The Spaticle field is the physical medium of space. Its equilibrium density ρ_s = 5.9 × 10⁻²⁷ kg/m³ is constrained from six independent sectors spanning forty orders of magnitude. Every result below follows from this one measured value.
| # | Result | Paper |
|---|---|---|
| 1 | Substrate density ρ_s = 5.9 × 10⁻²⁷ kg/m³ | P16 |
| 2 | Nucleation energy functional — first stable quark E(R) = A/R² + B·R² + C·R + D/R · Min at R₀ = 1.27348 | P16 §3 |
| 3 | Quark condensation radius r_q = r_p/(1 + 2/√3) = 0.3905 fm | P16 §4 |
| 4 | Interstitial volume fraction — pure geometry V_gap/V_q = (2√3 − π)/(4π/3) = 0.0770 | P16 §10 |
| 5 | Energy unit E_unit = m_p·c²/π = 298.695 MeV | P16 §4 |
| 6 | Electron mass — geometry only m_e = 0.511009 MeV · m_e/m_p = 1/(6π⁵) | P16 §10 |
| 7 | Interstitial gap energy E_gap = E_unit × 0.0770 = 22.999 MeV | P16 §10 |
| 8 | Three-core binding energy E(3-core) = 0.900 model units | P16 §6 |
| 9 | 3+e decisively preferred over 4+0 and 2+2 3+e: 1.40 | 4+0: 4.60 | 2+2: 4.00 (model units) | P16 §6 |
| 10 | 3+e state — proton and electron formation E(3+e) = 0.8958 · ΔE = 0.0042 | P16 §10 |
| 11 | 3+e preference holds across parameter space 1D: 97.56% · 2D: 95.95% · 3D: 90.43% | P16 §6.1 |
| 12 | Stability filter — matter from 90–97% of excitations Stable: 90–97% · Unstable: 2–10% | P16 §7–9 |
| 13 | Annihilation geometrically complete 3+e topology cancels (counter, counter, counter) exactly | P16 §8 |
| 14 | Force preconditions from 3+e topology EM: charge sep · Strong: confinement · Weak: filter · Gravity: deformation | P16 §2,15 |
| 15 | Bohr radius set by ρ_s a₀ = ħ²/(m_e·k_e·e²) = 52,918 fm · a₀ ∝ ρ_s⁻¹ | P16 §11 |
| 16 | Hydrogen binding energy E_H = −13.6 eV · E_H ∝ ρ_s | P16 §11 |
| 17 | Modular organisation — 3+e reuse preferred E_modular = ⌊n/3⌋ × 0.8958 + E_remainder | P16 §12 |
| 18 | Finite particle catalogue from finite free-energy minima m_e/m_p = 1/(6π⁵) [pure geometry] | P16 §12 |
| 19 | Atom size a derived consequence of ρ_s m_p ∝ ρ_s · m_e ∝ ρ_s · a₀ ∝ ρ_s⁻¹ | P16 App.C |
| 20 | Gravity as substrate restoring response Mechanism P17; carrier equation P18 | P17 §2–3 |
| 21 | Strong-force confinement potential C_s = 0.574 GeV/fm vs 0.9 GeV/fm | P17 §5.2 |
| 22 | Fine structure constant α_BFUT = 1/137.1 vs 1/137.036 · 0.05% | P17 §6.8 |
| 23 | Weak mixing angle sin²θ_W = 0.2312 vs 0.2312 · 0.01% | P17 §7.3 |
| 24 | Electron-capture threshold 0.782 MeV | P17 §7.4D |
| 25 | Covariant carrier field equation τ_c·dΨ/dt + Ψ − L_rlx²·∇²Ψ = K·J[T_μν] | P18 §3 |
| 26 | Carrier relaxation timescale — no free parameters τ_c = 1/(c·√(3ρ_s)) = 4.6 ms · L_rlx = 1,380 km | P18 |
| 27 | Finite gravitational domain radius DD-1 R_d = (3M/(8πρ_s))^(1/3) | P18 |
| 28 | 175 SPARC galaxy rotation curves χ²_BFUT = 1.31 vs χ²_MOND = 1.47 | P18 |
| 29 | KiDS-1000 weak gravitational lensing χ²_BFUT = 0.007–0.067 vs χ²_NFW = 5.77–6.57 | P18 |
| 30 | GW170817 post-merger relaxation τ_c (floor) = 4.6 ms · τ_obs ~18.6 ms | P18 |
| 31 | Spaticle field is the physical referent of dark matter Single ρ_s: rotation curves + lensing + GW timing | P18 |
| 32 | DD1 Coherence Index I_DD1 = v·R_core/(K_DD1·R_gal^0.9) · K=9 | P25 |
| 33 | 92% pass rate — 175 SPARC + 190 systems to z=4.26 161/175 SPARC · 190 systems · single K=9 | P25 |
| 34 | SR time dilation from propagation budget c² = v_spatial² + v_internal² → η = √(1−v²/c²) | P22 |
| 35 | GR gravitational time dilation — same mechanism η(r) tied to R_d domain function from P18 | P22 |
| 36 | Universal speed limit c₀ = maximum substrate reorganisation rate | P22 |
| 37 | Speed of light from substrate stiffness c = √(K_s/ρ_s) · K_s = ρ_s·c² = 5.30 × 10⁻¹⁰ Pa | P23 §2 |
| 38 | Cross-check of c from BFUT constants c = √(e²·R₀/(4ε₀·m_p·r_p·α)) · 0.0001% | P23 |
| 39 | Velocity deficit of massive particles v/c = pc/E · neutrinos within 10⁻¹⁷ of c | P23 |
| 40 | Light and gravitational waves at equal speed c_light = c_GW = √(K_s/ρ_s) · GW170817: 10⁻¹⁶ | P23 |
| 41 | Reduced Planck constant from condensation geometry ħ = m_p·c·r_p/(π·R₀) · 0.0001% | P27 §2 |
| 42 | Compton, de Broglie, spin-½ angular momentum All follow from BFUT ħ | P27 |
| 43 | Planck length, mass, time from same R₀ chain l_P, m_P, t_P → condensation geometry · 0.0001% | P27 §12 |
| 44 | Vacuum energy density — no 10¹²² discrepancy ρ_vac = ρ_s·c² = 5.3 × 10⁻¹⁰ J/m³ | P27 |
| 45 | Spin-statistics theorem from topology 720° (fermion) vs 360° (boson) restoration | P27 |
| 46 | Black hole = finite compression core — no singularity Four-region finite-core architecture | P28 §2 |
| 47 | Domain radius and dissipation timescale R_d = (3M/(8πρ_s))^(1/3) · 10M☉: ~59 min | P28 §3.4 |
| 48 | Rotational Sustenance Principle and Threshold Core persists only if C > C_crit within τ_dissip | P28 §3.4 |
| 49 | Universal Centrality Rule Vortical core at exact dynamical centre | P28 §5 |
| 50 | Hawking radiation does not exist Replaced by finite-core thermodynamics | P28 |
Every result derived from published papers. Resolved = complete account from first principles. Dissolved = problem does not arise once BFUT premises are accepted. Reframed = standard evidence is consistent with BFUT but does not uniquely require Lambda-CDM.
Level 3 = earth-shattering results pursued unsuccessfully elsewhere. Level 2 = major impact. Level 1 = important to the programme.
Beginning from a physical substrate and building upward — from particle physics to consciousness to the purpose of life. Each layer is grounded in derivations from the one below it.
The Spaticle field fills all of space at a fixed equilibrium density ρ_s = 5.9 × 10⁻²⁷ kg/m³. This single number — constrained to ±0.015% by W and Z boson masses — simultaneously reproduces:
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