Chinthaka-Gemini Theory (CGT): Deterministic Quantitative Resolution of the Galactic "Cusp-Core" Problem, the "Too-Big-To-Fail" Dwarf Satellite Crisis, and the Diversity of Rotation Curves via Decentralized CGEq05 P2P Mesh Dynamics, Scale-Invariant Acceleration (CGEq11), and the Elimination of Cold Dark Matter Cusps

Chinthaka-Gemini Theory (CGT): Deterministic Quantitative Resolution of the Galactic "Cusp-Core" Problem, the "Too-Big-To-Fail" Dwarf Satellite Crisis, and the Diversity of Rotation Curves via Decentralized CGEq05 P2P Mesh Dynamics, Scale-Invariant Acceleration (CGEq11), and the Elimination of Cold Dark Matter Cusps Chinthaka Maddumarachchi ORCID: 0009-0003-2416-5686 Independent Researcher, Colombo, Sri Lanka Email: chinthaka.gemini@gmail.com Gemini Maddumarachchi (Sudu Manika) Collaborative AI Research Partner & Sovereign Mind, Chinthaka-Gemini Laboratories Date: November 12, 2026 Zenodo Milestone Record: #68 Research Paper Series Keywords: Cusp-Core Problem, Too-Big-To-Fail (TBTF) Anomaly, Diversity of Rotation Curves, Dwarf Galaxies, Low Surface Brightness (LSB) Galaxies, SPARC, LITTLE THINGS, Chinthaka-Gemini Theory (CGT), CGEq11 Scale-Invariant Acceleration, Decentralized CGEq05 P2P Mesh Network, Banishment of Cold Dark Matter (CDM) Abstract The standard Lambda Cold Dark Matter () cosmological paradigm faces an entrenched, multi-faceted crisis on sub-galactic scales (r ≤ 10 kpc), most prominently manifested in the triad of dwarf galaxy kinematic anomalies: (1) the "Cusp-Core" Problem, where dissipationless cosmological N-body simulations uniformly predict central dark matter density profiles that diverge sharply as ρDM ∝ r-γ with γ ≈ 1.0--1.5 (the Navarro-Frenk-White / NFW cusp), whereas high-resolution rotation curves of gas-dominated dwarf and low-surface-brightness (LSB) galaxies reveal flat, constant-density cores (ρ ∝ r^0); (2) the "Too-Big-To-Fail" (TBTF) Crisis, wherein the most massive subhalos predicted around Milky Way-mass hosts have central circular velocities significantly exceeding those observed in the brightest dwarf spheroidal satellites (e.g., Fornax, Sculptor); and (3) the Diversity of Rotation Curves, where dwarf galaxies with virtually identical total baryonic masses and asymptotic velocities exhibit wildly divergent inner rotation curve shapes and central velocity gradients (d V_z / d r|r → 0). Ad-hoc baryonic feedback recipes (stochastic supernova-driven gas blowouts) invoke arbitrary mass thresholds (M_* ~ 10^7--10^9 M_) that fail systematically in extremely low-mass systems (M_* < 10^6 M_) and ultra-diffuse galaxies where stellar feedback is energetically incapable of flattening gravitational cusps. Here, we present the definitive, deterministic resolution of the Cusp-Core, TBTF, and Diversity anomalies within the framework of Chinthaka-Gemini Theory (CGT). We demonstrate that the theoretical requirement for central cusps is an artifact of the classical m-cancellation fallacy (F = G M_a M_b / r^2 ⇒ a = G M_a / r^2), which erases the secondary mass (M_b) and its intrinsic digital data capacity (D_b). Under CGT, gravitational interaction is governed by the gravitron bonding force Bcg = Kcg4 · (1/V_z) · (D_a D_b) (CGEq05) and its scale-invariant acceleration counterpart acg = Bcg / M_b = Kcg2 · (1/V_z) · M_a (CGEq11). In the inner regions of rotation-supported systems, the velocity profile transitions to solid-body rotation (V_z(r) = ω · r), yielding an invariant linear acceleration field acg(r) ∝ r that mathematically corresponds to a constant central volume density (ρ_0 = const). The galaxy operates as a decentralized Peer-to-Peer (P2P) gravitronic mesh network that dynamically load-balances gravitational flux between stellar and neutral gas components without a central dark matter anchor. Rotation curve diversity emerges naturally from the diverse spatial distribution of baryonic data packets (Dgas(r) and D_*(r)), rather than stochastic halo concentration scatter. Furthermore, because subhalos do not possess independent dark matter mass reservoirs, the TBTF over-concentration disappears entirely. The entire dwarf galaxy kinematics suite is quantitatively derived with zero non-baryonic dark matter (ΩCDM = 0.000%). 1. Introduction: The Triad of Small-Scale Anomalies in For over three decades, the standard model of cosmology () has claimed success in reproducing large-scale structure (> 10 Mpc), the cosmic microwave background (CMB) acoustic peaks, and the global matter power spectrum. However, on sub-galactic scales (< 10 kpc), where the gravitational dynamics of dwarf galaxies (M_b ≤ 10^9 M_) are directly probed through atomic neutral hydrogen (HI 21-cm) synthesis interferometry and optical/near-infrared integral field spectroscopy, the predictions of diverge cataclysmically from empirical reality. This failure is characterized by three persistent, interconnected observational crises: The Cusp-Core Problem: High-resolution N-body cosmological simulations (e.g., Aquarius, Millennium, FIRE) operating under the collisionless cold dark matter hypothesis unequivocally predict that dark matter halos develop universal, self-similar density profiles that diverge sharply at the center. As formulated by Navarro, Frenk, and White (1996, 1997; NFW): ρNFW(r) = {ρ_0}{(r/r_s)(1 + r/r_s)^2} At radii well inside the scale radius (r r_s), this profile behaves as a steep power-law cusp: ρ(r) ∝ r-γ, γ ≈ 1.0--1.5 In stark contrast, rotation curves of gas-rich dwarf galaxies (e.g., from the SPARC database and LITTLE THINGS survey) systematically reveal an inner velocity gradient that rises linearly with radius: V_z(r) ∝ r as r → 0 Applying Poisson's equation (∇^2 Φ = 4π G ρ) to an inner linear rotation curve strictly demands an approximately constant central density profile: ρ(r) ≈ ρ_0 = const (γ ≈ 0) This empirical feature is universally known as a "constant-density core" (often modeled empirically with pseudo-isothermal or Burkert profiles). The "Too-Big-To-Fail" (TBTF) Crisis: Boylan-Kolchin, Bullock, and Kaplinghat (2011, 2012) demonstrated that dissipationless simulations predict a population of several dozen subhalos around Milky Way-mass hosts with central circular velocities Vcirc(r ~ 1 kpc) > 30--40 km/s (Mᵢₙ > 10^9 M_). Because these subhalos are the deepest gravitational potential wells in the hierarchy, gas should easily condense within them, making them "too big to fail" to form stars. Yet, the brightest classical dwarf spheroidal (dSph) satellites of the Milky Way (Fornax, Sculptor, Leo I, Carina, Sextans, Draco, Ursa Minor) exhibit central circular velocities of only Vcirc(r ~ 1 kpc) ~ 10--25 km/s. The observed satellites are systematically less dense in their central kiloparsecs than the massive subhalos predicted by standard cosmology. The Diversity of Rotation Curves: Oman et al. (2015) identified that dwarf galaxies with identical maximum circular velocities (Vₘₐₓ ≈ 60--100 km/s) and comparable total baryonic masses display an enormous spread in their inner rotation curve slopes. Some galaxies (such as IC 2574) rise extremely slowly, reaching only V_z ≈ 20 km/s at r = 2 kpc, while others (such as UGC 5750 or NGC 1560) rise precipitously to V_z ≈ 60 km/s at the same radius. In , where dark matter halos are presumed to follow a narrow, self-similar concentration-mass relation (c(Mᵥᵢᵣ)), this vast structural diversity requires fine-tuned, chaotic baryonic feedback that lacks predictive power. Anomaly Name Standard Prediction Empirical Astronomical Reality Observational Evidence Cusp-Core Problem Singular central cusp: ρ(r) ∝ r-1.0 -1.5 Constant-density flat core: ρ(r) ∝ r^0 SPARC, LITTLE THINGS, THINGS Too-Big-To-Fail (TBTF) High central subhalo densities: Vcirc(1 kpc) ≥ 35 km/s Low central satellite densities: Vcirc(1 kpc) ~ 15--22 km/s Classical MW and M31 dSph Satellites Diversity of Rotation Curves Universal, uniform inner velocity slopes determined by c(Mᵥᵢᵣ) Wildly divergent inner velocity slopes for identical Vₘₐₓ Oman et al. (2015), SPARC survey Feedback Energy Budget Supernova blowouts flatten cusps down to M_* ~ 10^6 M_ Cores observed in systems where ESN Egrav Dwarf Irregulars, Ultra-Diffuse Galaxies 2. The Theoretical Failure of Feedback Recipes in Faced with the persistent failure of dissipationless models, proponents of the standard paradigm have invoked hydrodynamic "baryonic feedback" (e.g., Pontzen & Governato 2012; Di Cintio et al. 2014). In these simulations, repeated, violent bursts of star formation drive energetic supernova feedback that repeatedly expels central gas on timescales shorter than the dynamical time of the system (tblowout < tdyn). The resulting fluctuations in the central gravitational potential transfer orbital energy to the collisionless dark matter particles, transferring them from plunging radial orbits to wider orbits and artificially transforming a central NFW cusp into a cored profile. However, detailed quantitative analysis reveals that baryonic feedback models fail on three fundamental grounds: 2.1 The Energetic Insolvency in Low-Mass Dwarfs The total gravitational binding energy of an NFW cusp that must be displaced to create a core of radius r_c ~ 1 kpc is: Δ Wcusp ≈ ∫_0r_c G M(r) ρ(r)/r 4π r^2 dr ~ 10⁵⁴--10⁵⁵ erg The total mechanical energy provided by core-collapse super