,\\[4pt] \bar G_{\mu\nu}[\bar\Sigma] + \Lambda\,\bar\Sigma_{\mu\nu} &= \kappa\,\bar T_{\mu\nu}^{\text{total}}(x). \end{align*} This tensor \(\hat{g}_{\mu\nu}(x)\) is itself emergent, defined as the second Fréchet variation of the squared composite distance operator \(D^2(x,x')\), evaluated at the coincidence limit: \[ \hat{g}_{\mu\nu}(x) := \left. \frac{\partial^2}{\partial x^\mu \partial x'^\nu} D^2(x,x') \right|_{x' = x}, \] where \(D^2(x,x') := \hat{d}_{\mathrm{corr}}^2(x,x') + \hat{d}_{\mathrm{vac}}^2(x,x') + \hat{d}_{\mathrm{spec}}^2(x,x')\). Each \(\hat{d}_a(x,x')\) for \(a \in \{\mathrm{corr}, \mathrm{vac}, \mathrm{spec}\}\) is a Hermitian operator on \(\mathcal{H}_{\text{total}}\). Complementing the metric tensor that governs emergent space, the framework defines its temporal analogue: the \emph{operator-valued temporal curvature tensor} \(\hat{t}_{\mu\nu}(x)\) arises from the triadic operators of relational time. It is formally defined as the second Fréchet variation of the squared composite temporal displacement \(T^2(x,x')\) at the coincidence limit: \[ \hat{t}_{\mu\nu}(x) := \left. \frac{\partial^2}{\partial x^\mu \partial x'^\nu} T^2(x,x') \right|_{x' = x}, \] where \(T^2(x,x') := \hat{t}_{\mathrm{corr}}^2(x,x') + \hat{t}_{\mathrm{vac}}^2(x,x') + \hat{t}_{\mathrm{spec}}^2(x,x')\). Cosmology is posed as a timeless problem \(\hat{H}_{\text{univ}} |\overset{\circ}{\mathbf{\Psi}}\rangle = 0\) with \(\hat{H}_{\text{univ}} := \hat{H}_{\Phi} + \hat{H}_{\Theta} + \hat{H}_{\mathrm{int}}\): a universal quantum constraint fixes the realised state of the whole, while familiar evolutions appear when suitable internal clocks are conditioned from it. Within this discipline, the \emph{Standard Model} is the holosymmetric, Becchi–Rouet–Stora–Tyutin (BRST)-physical realisation of the Tantrakyma sector: the anomaly-free gauge stack \(G_{\mathrm{SM}}=SU(3)_C\times SU(2)_L\times U(1)_Y\) acting on the matter registers, with Yukawa couplings and family structure fixed by cohomological and duality selection rules; electroweak symmetry breaking is a Tantrakyma vacuum alignment that produces observed masses and mixings as operational expectation values. The dark sector—dark matter and dark energy—arises as complementary holosymmetric branches of the same operator-geometric substrate rather than as an ad hoc addition, so that the full cosmic stack is given by \begin{align*} \mathcal{G}_{\mathrm{Cosmos}} &= \underbrace{\mathcal{G}_{\mathrm{Chronogeometry}}}_{\text{acts on }\delta\hat\Sigma_{\mu\nu}=\hat h_{\mu\nu}\oplus\hat\tau_{\mu\nu}} \ \times\ \underbrace{G_{\mathrm{SM}}}_{\text{Tantrakyma (matter/gauge)}}\\[2pt] &= \bigl[\mathrm{Diff}_{\mathrm{rel}}\ltimes\bigl(\mathrm{SO}(1,3)_{\text{local}}\times \mathcal{G}_{\mathrm{Dark}}^{(\mathrm{eff})}\bigr)\bigr] \ \times\ \bigl[SU(3)_C\times SU(2)_L\times U(1)_Y\bigr]. \end{align*} With \[ \mathcal{G}_{\mathrm{Chronogeometry}} := \mathrm{Diff}_{\mathrm{rel}}(\mathcal X_q)\ \ltimes\ \bigl(\mathrm{SO}(1,3)_{\text{local}}\ \times\ \mathcal{G}_{\mathrm{Dark}}^{(\mathrm{eff})}\bigr). \] Here \(\mathrm{Diff}_{\mathrm{rel}}(\mathcal X_q)\) are relational diffeomorphisms on \((\mathcal X_q,\bar\Sigma)\), acting by pullback on fields and adjoint transport on internal fibres; \(\mathrm{SO}(1,3)_{\text{local}}\) are local Lorentz rotations; and \(\mathcal{G}_{\mathrm{Dark}}^{(\mathrm{eff})}\) is the \emph{effective} symmetry badge governing the proposed \(\tau\)–kairos (not SM matter): \begin{align*} \mathcal{G}_{\mathrm{Dark}}^{(\mathrm{eff})} \ \supset\ & \underbrace{\mathrm{Shift}_{\varphi_b}\times \mathrm{Shift}_{\varphi_L}\times \mathrm{Shift}_{\tilde\varphi}^{\mathrm{ax}}}_{\text{scalar shifts}} \\ & \times\ \underbrace{U(1)_{\tau}}_{\text{Chrono--Kymon phase}} \ \times\ \underbrace{U(1)_{\mathrm{hel}}}_{\text{helicity plane}} \ \times\ \underbrace{\mathbb{Z}_2^{\rm HS}}_{\text{HSP tag}}. \end{align*} The three Shift factors act on the breathing/longitudinal/axial scalars \((\varphi_b,\varphi_L,\tilde\varphi)\); \(U(1)_\tau\) is the proposed \emph{Chrono--Kymon} phase symmetry of the \(\tau\)-vector \(K^{(\tau)}\); \(U(1)_{\mathrm{hel}}\simeq SO(2)\) rotates the helicity doublet \((K^{(\tau)}_{+},K^{(\tau)}_{-})\); and \(\mathbb{Z}_2^{\rm HS}\) labels \emph{holosymmetric} (HSP) branch stability arising from algebra. All continuous factors are \emph{effective} and may be softly broken by the same operators (masses, mixings, potentials) that drive cosmology. \medskip \noindent In concise form, the emergence chain is \begin{align*} \text{Ontology} &\rightsquigarrow \text{Algebra} \rightsquigarrow \text{GNS/BRST}:\\ (\mathbf{\overset{\circ}{\Lambda}}),\ \mathcal A(\mathcal C_d) &\rightsquigarrow (\mathcal H_{\mathrm{em}},\hat Q_{\mathrm{BRST}}) \rightsquigarrow \mathcal H_{\mathrm{phys}} \simeq H^0_{\mathrm{BRST}}. \end{align*} On this arena, \(\hat{\mathbf\Phi}\) (geometry) and \(\hat{\mathbf\Theta}\) (matter), with their interaction correlators, enter a single action whose variation yields the Chronogeometric Einstein Equations, \[ S[|\overset{\circ}{\mathbf{\Psi}}\rangle] := \int_{\mathcal{X}_q} d^d x \; \sqrt{-\det \bar{\Sigma}(x)} \; \mathrm{Tr}\!\left( \big\langle \overset{\circ}{\mathbf{\Psi}} \big| \hat{\mathbf{G}}_\Lambda(x,x) \big| \overset{\circ}{\mathbf{\Psi}} \big\rangle \right). \] By rooting metrics, clocks, and spectra in the same fibred continuum and relational phase-geometry bundle, the framework unifies ontology, kinematics, and phenomenology without imported scaffolds, offering a clean trajectory from question to detection, from detector readout to cosmos, and from algebra to evidence. The evolution of any such subsystem is governed by this emergent dynamical law \begin{equation*} i\hbar \frac{d}{dt} |\overset{\circ}{\mathbf{\Psi}}(t)\rangle = \hat{H}_{\text{rel}}(t) |\overset{\circ}{\mathbf{\Psi}}(t)\rangle, \end{equation*} and the operator that drives this effective evolution is the \emph{total relational Hamiltonian} \(\hat{H}_{\text{rel}}\), which contains the entirety of cosmic phenomenology: \begin{equation*} \hat{H}_{\text{rel}} = \underbrace{\hat{H}_{\text{geometry}}[\hat{\Sigma}_{\mu\nu}]}_{\text{Dark Energy \& Dark Matter}} + \underbrace{\hat{H}_{\text{matter}}[\hat{\phi}, \hat{\psi}, \dots]}_{\text{Standard Model}}. \end{equation*} This single effective Hamiltonian is composed of two sectors: \noindent \textbf{The Geometric Hamiltonian (\(\hat{H}_{\text{geometry}}\))} This operator governs the dynamics of the Gaiamiti field (\(\hat{\Phi}\)), whose quanta are the \emph{apeirons}. Its ground state eigenvalue is the cosmological constant (\(\Lambda\)), the physical origin of \emph{Dark Energy}, while its large-scale coherent excitations are the physical manifestation of \emph{Dark Matter}. \vspace{1em} \noindent \textbf{The Matter Hamiltonian (\(\hat{H}_{\text{matter}}\))} This operator governs the dynamics of the Tantrakyma field (\(\hat{\Theta}\)), whose quanta are the \emph{kymons}. Its excitations and their interactions give rise to the entire particle zoo of the Standard Model.
borom s. 2025. A Theory on the Interdependent Origination and Entanglement of Chronogeometric Gravity, Matter and the Cosmos. PREPRINTS.RU. https://doi.org/