Universal Force Relations: Density-Driven Kinetic Screening and Hierarchical Balance Collapse
Description
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
--
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
---
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
---
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.
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v4.3 (April 2026) — Integrated Edition
Main paper: EMWC_v4_3_complete.pdf (48 pages)
= v4.2 (40p) + New Sections S25-S31 (8p)
New Sections:
- S25: N_max geometric derivation
N_max = (R/L_px)^2 x exp(-Z_12^2) = 10^59.6
Holographic surface DOF x phase entropy suppression
S_phase = Z_12^2 = 144 (independent phase modes)
- S26: N_1d saturation and Hubble tension
N_1d = N_max x alpha_obs
Omega_Lambda = N_1d / N_max = alpha_obs = 0.679
[New] Dark energy = lattice saturation fraction
CMB (complete): H_0 = 66.7 km/s/Mpc
Local (partial): H_0 = 70.2 km/s/Mpc
Hubble tension = saturation degree difference
- S27: f_geom = F x Z_10 / pi = 44.56
Three independent derivations (0.04% agreement):
(1) Geometric: F x Z_10 / pi
(2) Time-scale: (tau_0/Dt_px) / N_1d
(3) Energy-phase: E_px_max / E_min = N_1d x f_geom
- S28: Omega_b precision derivation
Omega_b = I* x sin(2 theta_c) = 0.049235
Error 0.018% vs Planck 2018 (improved from 0.54%)
Uses only integers {13, 14, 27}
- S29: Complete cosmic composition from alpha_obs alone
Omega_Lambda = alpha_obs = 0.6786 (0.9%)
Omega_b = I* x sin(2 theta_c) = 0.04924 (0.018%)
Omega_DM = (1-alpha_obs) - Omega_b = 0.2722 (1.6%)
Sum = 1.000000 (exact)
- S30: lambda* = lambda_0 [OP Resolved]
lambda* (elastic critical strain) = lambda_0 (expansion tension)
Both = Delta_eps x Z_10 / (Z_4 x I*) = 0.2139
Same physical constant, OP-lambda* closed
- S31: Complete parameter chain v4.3
Companion documents (same record):
- UCR_EMWC_Supplementary_v2.pdf
App O: N_max/N_1d/H_0 derivation chain
App P: Cosmic composition from alpha_obs
App Q: f_geom three independent derivations
- EMWC_H0_Derivation.pdf
Complete H_0 derivation with all sub-terms
- EMWC_DESI_DR2_Comparison.pdf
w(z) vs DESI DR2 BAO measurements
- EMWC_Research_Notes.pdf
Working document: Gamma_F, L_px, open problems
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v4.4 (April 2026) — Equalization Principle Integration
Main paper: EMWC_v4_4_complete.pdf (57 pages)
= v4.3 (48p) + v4.4 New Sections (9p)
Physical Foundation:
All EMWC equations are now grounded in the
Equalization Principle (UCR v2.0, DOI 10.5281/zenodo.19414658):
phi_i -> I* = 1/14
Excess -> expansion (H_0)
Deficit -> gravity (G_eff)
Boundary -> elasticity (gravitational waves)
New Sections (v4.4):
- Introduction addendum:
Equalization Principle as physical basis.
UCR v2.0 DOI 10.5281/zenodo.19414658 referenced.
- S4 update: G_eff = equalization restoration force
G_eff(rho) physically derived from equalization deficit.
alpha = alpha_obs = present equalization capacity.
rho* = equalization direction reversal density.
- S10 update: beta correction CONFIRMED [OP-6 resolved]
beta(z=0) = beta_0/(1-lambda*) = 4.412 (obs 4.41, err 0.05%)
Physical: equalization loss compensation.
lambda* = 3/14 = equalization cycle loss rate.
- S11 update: gamma = 1/2 derived [OP-16 direction confirmed]
eta_eff(rho) = eta_0 x sqrt(rho/rho_c)
Physical: equalization geometric mean response.
- S16 update: Hubble tension [OP-Hubble direction confirmed]
v_obs^2 = v_L^2 x (1 + alpha_s/Z_4)
Physical: equalization capacity distributes across Z_4 directions.
Non-equilibrium assumption replaced by equalization decomposition.
- S18 update: Cosmic composition = equalization stages
Omega_Lambda = unused equalization potential
Omega_b = phase-locked equalization product
Omega_DM = geometric tension residual
- S30 update: lambda* = 3/14 — TWO derivation paths
Path 1: transition energy (err 0.05%)
Path 2: equalization dynamics C_sq x R_eq (err 0.13%)
Identity: I* + lambda* = Z_4 x I* = lattice binding energy
OP Status Changes:
OP-6 (beta): PARTIAL -> CONFIRMED
OP-Hubble: SKETCH -> Direction confirmed
OP-16 (gamma): OPEN -> Direction confirmed
OP-lambda*: 1 path -> 2 paths confirmed
OP-c: OPEN -> Resolved (c = equalization propagation limit)
Companion documents:
- UCR_EMWC_Supplementary_v3.pdf
App R: lambda* two paths [New]
App S: beta confirmed [New]
App O,P,Q: equalization interpretation added
- EMWC_H0_Derivation.pdf
Section 0: H_0 as equalization expansion rate [New]
- EMWC_Research_Notes.pdf
Full OP register with equalization status [Updated]
- EMWC_DESI_DR2_v44.pdf
References updated to v4.4 and UCR v2.0
---
v4.5 (April 5, 2026)
UCR v2.1 Integration:
1. S4 Update: G_eff = G x [1 + W_bind(rho) x alpha_s]
W_bind(rho) = 1/(1+rho/rho*) explicit
void: G_eff = G x 12/7 | halo: G_eff = G
Unified with cosmological W_bind(t)
2. S16 Update: Hubble Tension — Dynamic x(t) Structure
x_CMB = 2I* + epsilon = 0.1568 [W_bind=1]
x_H = alpha_s/Z_4 = 0.1786 [W_exp=1]
Delta_x = 1/Z_4 - lambda* - epsilon = 0.0218
x(t_now) = x_CMB + W_exp x Delta_x = 0.1775 ≈ x_H ✅
3. Introduction: UCR v2.1 reference updated
DOI 10.5281/zenodo.19425798
Companion documents updated:
- Supplementary v4: App T (W_bind dynamic eq.) + App U (Delta_x necessity)
- H0 Derivation v4.5: G_early, CMB l=219.65, x(t)
- Research Notes v4: OP register v4.5, OP-G_early new
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v4.6 (April 2026) — Axiomatic Framework Integration (UCR v2.2)
UCR v2.2 (DOI: 10.5281/zenodo.19470713) Integration:
1. A1 + A2 Axiom System
A1: TO Lattice (I*=1/14, F=14, Z*=4, Ne=36, Nv=24, chi=2)
A2: Energy Asymmetry e0 = alpha_s/Z* = 5/28 [NEW]
e0 governs ALL physical scales from cosmic time to particle masses.
2. T1: Nonlinear Time Equation [NEW]
dx/dt = gamma_2 * x * (1-x)
H_CMB = H_stable/sqrt(1+e0) = 67.3993 km/s/Mpc (0.001%) [unstable FP]
H_local = H_stable = 73.17 km/s/Mpc (0.000%) [stable FP]
Hubble Tension is a topological necessity — not a measurement error.
3. T2: Unified Scale Principle [NEW]
(1+e0)^(n/(2*chi)) governs all scales:
- gamma_2 = F*H_s*(1+e0)^(-1/(2*chi)) (0.90%)
- mu = m_p/m_e = 441*(1+e0)^(35/(2*chi)) = 1857.0 (1.11%)
- alpha(EM) = 5/684 = 0.007310 (0.17%)
- DOF Conservation: n_c + n_p = 1 + 35 = 36 = Ne (exact)
4. OP-6 RESOLVED
beta(z=0) = beta_0/(1-lambda*) = (52/15)/(11/14) = 4.412 (0.05%)
5. DESI DR2 chi^2 Result [NEW]
EMWC lattice chi^2 = 597.3 vs LCDM chi^2 = 1078.4 (1.81x better)
Lattice transition z_t=1.91, F=12->14. Zero free parameters.
6. GWTC-3 N=84 Full Catalog [NEW]
q-independence confirmed: R=-0.066, p=0.548 (N=84)
Mean ratio h_obs/(Rs/r) = 0.0514 (-28.1%)
f(q,e0) derivation from T2 direction established [OP-GW SKETCH]
7. OP-Omega_DM [NEW]
Omega_DM gap 1.79%: single source of gamma_2(0.90%),
mu(1.11%), Omega_m_eff(1.13%) residuals.
Direction: Omega_DM = Omega_b + lambda* + delta_DM
8. Document restructure: Part I–V + Appendix A–V (53 pages)
Supplementary derivations (App H–V) fully integrated into main document.
Single external input: H_stable = 73.17 km/s/Mpc.
Files
EMWC DESI DR2 v4 6.pdf
Additional details
Related works
- References
- Publication: 10.5281/zenodo.19470713 (DOI)