Static Substrate and Local Perturbation: A Foundational Framework

1. Introduction: Achievements and Defects of the Traditional Paradigm

For more than a century, astronomical observation research has relied on the ΛCDM standard cosmological model based on the single Big Bang and global cosmic expansion. In order to continuously adapt to new abnormal astronomical observation results, researchers have successively put forward multiple ad-hoc auxiliary hypotheses such as cosmic inflation, cold dark matter and cosmological constant (Riess et al., 2022). Although ΛCDM can roughly fit most nearby galaxy observation data, there are irreconcilable core logical flaws: unsolvable cosmic singularity origin, unobservable essential nature of dark matter and dark energy, incompatibility between macroscopic general relativity and microscopic quantum mechanics, and the persistent Hubble tension between two independent Hubble constant measurement channels (Bonici et al., 2021). The need to continuously add supplementary patch theories to maintain internal consistency proves that the standard model has fundamental structural defects, and the academic community needs a new basic cosmological framework different from MOND and f(R) modified gravity systems.

This paper proposes the Original Static Substrate and Local Perturbation Cosmological System, reconstructs the underlying ontological logic of the universe, and uses a minimal unified axiom system to interpret all macroscopic and microscopic cosmic observation phenomena, fundamentally solving the internal contradictions of the ΛCDM paradigm.

Revision Notes for the Present Manuscript

• Three core mathematical tools (random matrix theory, renormalization group flow, coarse-grained entropy) are formally constructed, and the applicable boundary of each module is clearly marked.
• A comparative subsection of conformal scale transformation and overseas metric contraction models is added, distinguishing the present paradigm from coordinate-only shrinking metric preprints from four dimensions: chronological order, physical causality, applicable scope and mathematical equivalence (Scholl, n.d.).
• Only two core formula groups of redshift scale factor and Riemann zeta thermal constant are retained; galactic fractal scaling, complete conformal derivation and zeta dual symmetry analysis are moved to the appendix.
• Fine derivations of cosmic voids, galactic fractals and quasar redshift are transferred to V4.1 (Sheng, 2026); only the JWST high-redshift mature galaxy paradox (JWST Science Office, 2023) is retained in the main text as supporting evidence.
• All qualitative axioms and logical systems of V3.3 are completely retained without paradigm replacement; two observational interpretations of Self-Healing to gradient clock offset and runaway black hole stellar trails are supplemented as direct corollaries of Axiom 3, and complete quantitative processing is deferred to V4.1 (Sheng, 2026).
• Relevant literature on overseas metric contraction models is supplemented to clarify the independent deductive origin of the redshift mechanism; conformal transformation is only used as a post-hoc comparison tool without shared derivation logic with this paradigm.
• This manuscript has undergone two rounds of internal overall polishing, and no adjustments to core axioms and mathematical frameworks have been made; this version is finalized permanently.
• Three targeted revisions are completed: the ambiguous ontological description of redshift in Section 3.4.1 is revised; the internal Self-Healing to Origin solution of Hubble tension (Bonici et al., 2021) is integrated; brief supporting discussion of JWST early mature high-redshift galaxies (JWST Science Office, 2023) is added.

2. Core Axioms: The Underlying Logic of the Universe

The complete operating rules of the model are composed of one supreme premise and three core axioms, uniformly restricting vacuum fluctuation, gravitational evolution and microscopic quantum behavior.

• Supreme Premise (Ultimate Substrate)

The only ontological entity of the universe is an infinite, uniform, eternally macroscopically static original substrate. The substrate has no global displacement, expansion or contraction, but weak microscopic interactive fluctuations are distributed everywhere. The original substrate does not conform to the definition of conventional matter, and has no inherent primitive concepts of time and light. The substrate itself has no sequential past, present and future; time is only a representation attribute limited to the interior of perturbation bubbles and cannot be used to quantify the ontology of the substrate itself.

All matter and spacetime are derivative products generated by local perturbations superimposed on the substrate.

• Axiom 1 (Microscopic Fluctuation)

Weak microscopic interactive phenomena and diffuse energy states run through the entire original substrate. Time, space, matter and energy are not inherent attributes of the substrate.

Note: All human observations and logical reasoning depend on perturbation carriers; the original substrate is outside the cognitive boundary of all perturbation systems, and this description is only an existential qualitative statement. Weak diffuse fluctuations only exist at the microscopic scale of the substrate, while the overall global geometric position of the substrate remains static forever. The two phenomena respectively belong to the macroscopic ontology of the substrate and microscopic local undulation, and there is no logical contradiction between them.

2.1. Mathematical Supplement to Axiom 1

The energy level spacing of global microscopic fluctuations follows the statistical law of Gaussian Unitary Ensemble (Wigner, 1951). The distribution form of perturbations exceeding the critical threshold is:

$$P\left(s\right)\propto s^2{e}^{-A{s}^2}$$

where $s$ represents the fluctuation energy level spacing, and $A$ is the undetermined background coupling constant. The non-trivial zeros of the Riemann zeta function are used as an analogy to describe the eigenvalue spacing law of GUE; this manuscript does not assert a direct physical mapping between prime numbers and substrate fluctuations, and the extended discussion is placed in the appendix.

Applicable boundary: Valid in weak and moderate perturbation regions; deviation occurs under pure substrate or ultra-high energy extreme perturbation conditions.

• Axiom 2 (Local Perturbation)

The superposition of large-scale microscopic fluctuations accumulates local energy until the critical threshold is broken, triggering local phase transition defined as generation perturbation. The diffuse energy of the substrate is transformed into excited states such as matter and photons, which are observationally equivalent to the Big Bang phenomenon described by ΛCDM. The substrate itself has no time attribute; all cycles and time intervals mentioned in the text are internal analog quantities of perturbation bubbles, and there is no inherent chronological sequence at the substrate ontology level.

• Axiom 3 (Self-Healing to Origin)

The original substrate has a universal homogenizing Self-Healing to Origin tendency: all matter, energy and spacetime structures derived from perturbations will gradually homogenize and relax back to the diffuse static state of the substrate, which macroscopically manifests as the increase of thermodynamic entropy. The Self-Healing to Origin effect acts from the moment of perturbation generation; the Self-Healing to Origin flux is suppressed in dense aggregation regions in the early stage, and gradually dominates the evolutionary process as the density decreases, forming a complete chain of perturbation expansion and slow relaxation. Metric deformation only occurs inside perturbation bubbles, and the global substrate geometry remains invariant forever. Photons do not lose inherent energy during propagation, which naturally satisfies the local energy conservation law. The higher the perturbation aggregation density, the stronger the Self-Healing to Origin flux, the faster the local metric contraction speed and the slower the relative time elapse in the region. Satellite-ground clock deviation and extreme time dilation at black hole event horizons are direct observational manifestations of this rule.

2.3. Mathematical Supplement of Renormalization Group Flow

The renormalization group β-function describes the evolution law of perturbation coupling strength: pure substrate without perturbation corresponds to the stable fixed point of the flow.

$$\beta \left(g\right)={\displaystyle \frac{dg}{d\mathrm{l}\mathrm{n}\mu }}$$

where $g$ is the perturbation coupling strength, and $\mu$ is the evolutionary scale parameter. The perturbation bubble scale factor $a\left(\tau \right)$ is constrained by this flow equation.

Applicable boundary: This formula abandons the inherent spacetime assumption of traditional renormalization group field theory, and is only applicable to weak and moderate perturbation intervals; the flow form deviates under extreme strong perturbation and near-pure substrate conditions.

2.4. Thermodynamic Supplement of Coarse-Grained Entropy

The renormalization coarse-graining process is accompanied by monotonic entropy increase inside the perturbation bubble, and the differential form is defined as:

$$dS={\displaystyle \frac{\partial S}{\partial \mu }}d\mu$$

Applicable boundary: Only describes the internal thermodynamic entropy change of perturbation bubbles; the substrate itself has no entropy evolution attribute, and the formula is only valid in the near-equilibrium perturbation region.

2.5. Substrate Field Evolution: Unified Partial Differential Equation Formalism

In order to construct a standardized mathematical framework describing the spatiotemporal evolution of the original substrate under local perturbation and Self-Healing to Origin dynamics, this paper establishes a scalar field partial differential equation consistent with the equilibrium value of the undisturbed pure substrate. Let $\varphi \left(r,t\right)$ represent the scalar field amplitude of the original substrate at spatial coordinate $r=\left(x,y,z\right)$ and local perturbation time $t$, and ${\varphi }_0$ represent the uniform equilibrium value. Define:

$$\delta \varphi \left(r,t\right)=\varphi \left(r,t\right)-{\varphi }_0$$

The complete evolution equation of the substrate field is:

$${\displaystyle \frac{\partial \varphi }{\partial t}}=D{\nabla }^2\varphi -\alpha \left(\varphi -{\varphi }_0\right)+S\left(r,t\right)$$

Each term has clear physical meaning:

• $D{\nabla }^2\varphi$: Spatial diffusion term, describing the natural diffusion of perturbation energy on the continuous substrate; $D$ is the effective diffusion coefficient.
• $-\alpha \left(\varphi -{\varphi }_0\right)$: Self-Healing to Origin convergence term, quantifying the universal tendency of all perturbed regions to relax to the static equilibrium state ${\varphi }_0$; the coefficient $\alpha$ is positively correlated with the local perturbation density, consistent with the core rule of Axiom 3.
• $S\left(r,t\right)$: Local perturbation source term, corresponding to matter-energy excitation generated by substrate phase transition or violent celestial events.

2.5.1. Homogeneous Steady-State Equation (No External Source)

Under time-independent static equilibrium without active perturbation source ($\partial \varphi /\partial t=0$, $S\left(r,t\right)=0$):

$$D{\nabla }^2\varphi -\alpha \left(\varphi -{\varphi }_0\right)=0$$

2.5.2. Point-Source Steady-State Control Equation

Introduce Dirac delta distribution to mathematically describe point mass-energy sources with total intensity $k$:

$$D{\nabla }^2\varphi -\alpha \left(\varphi -{\varphi }_0\right)+k\delta \left(r\right)=0$$

This formula sets the boundary condition for deriving the gravitational potential around isolated galaxies, stars and black holes.

2.5.3. Intrinsic Characteristic Self-Healing Length

$$\lambda =\sqrt{{\displaystyle \frac{D}{\alpha }}}$$

$\lambda$ represents the effective action range of gravitational gradients generated by Self-Healing to Origin inside perturbation bubbles.

2.5.4. Complete Canonical Yukawa Steady-State Solution

$$\varphi \left(r\right)={\varphi }_0-{\displaystyle \frac{C}{r}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{r}{\lambda }}\right)$$

The constant $C$ is linearly proportional to the total source strength $k$ of point perturbation.

$$a\left(r\right)=-\nabla \varphi \left(r\right)\propto -\left({\displaystyle \frac{1}{r^2}}+{\displaystyle \frac{1}{\lambda r}}\right)\widehat{r}$$

This acceleration arises from the potential gradient of Self-Healing to Origin.

2.5.5. Linear Density Dependence of Self-Healing Coefficient

$$\alpha ={\alpha }_0\cdot {\displaystyle \frac{\rho }{{\rho }_0}}$$

where ${\alpha }_0$ and ${\rho }_0$ are reference Self-Healing intensity and reference perturbation density respectively. This relation is the core mathematical source of density-dependent metric contraction rate, and can naturally explain the Hubble tension (Bonici et al., 2021) without additional ad-hoc correction terms.

2.5.6. Asymptotic Limit for Low-Density Cosmic Voids

Inside cosmic voids, the perturbation density approaches zero ($\rho \to 0$) which makes $\alpha \to 0$ and the characteristic length $\lambda \to \mathrm{\infty }$. The exponential attenuation term disappears, the Yukawa potential degenerates into the standard Newtonian gravitational potential.

Applicable boundary: This set of partial differential equation systems is applicable to weak and moderate perturbation regions where the substrate remains continuous; it cannot describe extreme strong perturbation scenes such as black hole event horizons where the substrate continuity is torn.

3. A New Narrative of the Cosmos: From Origin to Ultimate Fate

3.1. Origin and Cosmic Structure

The universe does not originate from a mathematical singularity, but from local phase transition of the substrate to generate finite perturbation bubbles. Matter only propagates inside perturbation bubbles, and the global substrate remains static forever; spacetime only exists within the range of perturbations. Initial energy gradients naturally form galactic filament networks and low-density cosmic voids, consistent with large-scale astronomical observation results. The initial state of perturbation is spherical, and inherent angular momentum breaks spherical symmetry, becoming the dynamic source of celestial rotation and galactic rotation. The Big Bang described by standard cosmology is only an early stage of material evolution inside perturbation bubbles, which is compatible with primordial nucleosynthesis and CMB observational results.

Analysis of Fitting Data of Mainstream ΛCDM Model

• The cosmic age of 13.8 billion years and the observable boundary of 96 billion light-years are fitting values of the ΛCDM model (Planck Collaboration, 2020). After switching to the modified gravity framework of this paper, the spacetime scale estimation will produce systematic deviation.
• ΛCDM equates redshift to global spatial expansion, which is the exclusive metric definition of the standard model; this paper strictly distinguishes observational apparent phenomena from internal ontological evolution mechanisms.

3.2. The Essence of Gravity, Dark Matter and Dark Energy

The centripetal binding effect at the edge of galaxies comes from the potential gradient of Self-Healing to Origin, which is attributed to cold dark matter by ΛCDM (Milgrom, 2020). The apparent large-scale accelerated expansion effect comes from the dynamic balance between perturbation expansion and Self-Healing to Origin relaxation, and there is no need to introduce artificial cosmological constant (dark energy) hypothesis.

$$a\left(r\right)=-\nabla \Phi \left(r\right)$$

This acceleration arises from the potential gradient of Self-Healing to Origin.

This gradient relation can be strictly derived from the Yukawa steady-state solution in Section 2.5.4.

Note: This equation is a transitional quantitative construction and the core derivation formula of modified gravity in this paradigm.

3.3. Black Holes: Local Exposure of the Original Substrate

Black holes are divided into two categories: residual structures left by incomplete phase transition at the time of perturbation generation, and substrate cracks torn by violent perturbation of massive celestial bodies. Both are windows exposing the substrate inside the perturbation bubble, with extremely strong Self-Healing to Origin flux. Original black holes form in the early stage of perturbation and are not limited by the 13.8 billion year evolution time limit of ΛCDM (Planck Collaboration, 2020). They can rapidly accrete matter as gravitational cores to form large galaxies, which directly explains the mature supermassive galaxies observed by JWST at redshift $z>10$ (JWST Science Office, 2023).

Galaxy collisions and perturbation superposition can produce runaway black holes moving at high speed along the Self-Healing to Origin gradient. The Self-Healing to Origin flux in the passing area is suppressed, leading to continuous accumulation of perturbation matter and forming stellar trails with a length of hundreds of thousands of light-years observed by Hubble and JWST. This interpretation does not require two auxiliary assumptions of gravitational wave recoil and uniform interstellar medium. Black holes eliminate surrounding perturbation matter through Hawking radiation (Hawking, 1974) and return to the substrate after complete dissipation. The complete quantitative deduction of high-redshift black holes is placed in V4.1 (Sheng, 2026).

3.4. The Nature of Light and Cosmological Redshift

Light is only high-intensity fluctuation unique to the interior of perturbation bubbles; the concepts of light and wave do not exist on the pure substrate.

3.4.1. Formula of Intrinsic Redshift Scale Factor

$$1+z={\displaystyle \frac{a\left(t_{obs}\right)}{a\left(t_{emit}\right)}}$$

Observationally, this formula presents the overall expansion effect of perturbation bubbles; ontologically, redshift comes from the continuous contraction of local metric driven by Self-Healing to Origin inside perturbation bubbles. As fluctuation carriers, photons do not lose inherent energy and wavelength during propagation; the measured wavelength stretching only comes from the contraction of local metric scales at the time of observation. Self-Healing to Origin is the inherent dissipation tendency of all perturbation bubbles to the uniform substrate. With the decrease of perturbation aggregation density, the metric contraction effect weakens and the redshift growth rate slows down. After the perturbation is completely relaxed and the local metric returns to the substrate reference scale, the redshift phenomenon disappears. This internal mechanism can fundamentally solve the Hubble tension (Bonici et al., 2021).

3.4.2. Equivalent Mathematical Comparison of Conformal Transformation

Overseas metric contraction preprints only use coordinate transformation to fit redshift numerical values, without the static substrate and Self-Healing to Origin ontological basis (Scholl, n.d.).

Boundary Distinction Statement

• Time boundary: The redshift causal chain of this paper is independently deduced based on the substrate axiom; conformal transformation is only a post-hoc comparison tool, not the starting point of theoretical derivation.
• Physical causality boundary: Overseas geometric transformation models have no global static substrate carrier, and metric contraction is only a coordinate mathematical skill; the metric deformation of this paper is the natural evolution result of Self-Healing to Origin, uniquely determined by perturbation density.
• Applicable scope boundary: Pure coordinate contraction models can only fit redshift data, and cannot explain black holes, CMB, satellite clock difference and microscopic quantum phenomena at the same time.
• Mathematical equivalence boundary: The numerical consistency of redshift calculation is limited to the single physical quantity of redshift; the two frameworks have completely different underlying spacetime ontology and evolution driving force, and this paper cannot be classified as a branch of geometric metric contraction theory.

Riemann Zeta Constant Matching CMB Thermodynamics

$$u\propto \zeta \left(4\right)T^4, \zeta \left(4\right)={\displaystyle \frac{{\pi }^4}{90}}$$

Applicable boundary: Only valid in thermal equilibrium radiation scenes.

CMB isotropy is jointly guaranteed by three factors: uniform single perturbation source in the early stage, spherical thermal equilibrium state, and full coupling of matter and radiation, which eliminates the cosmic inflation hypothesis. The Olbers paradox is naturally solved by the finite evolution time of perturbation bubbles and the long-wavelength stretching effect of photons.

3.5. Gravitational Waves: Dynamic Geometric Ripples of Spacetime Inside Perturbation Bubbles

Gravitational waves are spacetime distortion ripples generated by violent celestial events such as binary neutron star and binary black hole mergers (LIGO Scientific Collaboration & Virgo Collaboration, 2022), propagating at the speed of light consistent with multi-messenger astronomical observation results. Gravitational waves follow the same redshift conversion formula as photons, and their carried perturbation energy will eventually homogenize and return to the substrate. The complete statistical analysis of cosmic rays is placed in V4.1 (Sheng, 2026).

4. Unification of the Microscopic World: Dialogue with Quantum Mechanics

4.1. High Consistency of Underlying Microscopic Mechanism

The ubiquitous microscopic fluctuation of the substrate corresponds to the quantum vacuum zero-point energy. Continuous micro-undulation generates all macroscopic matter structures; the substrate can never reach an absolute zero perturbation state.

4.2. Isomorphic Verification of Particle Spin

Particle spin is the smallest stable local perturbation unit, forming a microscopic binary structure of “static substrate + local perturbation”, isomorphic to cosmic perturbation bubbles. The superposition of multiple micro-spins generates the rotation characteristics of galaxies and stars.

4.3. Perturbation Interpretation of Double-Slit Interference

Photons and electrons are extended coherent perturbation regions; measuring equipment introduces external disturbance to break coherence and eliminate interference fringes, which has nothing to do with observer consciousness.

4.4. Quantum Entanglement: Separated Seed-Particles from a Homologous Perturbation-Bubble

Entangled-particle pairs originate from seed-particles that become separated within the same primitive perturbation-bubble during cooling, and share the original overall fluctuation phase. Correlation does not rely on superluminal signal transmission, and the static attribute of the substrate remains unchanged during the whole process. The detailed decoherence mechanism is supplemented in V4.1 (Sheng, 2026).

4.5. Spacetime Compatibility with General Relativity

$$d{s}^2=-c^{2}d{t}^2+d{x}^2+d{y}^2+d{z}^2$$

After the perturbation is completely dissipated, spacetime disappears, which is consistent with the core view of loop quantum gravity that time is not fundamental.

4.6. Superposition of Multi-Layer Extremely Low Probabilities

Four layers of low-probability superposition events (cosmic genesis, galaxy formation, biological evolution, the proposal of this paradigm) and their joint probability quantitative deduction are fully sorted out in V4.1 (Sheng, 2026).

5. Epistemological Boundary and Model Positioning

5.1. Three-Layer Cognitive Limitation

All human observation and logical reasoning are limited by sensing instruments and logical systems, and all cognition depends on perturbation carriers. Human sequential logic is only adapted to the evolution inside perturbation bubbles, and cannot intuitively understand the timeless and scale-less substrate ontology.

Cognition derived from perturbation phenomena cannot reach the ultimate nature of the substrate itself.

5.2. Applicable Boundary of Falsifiability

Popper’s falsification standard is only applicable to repeatable local laboratory and astronomical observation experiments, and cannot be used to judge the transcendental substrate ontology; there is a logical mismatch between judging the whole by local physical laws.

5.3. Ontological Positioning of This Model

This paper constructs a set of effective cosmological theoretical systems based on existing astronomical observation results, and does not claim to completely reveal the absolute ultimate essence of the universe. Its academic value lies in internal self-consistency and the unified interpretation ability of multi-scale observation phenomena. Acknowledging the cognitive limitation of human observers is the embodiment of academic rigor rather than theoretical defect.

5.4. Testable Predictions of the Model

Observable predictions include spherical matter distribution gradient, galactic Self-Healing to Origin gravitational curve, black hole evolution law, CMB temperature constraint, gravitational wave redshift difference and density-dependent Hubble constant. All detailed quantitative prediction tables are collected in V4.1 (Sheng, 2026).

5.5. The Nature of Time and Relativity

$$\Delta t\mathrm{\text{'}}={\displaystyle \frac{\Delta t}{\sqrt{1-v^2/c^2}}}$$

Time only exists with perturbation structures; four-dimensional spacetime does not exist on the pure substrate. Complete evolutionary chain: timeless substrate → perturbation spacetime generation → spacetime dissipation after full Self-Healing to Origin. The gradient of Self-Healing to Origin flux controls the local time flow rate, which uniformly explains satellite-ground clock difference and black hole extreme time dilation phenomenon.

6. Comprehensive Comparison Between This Model and Singular Big Bang ΛCDM Model

6.1. Comparison of Underlying Logic

ΛCDM: Originated from mathematical singularity, unsolvable cosmic initial state, multiple independent auxiliary hypotheses of inflation, dark matter and dark energy, and continuous patch modification with the accumulation of abnormal observation results.

Original Static Substrate Paradigm: Only one supreme substrate premise + three core axioms, no unobservable hypothetical exotic substances, unified interpretation of macroscopic gravity and microscopic quantum phenomena at the ontological level.

6.2. Comparison of Cognitive Logic

The apparent expansion of the universe is only the observational illusion generated by internal metric contraction; the numerical fitting result is equivalent to ΛCDM, but the underlying ontology and evolution driving force are completely different, and the Hubble tension (Bonici et al., 2021) can be fundamentally eliminated without auxiliary correction terms.

6.3. Comparison of Explanatory Coverage

Unified interpretation of substrate ontology, emergent time, cosmological redshift, black hole evolution, runaway stellar trails, relativistic clock deviation, quantum phenomena, Hubble tension and JWST high-redshift mature galaxies (JWST Science Office, 2023). Complete numerical comparison data with ΛCDM is placed in V4.1 (Sheng, 2026).

6.4. Comparison of Future Expansion Potential

The internal logical frame of ΛCDM is rigid, and new abnormal phenomena need to add new independent hypotheses; this paradigm has clear layered expansion channels: this manuscript is the mathematical skeleton, and V4.1 carries out complete astronomical quantitative derivation and observation prediction (Sheng, 2026).

7. Conclusions and Prospect: Scientific Value and Ideological Significance

This paradigm constructs a logically closed cosmic theoretical system based on existing multiband astronomical observation data, and does not claim to obtain absolute ultimate truth, avoiding the binary opposition between theology and nihilism cosmology. Different from MOND, f(R) and other patch modified gravity theories, this paper reconstructs the complete evolution logic starting from the most basic ontology, and realizes the unification of macroscopic gravity and microscopic quantum mechanism at the axiom level. All complete quantitative astronomical derivations and multi-band observation predictions are attached to the companion manuscript V4.1 (Sheng, 2026).

This manuscript completes the construction of the core mathematical skeleton, completely inheriting all axioms and logical systems of V3.3 without paradigm replacement. Two new qualitative interpretation modules of Self-Healing to Origin clock deviation and runaway black hole stellar trails are added, and a comparative subsection of conformal transformation and overseas metric contraction models is supplemented. Fractal scaling and complete conformal mathematical content are transferred to the appendix, only two core formula groups are retained. Three targeted revisions are completed: the ambiguous ontological description of redshift in Section 3.4.1 is revised; the internal Self-Healing to Origin solution of Hubble tension (Bonici et al., 2021) is integrated; brief supporting discussion of JWST early mature high-redshift galaxies (JWST Science Office, 2023) is added. All mathematical tools in this paper are transitional modeling tools, and will be further optimized according to multi-band and gravitational wave observation data in subsequent iterative versions. The repetitive redundant sentences in the full text are streamlined to make the argument compact, while the monistic substrate core logic is completely retained without deletion or modification. This manuscript and V4.1 are uploaded to the Zenodo platform synchronously as complementary serial manuscripts for cross-reference reading by researchers.