Universal Force Relations: Density-Driven Kinetic Screening and Hierarchical Balance Collapse

Universal Force Relations: Density-Driven Kinetic Screening and Hierarchical Balance Collapse

 

[Abstract]

This paper proposes a scalar-tensor effective theory with density-dependent kinetic screening. The scalar degree of freedom is interpreted as a pseudo-Goldstone mode. The critical density ρ* ≈ 0.026 ρ_crit induces an environment-dependent modified gravity:

 

G_eff(ρ) = G [1 + α / (1 + ρ/ρ*)]

 

v3.5 core addition: The functional form of G_eff and the critical value I* = 0.071 are geometrically derived from z-axis phase difference dynamics of space pixels. I* = 7.1% is established as a necessary consequence of spatial structure — The Universal Critical Ratio (UCR). This value is independently confirmed in a companion paper (UCR Paper v1.0, DOI: 10.5281/zenodo.19140461) via the 1/14 face partition of the Truncated Octahedron lattice with formal Lemma-Theorem structure and LSM simulation confirmation.

 

[Key Results]

- G_eff functional form geometrically derived from pixel z-axis phase dynamics

- I* = UCR = 0.071 established as universal critical value

- fσ₈ = 0.440 (within observational range 0.40–0.45)

- Void peculiar velocity excess +17.8% (Euclid verification target)

- All solar system and GW constraints satisfied

 

[Note]

Version: v3.5

Author: Sonkichul (Son Kichul), Independent Researcher

AI Research Assistance: Gemini, Claude (calculation verification)

Contact: shionup@gmail.com

 

 

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v3.6 (March 2026)

- §3.4 added: Relation to Horndeski and Extended Scalar-Tensor (EST) 

  theories — EMWC formally positioned within EST framework

- §3.4.1 added: UCR as kinetic screening threshold within EST framework

- Energy, information, and pressure established as identical critical 

  structure — all expressions of TO lattice geometry (UCR Paper v1.1)

- UCR Paper v1.1 reference updated (DOI: 10.5281/zenodo.19158694)

- References added: Horndeski (1974), Deffayet (2009), 

  Kobayashi (2011), Zumalacárregui & García-Bellido (2014)

 

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v3.7 (March 2026)

- Parameter corrections

   (β₀=3.467, λ₀=0.214),

   OP-16 density-dependent η_eff,

   OP-17 galaxy rotation curve formula,

   GW strain h_obs=I*×Rs/r

 

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   v3.8 (March 2026)

   - Section 10: μ geometric origin

     μ=-(Z+1)/(Z-1)×σ², μ₀=-5/6

     μ(T_m) linear form derived from Z=4

   - Section 11: α phase structure

     α_s=1-Z×I*=5/7, α_d=30/49, α_avg=65/98

   - Section 12: Hubble Tension resolved

     H₀_local=H₀_CMB×√(1+α_s/Z)=73.17

     Precision 0.001%

   - Section 13: MOND a₀=I*×a_max

   - Appendix: Python verification code

 

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v3.9 (March 2026)

- Section 14: Cosmological composition correspondence

  Ω_Λ ≈ α_obs = 0.680 (0.73%)

  1-α_obs = 0.320 ≈ Ω_m = 0.317 (0.003)

  Ω_b = Ω_DM/(α_obs×8) = 0.04926 (0.54%)

  TO lattice fully explains all cosmic components

- Section 15: Discrete lattice structural loss

  ε = 2/Z₁₂² = 2/144 = 0.01389 (0.8%)

  N_s = χ = 2 (Euler characteristic, topological invariant)

  144 = Z₁₂² = energy superposition states (coordination²)

  λ₀×I* ≈ ε: expansion tension = structural loss (pending)

- Section 16: Lattice degeneration model

  Early universe: F=12, Z=10 → H₀=67.4 km/s/Mpc

  Present:        F=14, Z=12 → H₀=73.17 km/s/Mpc

  H₀(z) evolution direction consistent with DESI DR2

- Section 17: SPARC BTFR full verification (136 galaxies)

  V_c⁴ = G×M_b×a₀, a₀=1.219×10⁻¹⁰ m/s²

  High mass (47): R²=0.964, mean -9.0%

  Mid mass  (44): R²=0.826, mean -6.1%

  Low mass  (45): R²=0.803, mean +8.4%

  Overall mean: -0.5% ✅

  EMWC consistently 0.3~0.4% better than MOND

 

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v4.0 (March 2026)

- Section 18: λ₀ geometric origin

  λ₀ = (2/Z₁₀² − 2/Z₁₂²) × Z₁₀/(Z₄×I*) = 0.2139

  Observed 0.214, error 0.052%

  Physical model: lattice transition Z=10→12

  releases structural loss Δε as expansion wave λ₀

  Δε = 11/1800, λ₀×I* = 11/720

- Section 19: 4D geometric-phase integration

  TO 14 channels (6 orthogonal + 8 diagonal)

  DOF_geom = 14 - rank(4 constraints) = 10 = Z₁₀

  → Z₁₀=10 is mathematical necessity, not assumption

  DOF_phase = Euler χ = 2 (topological invariant)

  DOF_total = 10 + 2 = 12 = Z₁₂ (derived)

  Δε = 2/144 fully derived from DOF structure

  No free parameters remain in the framework

- Appendix B: Scope of explanation

  B.1: Confirmed — Planck CMB parameter set

       explained by TO lattice geometry

  B.2: Pending — BAO (SDSS), σ₈ (KiDS),

       CMB peak, BBN lithium

  B.3: Interpretation

  B.4: Circular reasoning RESOLVED

       Z₁₀=10 derived from conservation laws,

       not fitted to cosmological data

 

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v4.1 (April 2026)

Changes from v4.0

1. Full structural integration (v3.5→v4.1)

Previous versions accumulated section additions in-sequence. v4.1 restructures all content into a single unified document with continuous section numbering (§1–§24) and consolidated appendices (App.A–G) at the document end.

2. UCR v1.9.3 reference update

All references updated to the canonical companion paper: UCR v1.9.3, DOI: 10.5281/zenodo.19368813. The relationship is clarified throughout: UCR establishes I* = 1/14 geometrically; EMWC applies I* as a cosmological input via single-direction reference.

3. Parameter consistency audit

All parameter values cross-checked across versions. Retired values (β₀=4.1, β₀=3.9, λ*=0.111) documented with explicit retirement notices and replacement derivations. Version-by-version change history consolidated in §1.2.

4. Appendix consolidation

Intermediate appendices scattered mid-document in v3.5–v4.0 are unified at document end as App.A–G. The Management Section is retired from the main body as its content has been incorporated into the relevant sections.

5. Open Problems register (App.G)

All open problems from v3.5–v4.1 consolidated with current status (✓ / SKETCH / OPEN) and missing piece identification.

No new physics results in v4.1. All theoretical content is preserved from v4.0.