#1
DerivedCondensation minimum
E(R)=A/R²+BR²+C+D/R; R₀=1.27348221
E(R)=A/R²+BR²+C+D/R; R₀=1.27348221
72 numbered write-ups. Confirmed means the observation already ran the way BFUT required: mature high-z galaxies, the century-long rise in inferred age and reach, the downward move in H0 under more robust methods, the persistence of the Hubble tension, ALPHA-g antihydrogen fall. Testing means live data already points the same way (JWST, cosmic web, large rotating basins, S8, null WIMP searches). Untested means the specific measurement has not been done yet. Number 30 was not in the source file.
#1
DerivedE(R)=A/R²+BR²+C+D/R; R₀=1.27348221
E(R)=A/R²+BR²+C+D/R; R₀=1.27348221
#2
Derivedδ_d=2δ_u from the three-sphere geometry
δ_d=2δ_u from the three-sphere geometry
#3
DerivedA_void/6 as the geometric void correction
A_void/6 as the geometric void correction
#4
Derivedm_e_vss=mₚ/(6π⁵)
m_e_vss=mₚ/(6π⁵)
#5
Derivedħ_vss=mₚcrₚ/(πR₀), with h_vss=2πħ_vss
ħ_vss=mₚcrₚ/(πR₀), with h_vss=2πħ_vss
#6
Derivedα_vss=e²/(4πε₀ħ_vss c) within the BFUT derivation chain
α_vss=e²/(4πε₀ħ_vss c) within the BFUT derivation chain
#7
DerivedR₀=4ε₀mₚc²rₚα_vss/e²
R₀=4ε₀mₚc²rₚα_vss/e²
#8
Derivedc_vss²=e²R₀/(4ε₀mₚrₚα_vss)
c_vss²=e²R₀/(4ε₀mₚrₚα_vss)
#9
DerivedKₛ=ρₛc²
Kₛ=ρₛc²
#10
Derivedaₛ=c√(Gρₛ/3)
aₛ=c√(Gρₛ/3)
#11
DerivedR_d=[3M/(8πρₛ)]^(1/3)
R_d=[3M/(8πρₛ)]^(1/3)
#12
DerivedR_eff=R_d(1+v_rot²/c²)^(1/3)
R_eff=R_d(1+v_rot²/c²)^(1/3)
#13
Derivedv²=v_b²[1+aₛR/v_b²]^(1/2)
v²=v_b²[1+aₛR/v_b²]^(1/2)
#14
Derivedv⁴≈GMaₛ
v⁴≈GMaₛ
#15
Derivedv∝M^(1/4) in the deep DME regime at fixed ρₛ
v∝M^(1/4) in the deep DME regime at fixed ρₛ
#16
Derivedv/M^(1/4)=[G c√(Gρₛ/3)]^(1/4)
v/M^(1/4)=[G c√(Gρₛ/3)]^(1/4)
#17
DerivedR_t=√(GM/aₛ) when aₛR/v_b²=1
R_t=√(GM/aₛ) when aₛR/v_b²=1
#18
Derivedg_DME=√[g_b(g_b+aₛ)]; high-g: g≈g_b+aₛ/2; low-g: g≈√(aₛg_b)
g_DME=√[g_b(g_b+aₛ)]; high-g: g≈g_b+aₛ/2; low-g: g≈√(aₛg_b)
#19
DerivedR_d∝M^(1/3) at fixed ρₛ
R_d∝M^(1/3) at fixed ρₛ
#20
DerivedMean density inside R_d is 2ρₛ
Mean density inside R_d is 2ρₛ
#21
Derivedg_d=GM/R_d²=GM^(1/3)(8πρₛ/3)^(2/3)
g_d=GM/R_d²=GM^(1/3)(8πρₛ/3)^(2/3)
#22
DerivedL_nat=λ_u/√(3ρₛ)=45.17 AU; τ_nat=L_nat/c=6.26 h
L_nat=λ_u/√(3ρₛ)=45.17 AU; τ_nat=L_nat/c=6.26 h
#23
Derivedμₛ²=3Gρₛ/c²
μₛ²=3Gρₛ/c²
#24
DerivedaₛL_s=c²/3, where L_s=1/μₛ
aₛL_s=c²/3, where L_s=1/μₛ
#25
Derivedg/g_N=e^(−r/R_eff)(1+r/R_eff) for the settled exponential carrier component
g/g_N=e^(−r/R_eff)(1+r/R_eff) for the settled exponential carrier component
#26
Derived(g−g_N)/g_N≈−½(r/R_eff)² for r≪R_eff
(g−g_N)/g_N≈−½(r/R_eff)² for r≪R_eff
#27
Derivedd ln(g/g_N)/dr→−1/R_eff for r≫R_eff
d ln(g/g_N)/dr→−1/R_eff for r≫R_eff
#28
Derivedv²=(GM/r)e^(−r/R_eff)(1+r/R_eff)
v²=(GM/r)e^(−r/R_eff)(1+r/R_eff)
#29
DerivedE_min=2.25 meV
E_min=2.25 meV
#30
DerivedL_persist=L_rlx(E/E_min)²
L_persist=L_rlx(E/E_min)²
#31
DerivedL_persist=L_rlx(E/E_min)⁴
L_persist=L_rlx(E/E_min)⁴
#32
Derivedd ln L_persist/d ln E=2 above E_min and 4 below E_min
d ln L_persist/d ln E=2 above E_min and 4 below E_min
#33
Derivedρ̄_max=3c⁶/(4πG³M²)
ρ̄_max=3c⁶/(4πG³M²)
#34
DerivedR_max=GM/c²
R_max=GM/c²
#35
DerivedR_max/M=G/c²
R_max/M=G/c²
#36
DerivedA∝M^(2/3), hence BFUT organised-deformation entropy scaling S∝M^(2/3)
A∝M^(2/3), hence BFUT organised-deformation entropy scaling S∝M^(2/3)
#37
Derivedu_vac=ρₛc²
u_vac=ρₛc²
#38
Derivedλ_H_vss=2AR₀/π²; v_vss=6E_unit/α_vss; m_H_vss=v_vss√(2λ_H_vss)=124.75 GeV/c²
λ_H_vss=2AR₀/π²; v_vss=6E_unit/α_vss; m_H_vss=v_vss√(2λ_H_vss)=124.75 GeV/c²
#39
Derivedαₛ_vss∝BR₀⁴/A
αₛ_vss∝BR₀⁴/A
#40
Derivedω_c²R₀²/c²
ω_c²R₀²/c²
#41
DerivedR_peri=Σ(peri-window power)/Σ(off-peri power)
R_peri=Σ(peri-window power)/Σ(off-peri power)
#42
DerivedT_PSR=ΣW_pR_i/√(ΣW_p²σ_i²)
T_PSR=ΣW_pR_i/√(ΣW_p²σ_i²)
#43
DerivedProof-of-concept rotational collapse gives S8=0.7805 versus 0.832 radial, a 6.2% deficit
Proof-of-concept rotational collapse gives S8=0.7805 versus 0.832 radial, a 6.2% deficit
#44
Derivedm_Z_vss=π⁴mₚ=91.396 GeV/c²
m_Z_vss=π⁴mₚ=91.396 GeV/c²
#45
Derivedm_W_vss=256M=80.066 GeV/c²
m_W_vss=256M=80.066 GeV/c²
#46
Derivedsin²θ_W_vss=1−(m_W_vss/m_Z_vss)²=0.23257
sin²θ_W_vss=1−(m_W_vss/m_Z_vss)²=0.23257
#47
Derivedm_Shankar c² = [E(2+2) − E(3+1)]E_unit = 2.60E_unit = 776.5 MeV
m_Shankar c² = [E(2+2) − E(3+1)]E_unit = 2.60E_unit = 776.5 MeV
#48
Derivedm_BFUT c² = [E(4+0) − E(3+1)]E_unit = 4.70E_unit = 1403.7 MeV
m_BFUT c² = [E(4+0) − E(3+1)]E_unit = 4.70E_unit = 1403.7 MeV
#49
StatedEvery 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.
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.
#50
StatedDDR enhancement should saturate with galaxy or cluster rotation.
DDR enhancement should saturate with galaxy or cluster rotation.
#51
StatedLarge coherent systems should retain a non-zero enhancement floor, approximately 14–20% in the P26 analysis.
Large coherent systems should retain a non-zero enhancement floor, approximately 14–20% in the P26 analysis.
#52
StatedLow-baryonic-support systems should show substantially larger Spaticle field enhancement, reaching about 50–60% in the P26 sample.
Low-baryonic-support systems should show substantially larger Spaticle field enhancement, reaching about 50–60% in the P26 sample.
#53
StatedMass-matched galaxies embedded in rich clusters should show a higher enhancement floor than comparable isolated field galaxies if nested-domain reinforcement operates.
Mass-matched galaxies embedded in rich clusters should show a higher enhancement floor than comparable isolated field galaxies if nested-domain reinforcement operates.
#54
StatedCompact seed cores formed through collapse or explosive release should persist only when surrounding matter provides sufficient rotational coherence.
Compact seed cores formed through collapse or explosive release should persist only when surrounding matter provides sufficient rotational coherence.
#55
Stated#56
StatedAntihydrogen should fall under gravity identically to ordinary hydrogen.
Antihydrogen should fall under gravity identically to ordinary hydrogen.
#57
StatedOrdinary formation conditions should not produce macroscopic stable antimatter domains.
Ordinary formation conditions should not produce macroscopic stable antimatter domains.
#58
StatedMatter and antimatter configurations should annihilate through cancellation of the opposing substrate topologies.
Matter and antimatter configurations should annihilate through cancellation of the opposing substrate topologies.
#59
StatedThe CMB should be continuously maintained as a thermal-equilibrium radiation field, not require a relic origin from a finite-age event.
The CMB should be continuously maintained as a thermal-equilibrium radiation field, not require a relic origin from a finite-age event.
#60
StatedCosmic redshift should be explainable through source-observer dynamics and photon propagation through a static substrate.
Cosmic redshift should be explainable through source-observer dynamics and photon propagation through a static substrate.
#61
StatedApparent cosmic acceleration should correlate with observer motion and directional sampling effects without requiring a separate dark-energy component.
Apparent cosmic acceleration should correlate with observer motion and directional sampling effects without requiring a separate dark-energy component.
#62
StatedThe rise in Gunn-Peterson/Lyman-alpha opacity should admit a substrate absorption/percolation interpretation without uniquely requiring an expanding-universe interpretation.
The rise in Gunn-Peterson/Lyman-alpha opacity should admit a substrate absorption/percolation interpretation without uniquely requiring an expanding-universe interpretation.
#63
StatedObserved ISW temperature correlations should admit local Spaticle field temperature variations as a physical contribution.
Observed ISW temperature correlations should admit local Spaticle field temperature variations as a physical contribution.
#64
StatedRotational suppression should be stronger at low redshift and diminish toward high redshift in the P13 proof-of-concept framework.
Rotational suppression should be stronger at low redshift and diminish toward high redshift in the P13 proof-of-concept framework.
#65
StatedRecovered 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.
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.
#66
StatedCompact objects should possess finite organised compression cores, with the macroscopic mapping testable by future observations.
Compact objects should possess finite organised compression cores, with the macroscopic mapping testable by future observations.
#67
StatedObservations of compact objects should not require a physically realised infinite-density singularity.
Observations of compact objects should not require a physically realised infinite-density singularity.
#68
StatedBFUT compact-object dynamics should retain information in organised substrate deformation and permit outward carrier relaxation.
BFUT compact-object dynamics should retain information in organised substrate deformation and permit outward carrier relaxation.
#69
StatedGalaxy and lensing anomalies should be reproducible through organised Spaticle field deformation without introducing a dark-matter particle.
Galaxy and lensing anomalies should be reproducible through organised Spaticle field deformation without introducing a dark-matter particle.
#70
StatedIn interacting systems, substrate-associated gravitational effects should track the organised motion of the dominant galactic matter and respond to redistribution during the merger.
In interacting systems, substrate-associated gravitational effects should track the organised motion of the dominant galactic matter and respond to redistribution during the merger.
#71
StatedSystems such as DF2, DF4 and FCC224 should remain compatible with the stellar-mass-dominated line under the BFUT interpretation.
Systems such as DF2, DF4 and FCC224 should remain compatible with the stellar-mass-dominated line under the BFUT interpretation.
#72
StatedThe same Spaticle field should support a continuous hierarchy from microscopic condensations through galactic and cosmological structures.
The same Spaticle field should support a continuous hierarchy from microscopic condensations through galactic and cosmological structures.