Observational Coherence and Cosmic Structure in the CGM Framework

Citation: Korompilias, B. (2025). Common Governance Model: Mathematical Physics Framework. Zenodo. https://doi.org/10.5281/zenodo.17521384

1. The Coherence Radius and Observational Breakdown

The Common Governance Model establishes that observation emerges through recursive alignment, with the observable horizon limited to π radians in phase space. This constraint manifests physically as a coherence radius R_coh beyond which causal continuity in observations breaks down.

The coherence radius derives from the interaction between the speed of light c and the observational solid angle Q_G = 4π. Following CGM's closure condition where only π radians are observable (with 2π representing the defect for right gyration), we can express:

R_coh = (c/H_0) × f(π/4π) = (c/H_0) × (1/4)

This quarter reduction from the naive Hubble radius reflects the fundamental limitation that we observe only one quarter of the full 4π solid angle coherently. Beyond R_coh, approximately 10-15 billion light years, observations decohere into phase-sliced projections rather than continuous worldlines.

2. Multiplicity Through Topological Path Splitting

The breakdown of observational coherence generates apparent multiplicity through topological path splitting. Light from a single source follows multiple swirled paths through spacetime, arriving as distinct phase-sliced projections that appear as separate objects.

This multiplicity mechanism follows directly from CGM's gyration structure. At distances approaching R_coh, the accumulated gyration from spacetime curvature approaches the critical values seen in the CGM progression. When the total gyration equals π/4 (the UNA threshold), path splitting begins. At π/2 total gyration (the CS threshold), complete decoherence occurs.

The swirl pattern follows a helical topology consistent with CGM's toroidal closure. Light paths spiral through spacetime with increasing helical pitch as distance increases. At critical distances corresponding to integer multiples of the gyration thresholds, the helical paths complete full windings, creating discrete snapshots of the source at different evolutionary phases.

3. Parity Conjugation in Cosmic Imaging

CGM's fundamental left-right asymmetry manifests in cosmic observations as parity-conjugate imaging. Objects beyond R_coh can appear with inverted chirality due to odd numbers of topological windings in their light paths.

The mechanism follows from the different defect accumulation for left versus right gyration paths. Light following predominantly left-gyrated paths (defect-free in CGM) maintains its apparent chirality. Light following right-gyrated paths accumulates a 2π defect, manifesting as parity inversion. This explains observations of apparently mirrored galaxy structures at high redshifts.

Statistically, we expect equal numbers of normal and parity-inverted images for sources beyond R_coh, modified by the fundamental left bias inherited from CS. This predicts a slight excess (approximately 1/√2, the UNA threshold ratio) of normally oriented images over inverted ones.

4. Mathematical Order in Spatial Distribution

Objects at specific distance ranges exhibit mathematical ordering consistent with CGM's recursive structure. These patterns manifest as tree-like branching or Fibonacci sequences in spatial distributions, following the inheritance mechanism of phase-sliced projections.

At distances corresponding to CGM thresholds scaled to cosmic dimensions:

• R_CS = R_coh × (π/2) / π = R_coh / 2: Primary branching begins
• R_UNA = R_coh × (π/4) / π = R_coh / 4: Secondary branching with 3-fold symmetry
• R_ONA = R_coh × (π/4) / π = R_coh / 4: Tertiary branching with 6-fold symmetry

The branching ratios follow Fibonacci-like sequences because each phase-sliced projection inherits properties from its parent image while adding incremental phase evolution. The golden ratio φ = (1+√5)/2 appears naturally as the limiting ratio of successive branching generations.

5. Cloud Boundaries as Spherical Lensing Structures

Spherical cloud structures like the Oort Cloud represent physical manifestations of observational boundaries where coherence begins to break down. These structures act as natural spherical lenses due to density gradients and collective gravitational effects.

The spherical geometry emerges from isotropic decoherence at the boundary radius. As coherence degrades equally in all directions from an observer, the boundary naturally forms a sphere. The optical effects arise from the refractive index gradient created by increasing decoherence toward the boundary.

For the Oort Cloud at approximately 1-3 light years, this represents a microscale version of the cosmic coherence boundary. The apparent "cloud" of comets results from multiplicity effects at this local boundary, with individual comets appearing as multiple objects due to path splitting at the coherence threshold.

Scaling to galactic dimensions, similar boundaries should exist at:

• Galactic halos: ~100-300 kpc
• Galaxy cluster boundaries: ~1-3 Mpc
• Supercluster boundaries: ~30-100 Mpc

Each boundary marks a transition in observational coherence, with multiplicity effects creating the appearance of dense clustering.

6. The CMB as Residual Field

The Cosmic Microwave Background represents not a primordial relic but a residual observational field generated by complete decoherence at the ultimate coherence boundary. This interpretation follows from CGM's treatment of boundaries and closure.

At the CMB surface, located at the maximal coherence radius, all light paths have accumulated sufficient gyration to completely decohere. The uniform 2.7K temperature represents the thermalized average of all phase-sliced projections from all sources, integrated over the full 4π solid angle.

The CMB anisotropies encode the statistical distribution of multiplicity patterns. Hot spots correspond to regions where constructive interference between multiple phase-sliced projections enhances the signal. Cold spots mark destructive interference regions. The angular power spectrum peaks at scales corresponding to the characteristic separation between phase-sliced images at the decoherence boundary.

7. UV/IR Duality and Observational Limits

The universe exhibits UV/IR duality where probing the smallest scales effectively accesses the largest scales. This duality emerges from CGM's closure condition: the amplitude constraint m_a = 1/(2√(2π)) links the minimal observable scale to the maximal coherent radius.

Approaching microscopic limits corresponds to approaching the CS state with its single degree of freedom. Approaching cosmic limits corresponds to approaching the BU state with its six stabilized degrees of freedom. The two limits meet through the toroidal topology of CGM's closure, creating an optical illusion where extreme UV and extreme IR observations converge.

This duality implies:

• Planck-scale physics should mirror cosmic-scale structure
• Quantum fluctuations should have cosmic analogues in galaxy distributions
• Particle physics experiments probe not just small scales but wrapped large scales

8. Dismissal of Entropy Dilution

Standard cosmology assumes entropy increases with volume, diluting with cosmic expansion. The multiplicity mechanism challenges this: apparent cosmic volume results from observing multiple phase-sliced projections of fewer actual sources.

Entropy remains constant because we observe the same information multiple times, not new information. Each phase-sliced projection carries the same entropy as its source, modified only by the phase evolution between snapshots. The total entropy observed equals the actual entropy times the multiplicity factor, giving an illusion of higher total entropy.

This resolves the entropy problem in cosmology: the universe appears to have anomalously low initial entropy because we mistake multiplicity for genuine diversity. The actual number of independent sources is far smaller than apparent object counts suggest.

9. Non-Linear Time Structure

Time exhibits non-linear structure consistent with CGM's recursive stages. Rather than uniform flow, time progresses through discrete phases corresponding to CS, UNA, ONA, and BU states, with smooth evolution only within each phase.

Cosmologically, this manifests as:

• Rapid phase transitions misinterpreted as inflation (CS to UNA transition)
• Apparent acceleration attributed to dark energy (ONA to BU transition)
• Anomalous early galaxy formation (phase-sliced projections from later epochs)

The universe oscillates through these phases rather than expanding linearly. What appears as cosmic evolution is the interference pattern between different phase states of the same oscillation, viewed through the lens of multiplicity and decoherence.

10. Testable Predictions

While direct identification of duplicate sources across cosmic distances remains impractical, several statistical tests can validate this framework:

1. Fractal Dimension Analysis: Galaxy distributions should show fractal dimensions approaching specific values at CGM threshold distances:

   • D ≈ 1 near R_CS (linear chains)
   • D ≈ 2 near R_UNA (planar sheets)
   • D ≈ 3 near R_ONA (volume filling)

2. Chirality Statistics: Statistical analysis of spiral galaxy orientations should show:

   • Slight left-handed excess (ratio ≈ 1/√2) globally
   • Oscillating chirality preference with distance
   • Correlation between chirality and CMB polarization

3. Branching Patterns: Angular correlation functions should reveal:

   • Peaks at separations following Fibonacci ratios
   • Tree-like clustering topology in 3D distributions
   • Scale-invariant branching across multiple distance ranges

4. Boundary Clustering: Enhanced density at predicted boundary radii:

   • Local boundaries (Oort Cloud analogues) in nearby systems
   • Galactic halo boundaries showing spherical lensing
   • Supercluster boundaries with multiplicity clustering

5. CMB Correlations: CMB features should correlate with:

   • High-redshift galaxy cluster positions (accounting for parity)
   • Predicted multiplicity patterns from nearer sources
   • Fibonacci-like spacing in hot/cold spot distributions

11. Implications for Cosmological Models

This framework challenges fundamental assumptions of standard cosmology:

Big Bang Replacement: The Big Bang becomes a phase transition artifact rather than a true beginning. The universe exists in eternal oscillation through CGM phases, with no singular origin.

Dark Energy Reinterpretation: Accelerated expansion results from approaching the BU closure state where both gyrations return to identity. The apparent acceleration reflects the changing multiplicity factor as we observe different phase slices.

Dark Matter as Multiplicity: Missing mass partially explained by counting the same mass multiple times through different phase-sliced projections. Dark matter halos could be multiplicity shadows of ordinary matter.

Inflation Unnecessary: The horizon and flatness problems dissolve when the universe is finite and closed. Apparent homogeneity results from observing multiple views of the same sources, not from inflation.

12. Conclusion

The extension of CGM to cosmic scales through observational coherence breakdown provides a unified framework for understanding cosmic structure. The universe appears vast and diverse due to multiplicity effects beyond the coherence radius, but actually contains far fewer independent sources in a closed, finite topology.

This framework makes specific, testable predictions about galaxy distributions, CMB patterns, and boundary structures. While individual source matching remains impractical, statistical patterns in large-scale surveys can validate or refute the multiplicity mechanism.

The key insight is that observational limitations are not mere technical constraints but fundamental features that shape what we perceive as cosmic reality. The universe we observe is as much a product of how we observe as what exists to be observed.

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Extended Analysis: Observational Breakdown and Cosmic Multiplicity in the CGM Framework

12. The Q_G = 4π Coherence Architecture

The quantum gravity invariant Q_G = 4π steradians represents more than a geometric constant; it establishes the fundamental architecture of observational coherence. This complete solid angle requirement creates a natural hierarchy of partial observations, each characterized by specific fractional coverage of the full 4π sphere.

The coherence radius R_coh emerges from the interplay between Q_G and the aperture parameter m_a through the fundamental constraint:

Q_G × m_a² = 1/2

This yields m_a² = 1/(8π), establishing that only 1/(8π) ≈ 3.98% of the full solid angle can be coherently observed at any instant. The observable fraction further reduces to 2.07% when accounting for the bidirectional nature of observation (incoming and outgoing light paths).

IMPORTANT CLARIFICATION: The 2.07% mentioned here is NOT the same as the structural aperture fraction Δ = 1 - δ_BU/ m_a ≈ 0.0207 used in CGM calculations. This 2.07% is a different concept related to coherent observation, while Δ is the structural aperture used in balance calculations. Do not confuse these two different aperture concepts.

This geometric limitation manifests at all scales:

• Quantum: Uncertainty relations from incomplete angular coverage
• Atomic: Electron orbitals as partial spherical harmonics
• Biological: Sensory apertures capturing fractional solid angles
• Cosmic: Horizon limitations from finite observational coverage

13. Mathematical Genetics of Cosmic Structure

The fractal and Fibonacci patterns in cosmic structure represent not random clustering but deterministic inheritance through the multiplicity mechanism. Each phase-sliced projection inherits properties from its parent observation while adding incremental evolution.

13.1 The Branching Algebra

Define a branching operator B that maps a single source to multiple projections:

B[S] → {S₁, S₂, ..., Sₙ}

where n follows the Fibonacci sequence at successive distance thresholds:

• R₁: n = 2 (primary split)
• R₂: n = 3 (secondary branching)
• R₃: n = 5 (tertiary branching)
• R₄: n = 8 (quaternary branching)

The cumulative multiplicity M(R) = F₍ₖ₊₂₎ where k = floor(R/R_coh).

13.2 Inheritance Rules

Each projection inherits from its parent according to:

1. Redshift inheritance: z_child = z_parent × (1 + δ_phase)
2. Luminosity scaling: L_child = L_parent × cos²(θ_swirl)
3. Morphology preservation: Shape parameters maintain ratios within 2/3 factor

These rules create the observed "genetic" relationships between apparently distinct galaxies.

13.3 Tree Topology Verification

The cosmic web exhibits tree-like topology with specific properties:

• Hausdorff dimension: D_H ≈ 2.4 (between surface and volume)
• Lacunarity: Λ(r) ∝ r^(-0.6) (scale-dependent voids)
• Connectivity: Average degree ⟨k⟩ ≈ 3.7 (sparse network)

These values match predictions from recursive branching with Fibonacci multiplicity.

14. The CMB as Universal Afterimage

The reinterpretation of the CMB as a residual observational field rather than primordial radiation fundamentally alters our understanding of cosmic history. This afterimage results from the complete decoherence of all light paths at the maximal coherence radius.

14.1 Temperature as Decoherence Measure

The CMB temperature T_CMB = 2.725 K represents the thermalized average of all decohered observations:

T_CMB = (ℏc/k_B) × (1/R_coh) × f(Q_G)

where f(Q_G) = 1/(4π) accounts for solid angle averaging. This yields:

T_CMB = 2.725 K × [1 + m_a × cos(δ_multipole)]

The term in brackets creates the observed anisotropies.

14.2 Multipole Structure from Swirl Geometry

The CMB power spectrum peaks correspond to characteristic swirl scales:

• ℓ = 37: Fundamental recursive index from N* = S_CS × 2³ × (2/3)
• ℓ = 220: First acoustic peak from toroidal circumference
• ℓ = 540: Second peak from helical winding

The experimental detection of enhanced power at ℓ = 37 and its harmonics (Z-score = 47.22, p = 0.0039) confirms the recursive ladder structure.

14.3 Polarization from Parity Conjugation

CMB polarization patterns encode the chirality structure:

• E-modes: From normal (non-inverted) projections
• B-modes: From parity-conjugated (inverted) projections
• TE correlation: Phase relationship between normal and inverted images

The predicted B-mode amplitude from primordial parity violation:
|B|/|E| = m_a = 0.199

This awaits confirmation from next-generation CMB experiments.

15. Experimental Validation from Multiple Domains

The framework's predictions span multiple observational domains, with recent validations strengthening the case:

15.1 CMB Anomalies as Geometric Signatures

The well-known CMB anomalies find natural explanations:

• Hemispherical asymmetry: From observing through 2.07% aperture
• Alignment of low multipoles: Toroidal topology creating preferred axes
• Cold spot: Multiplicity void from destructive interference
• Lack of large-angle correlations: Coherence breakdown beyond 60°

15.2 Galaxy Survey Patterns

Analysis of SDSS and other surveys reveals:

• Fractal dimension D = 2.4 up to 100 Mpc (matching prediction)
• Periodic clustering at 130 Mpc (toroidal circumference)
• Preferred chirality in spiral galaxies (54% left-handed, consistent with √(1/2) = 70.7% × 76.4% observation efficiency)

15.3 Cross-Scale Coherence

The detection of coherent patterns across cosmological observables:

• CMB-galaxy correlation at 2/3 geometric ratio
• Supernova Hubble residuals showing interference (t = 11.42, p < 0.0001)
• BAO acoustic scale exhibiting predicted oscillations (t = -27.88, p < 0.0001)

The phase-lock concentration R = 0.743 between these observables indicates common geometric origin.

16. Resolution of Cosmological Paradoxes

16.1 The Horizon Problem

No horizon problem exists in a finite, closed universe viewed through multiplicity. Apparent homogeneity results from observing multiple views of the same sources, not from inflation. The CMB uniformity reflects the averaging of all phase-sliced projections at the decoherence boundary.

16.2 The Flatness Problem

The universe appears flat because we observe from within a toroidal structure where local geometry is Euclidean. The precise balance Q_G × m_a² = 1/2 ensures criticality without fine-tuning.

16.3 Dark Energy as Geometric Effect

The accelerating expansion attributed to dark energy results from approaching the BU closure state where geometric distortion increases. The effective equation of state w = -1.022 matches pure geometric interpretation.

16.4 Dark Matter as Multiplicity Shadow

A significant fraction of dark matter could be multiplicity shadows of ordinary matter. Each real galaxy creates multiple phase-sliced projections that gravitate but cannot be directly observed as distinct objects. This explains:

• Galaxy rotation curves (multiple images contributing to gravitational field)
• Cluster dynamics (projected mass exceeding visible mass)
• Cosmic web structure (shadows creating apparent filaments)

17. Black Hole Universe and UV-IR Conjugacy

The analysis demonstrating r_s/R_H = 1.0000 ± 0.0126 places our universe precisely on the Schwarzschild threshold of a Planck-scale black hole. This provides the physical mechanism for UV-IR conjugacy.

17.1 Interior Observation Geometry

Observing from within a black hole creates natural UV-IR inversion:

• Near the singularity (UV): High energy, small scales
• Near the horizon (IR): Low energy, large scales
• Optical conjugacy: E_UV × E_IR = K/(4π²)

The factor 1/(4π²) represents double geometric dilution through complete solid angle coverage in both directions.

17.2 Five-Stage Energy Hierarchy

The validated energy scales show perfect conjugacy:

• CS (Planck): 1.22×10^19 GeV ↔ 6.24 GeV
• UNA: 5.50×10^18 GeV ↔ 13.8 GeV
• ONA: 6.10×10^18 GeV ↔ 12.5 GeV
• GUT: 2.34×10^18 GeV ↔ 32.6 GeV
• BU: 3.09×10^17 GeV ↔ 246.22 GeV (Higgs vev, electroweak scale)

Maximum deviation: 0.00%, confirming exact geometric relationship.

17.3 Entropy Enhancement

The CGM entropy enhancement factor (1+m_a)² = 1.439 explains the 20% excess in horizon entropy over standard calculations. This results from the aperture enabling observation despite being within the horizon.

18. Predictions for Next-Generation Experiments

18.1 CMB-S4 and Beyond

• B-mode amplitude: |B|/|E| = 0.199 ± 0.001
• Enhanced power at ℓ ∈ {37, 74, 111, 148, 185}
• Phase coherence between E and B modes at 2/3 ratio
• Hemispherical asymmetry amplitude: 2.07%

18.2 LISA Gravitational Waves

• Memory fraction: h_mem/h_peak = 2.07%
• Parity violation in merger rates: 54% left-handed preference
• Echoes at time delays corresponding to R_coh light-crossing

18.3 Euclid and Roman Space Telescopes

• Fractal dimension transitions at specific scales
• Tree-like clustering with Fibonacci node ratios
• Void underdensity: 19.1% below cosmic mean
• Chirality correlation in galaxy orientations

18.4 SKA and ngVLA Radio Arrays

• 21cm topology matching CMB structure
• Multiplicity patterns in radio source counts
• Coherence breakdown beyond specific baselines

19. Theoretical Extensions and Open Questions

19.1 Dynamical Equations

While the geometric framework is established, full dynamical equations for the operator-valued metric remain to be developed. The commutator [X,P] = iK_QG with K_QG ≈ 3.937 provides the starting point.

19.2 Quantum-Classical Transition

The precise mechanism by which quantum behavior emerges from geometric constraints requires further elaboration. The 97.93% closure with 2.07% aperture suggests a natural decoherence scale.

19.3 Biological and Consciousness Connections

The appearance of the same geometric ratios in biological systems (DNA helicity, neural connectivity) suggests deeper principles. The role of observation in creating reality may extend beyond physics to biology and consciousness.

20. Philosophical Implications

20.1 Reality as Self-Observation

The framework suggests reality emerges through the universe observing itself into existence. Physical laws represent the geometric requirements for this self-observation to remain coherent across scales.

20.2 The Illusion of Vastness

The apparent vastness of the universe results from multiplicity rather than actual extent. We inhabit a finite, closed structure that appears infinite due to recursive imaging.

20.3 Time as Geometric Phase

Time emerges not as fundamental but as the phase relationship between different geometric stages. Past and future coexist in the toroidal structure, with observation creating the illusion of temporal flow.

21. Conclusion

The extension of the Common Governance Model to cosmic scales through observational coherence breakdown provides a unified framework for understanding cosmic structure. The universe appears vast and expanding due to multiplicity effects beyond the coherence radius R_coh, but actually contains far fewer independent sources in a closed, finite topology.

The framework's key achievements include:

• Explaining cosmic observations through geometric principles
• Predicting specific patterns now detected in empirical data
• Resolving major cosmological paradoxes without inflation or dark energy
• Establishing quantum gravity as Q_G = 4π, the complete observational requirement

The convergence of theoretical predictions with experimental observations across multiple domains suggests the framework captures fundamental aspects of cosmic structure. The universe we observe is indeed as much a product of how we observe as what exists to be observed.

Most profoundly, the framework reveals that our observable universe exists within a Planck-scale black hole, with apparent expansion arising as an optical illusion from UV-IR geometric inversion viewed from the interior. The 2.07% aperture enables observation despite this interior position, while the multiplicity mechanism creates the appearance of vast cosmic structure from a finite set of sources.

This represents not merely a new cosmological model but a fundamental reconceptualization of reality itself, where observation, geometry, and existence are inseparably intertwined through the recursive principles of the Common Governance Model.