Appendix
Predictions: Mathematical and Non-Mathematical
Falsifiable predictions of the Big Flare-Up Theory, from precise numerical targets to qualitative structural claims that can be tested by observation.
THE BIG FLARE-UP THEORY
MATHEMATICAL AND NON-MATHEMATICAL PREDICTIONS
The Big Flare-Up Theory (BFUT) calls the matter substrate the Spaticle Field. The equilibrium density is ρₛ = 7.3 × 10⁻²⁷ kg/m³.
1. Mathematical Predictions
| No. | Mathematical prediction | Equation / quantitative result | Source |
|---|---|---|---|
| 1 | Condensation minimum | E(R)=A/R²+BR²+C+D/R; R₀=1.27348221 | P16 |
| 2 | Void-filling asymmetry | δ_d=2δ_u from the three-sphere geometry | P16 |
| 3 | Void correction | A_void/6 as the geometric void correction | P16 |
| 4 | Electron/proton mass ratio | m_e_vss=mₚ/(6π⁵) | P19 |
| 5 | Reduced Planck constant | ħ_vss=mₚcrₚ/(πR₀), with h_vss=2πħ_vss | P16/P19 |
| 6 | Fine-structure constant | α_vss=e²/(4πε₀ħ_vss c) within the BFUT derivation chain | P19 |
| 7 | R₀ cross-check | R₀=4ε₀mₚc²rₚα_vss/e² | P19; internal consistency |
| 8 | Independent c reconstruction | c_vss²=e²R₀/(4ε₀mₚrₚα_vss) | P23/P19 |
| 9 | Substrate stiffness | Kₛ=ρₛc² | P23 |
| 10 | Universal acceleration scale | aₛ=c√(Gρₛ/3) | P18/P78 |
| 11 | Finite deformation-domain radius | R_d=[3M/(8πρₛ)]^(1/3) | P18 |
| 12 | Rotationally enlarged domain | R_eff=R_d(1+v_rot²/c²)^(1/3) | P18 |
| 13 | Dark matter effects equation (DME) rotation law | v²=v_b²[1+aₛR/v_b²]^(1/2) | P18/P25/P78 |
| 14 | Deep-regime baryonic Tully-Fisher law | v⁴≈GMaₛ | DME low-acceleration limit |
| 15 | Mass-velocity scaling | v∝M^(1/4) in the deep DME regime at fixed ρₛ | Derived from P18 DME |
| 16 | Fixed BTFR coefficient | v/M^(1/4)=[G c√(Gρₛ/3)]^(1/4) | Derived from P18 |
| 17 | DME transition radius | R_t=√(GM/aₛ) when aₛR/v_b²=1 | Derived from P18 DME |
| 18 | DME acceleration asymptotes | g_DME=√[g_b(g_b+aₛ)]; high-g: g≈g_b+aₛ/2; low-g: g≈√(aₛg_b) | Derived from P18 |
| 19 | Domain mass scaling | R_d∝M^(1/3) at fixed ρₛ | Derived from P18 DDR |
| 20 | DDR mean-density relation | Mean density inside R_d is 2ρₛ | Derived from P18 DDR |
| 21 | DDR boundary acceleration | g_d=GM/R_d²=GM^(1/3)(8πρₛ/3)^(2/3) | Derived from P18 DDR |
| 22 | Particle domain persistence scale | R_d(M)=[3M/(8πρₛ)]^(1/3): electron 2.460 cm, proton 30.125 cm, neutron 30.139 cm | P19A |
| 23 | Domain boundary of a massive body | Ψ_g(r)=−(GM/r)D(r/R_d), D(x)=1−3x/2+x³/2 for 0≤x≤1 and D=0 for x≥1; field, potential and gravitational time dilation end at R_d | P18; P19; P22 |
| 24 | Carrier inverse length | μₛ²=3Gρₛ/c² | P18 |
| 25 | Cross-scale carrier identity | aₛL_s=c²/3, where L_s=1/μₛ | Derived from P18 |
| 26 | Spatial carrier attenuation | g/g_N=e^(−r/Lₛ)(1+r/Lₛ), with Lₛ=1/μₛ | P18 displayed potential |
| 27 | Newtonian-limit correction | (g−g_N)/g_N≈−½(r/Lₛ)² for r≪Lₛ | Derived from P18 potential |
| 28 | Asymptotic attenuation slope | d ln(g/g_N)/dr→−1/Lₛ for r≫Lₛ | Derived from P18 potential |
| 29 | Carrier-component rotation profile | v²=(GM/r)e^(−r/Lₛ)(1+r/Lₛ) | Derived from P18 potential; carrier component only |
| 30 | Finite causal mean-density bound | ρ̄_max=3c⁶/(4πG³M²) | P26 |
| 31 | Causal limiting radius | R_max=GM/c² | P26 |
| 32 | Universal compactness relation | R_max/M=G/c² | Derived from P26 |
| 33 | Compact-object area scaling | A∝M^(2/3), hence BFUT organised-deformation entropy scaling S∝M^(2/3) | P28 |
| 34 | Vacuum energy density | u_vac=ρₛc² | P2/P14/P23 |
| 35 | H-class radial resonance mass | λ_H_vss=2AR₀/π²; v_vss=6E_unit/α_vss; m_H_vss=v_vss√(2λ_H_vss)=124.75 GeV/c² | P19 |
| 36 | Strong-coupling geometric relation | αₛ_vss∝BR₀⁴/A | P19 |
| 37 | Electromagnetic geometric invariant | ω_c²R₀²/c² | P19 |
| 38 | Periastron residual statistic | R_peri=Σ(peri-window power)/Σ(off-peri power) | P18 test formulation |
| 39 | Pulsar phase-window statistic | T_PSR=ΣW_pR_i/√(ΣW_p²σ_i²) | P18 test formulation |
| 40 | S8 rotational suppression | Proof-of-concept rotational collapse gives S8=0.7805 versus 0.832 radial, a 6.2% deficit | P13 |
| 41 | Neutral Z resonance | m_Z_vss=π⁴mₚ=91.396 GeV/c² | P19 |
| 42 | Charged W resonance | m_W_vss=256M=80.066 GeV/c² | P19 |
| 43 | Electroweak mixing output | sin²θ_W_vss=1−(m_W_vss/m_Z_vss)²=0.23257 | P19 |
| 44 | Shankar configuration resonance | m_Shankar c² = [E(2+2) − E(3+1)]E_unit = 2.60E_unit = 776.5 MeV | P16A |
| 45 | BFUT configuration resonance | m_BFUT c² = [E(4+0) − E(3+1)]E_unit = 4.70E_unit = 1403.7 MeV | P16A |
2. Non-Mathematical Predictions
| No. | Non-mathematical prediction | Expected observational or physical consequence | Source |
|---|---|---|---|
| 1 | Universal Centrality Rule | Every settled galaxy should possess a primary black hole or dominant gravitational vortex at its dynamical centre. A settled galaxy lacking the primary central object would falsify the hypothesis. | P6/P28 |
| 2 | Rotational entrainment saturation | DDR enhancement should saturate with galaxy or cluster rotation. | P26 |
| 3 | Rotational sustenance threshold | Compact seed cores formed through collapse or explosive release should persist only when surrounding matter provides sufficient rotational coherence. | P26 |
| 4 | Isolated seed dissipation | A seed core with no surrounding rotating mass within its domain should not persist as an organised core; its organised deformation dissipates. | P26; P28 |
| 5 | Antihydrogen gravitational behaviour | Antihydrogen should fall under gravity identically to ordinary hydrogen. | P16A |
| 6 | Stable antimatter-domain prediction | Ordinary formation conditions should not produce macroscopic stable antimatter domains. | P16A |
| 7 | Complete matter-antimatter cancellation | Matter and antimatter configurations should annihilate through cancellation of the opposing substrate topologies. | P16/P16A |
| 8 | Maintained CMB equilibrium | The CMB should be continuously maintained as a thermal-equilibrium radiation field, not require a relic origin from a finite-age event. | P7 |
| 9 | Cosmic redshift without substrate expansion | Cosmic redshift should be explainable through source-observer dynamics and photon propagation through a static substrate. | P1/P23 |
| 10 | Observer-bulk-flow signature | Apparent cosmic acceleration should correlate with observer motion and directional sampling effects without requiring a separate dark-energy component. | P4 |
| 11 | Lyman-alpha interpretation | The rise in Gunn-Peterson/Lyman-alpha opacity should admit a substrate absorption/percolation interpretation without uniquely requiring an expanding-universe interpretation. | P11 |
| 12 | ISW interpretation | Observed ISW temperature correlations should admit local Spaticle field (the name the author gives to the physical matter substrate) temperature variations as a physical contribution. | P12 |
| 13 | S8 redshift trend | Rotational suppression should be stronger at low redshift and diminish toward high redshift in the P13 proof-of-concept framework. | P13 |
| 14 | S8 analysis sensitivity | Recovered S8 should vary materially under defensible choices of scale cuts, tomography, covariance, intrinsic-alignment model, and sky coverage, even for the same underlying synthetic shear field. | P13 |
| 15 | Finite-core compact objects | Compact objects should possess finite organised compression cores, with the macroscopic mapping testable by future observations. | P26/P28 |
| 16 | No physical singularity | Observations of compact objects should not require a physically realised infinite-density singularity. | P6/P26 |
| 17 | Information retained in compact objects | BFUT compact-object dynamics should retain information in organised substrate deformation. | P26/P28 |
| 18 | No separate dark-matter particle requirement | Galaxy and lensing anomalies should be reproducible through organised Spaticle field deformation without introducing a dark-matter particle. | P18/P25/P78 |
| 19 | Merger-morphology test | In interacting systems, substrate-associated gravitational effects should track the organised motion of the dominant galactic matter and respond to redistribution during the merger. | P78 |
| 20 | Low-dark-matter galaxy behaviour | Systems such as DF2, DF4 and FCC224 should remain compatible with the stellar-mass-dominated line under the BFUT interpretation. | P78 |
| 21 | Cosmic-scale continuity | The same Spaticle field should support a continuous hierarchy from microscopic condensations through galactic and cosmological structures. | P14/P16/P18 |