| ================================================================================ |
| I. GRAVITY CONSISTENCY TEST (OPERATOR U) |
| ================================================================================ |
| G_Base (Soliton Base) = 2.7802522591364D+32 m^3 kg^-1 s^-2 |
|
|
| --- ANALYSIS OF VOLUME DEFICIT FACTORS (PUSH-OUT LOGIC) --- |
| N_nu_max (Absolute Max): 5.300415534439117e+54 |
| N_nu_statutory (Background): 3.298651882390107e+52 |
| N_nu_geom (Effective EMC): 6.252517621935487e+48 |
|
|
| --- CALCULATION OF G_MODEL VARIANTS --- |
| G_EWT_RAW (Pure K+1) = 6.680436961490046e-11 m^3 kg^-1 s^-2 |
| G_EWT_UNIFIED (Alpha-Link) = 6.674305000000013e-11 m^3 kg^-1 s^-2 |
| G_CODATA (Target Value) = 6.674305000000000e-11 m^3 kg^-1 s^-2 |
|
|
| --- G-FACTOR VERIFICATION RESULT --- |
| Absolute Difference (|Model - CODATA|) = 1.29246970711410574199e-25 |
| Percentage Error relative to CODATA = 0.000000000000194 % |
| Raw Geometry Gap (Pre-Alpha) = 0.0918741575 % |
| ----------------------------------------------------- |
| EMC DILUTION (X_eff): 5275.7178497467 |
| Lattice Projection (L_p): 1.1486801482 |
| ================================================================================ |
|
|
| ================================================================================ |
| I B. GEOMETRIC VARIANT (L_p = 2 / sqrt(3), alpha_geom) |
| ================================================================================ |
| alpha_geom (with eps_M) = 0.007297338549 |
| L_p_geo (2/sqrt(3)) = 1.154700538379252 |
| C_Unif_geo = 1.102011616800936 |
| N_nu_effective_geo = 6.252457803455382e+48 |
| G_EWT_GEO = 6.674336927110799e-11 m^3 kg^-1 s^-2 |
| G_CODATA = 6.674305000000000e-11 m^3 kg^-1 s^-2 |
| Absolute difference = 3.19271107990139353942e-16 |
| Relative error = 0.000478358583 % (4.78 ppm) |
| ================================================================================ |
|
|
| ================================================================================ |
| II. NEUTRINO RADIUS VALIDATION (1/5 POWER LAW TEST) |
| ================================================================================ |
| r_e (Classical Electron Radius) = 0.00000000000000282 m |
| r_nu_val (Model Statutory Value) = 0.00000000000000003 m |
|
|
| Ratio (r_e / r_nu_val) = 100.000011575831991 |
| K_nu_implied (Factor from 1/5 Law) = 10000005787.9173355 |
|
|
| --- VALIDATION RESULT --- |
| Target Geometric Order (10^10) = 10000000000 |
| Percentage Difference (to 10^10) = 0.0000578791733551 % |
| ================================================================================ |
|
|
| ================================================================================ |
| III. BASE GEOMETRIC MOMENT (a_Base^Geom) |
| ================================================================================ |
| --- MASS-TO-GEOMETRY IDENTITY --- |
| Mass-to-Radius Identity exponent = 1/5 |
|
|
| --- GEOMETRIC AMM CALCULATION (a_Base^Geometric) --- |
| --- IDENTITY CHECK: |epsilon_M| * pi^3 = 1/N_final --- |
| Calculated |epsilon_M| * pi^3 = 0.00128399682861514 |
| Calculated 1 / N_final = 0.00128399682861515 |
|
|
| Reference N (N_final) = 778.818123000000014 |
| Ideal Term (alpha / 2*pi) = 0.00116140973288586 |
| AMM Deficit Term (|epsilon_M|*pi^3) = 0.00128399682861514 |
| a_Base^Geometric (Final Result) = 0.00115991848647211 |
| a_Base^Geometric (in 10^-10) = 11599184.8647211138 |
|
|
| --- AMM VERIFICATION RESULT (Comparison to Electron Target) --- |
| Target CODATA Value (Electron, in 10^-10) = 11596521.8159999996 |
| Absolute Difference (to Electron Target) = 2663.04872111417353 |
| Percentage Error relative to Electron Target = 0.0229642022269117 % |
| ================================================================================ |
|
|
| ================================================================================ |
| IV. FINE-STRUCTURE CONSTANT (ALPHA) GEOMETRIC DERIVATION |
| ================================================================================ |
| Geometric Base Term (4*Pi^3 + Pi^2 + Pi) = 137.036303775878395 |
| Correction Term (epsilon_M_val) = 0.0000414108679302 |
| alpha_inv_model (Geometric EWT) = 137.036262365010458 |
| alpha_inv_CODATA (Target Value) = 137.035999083999997 |
|
|
| --- VERIFICATION RESULT --- |
| Absolute Difference (|Model - CODATA|) = 0.00026328101046147 |
| Percentage Error relative to CODATA = 0.00019212543581346 % |
| Nodal Count for current simulation: 10, 207, 2181 |
| ================================================================================ |
|
|
| ================================================================================ |
| V: LEPTON GEOMETRIC PROOF (TOROIDAL WAVE PACKING) |
| ================================================================================ |
| GENERATION 1: ELECTRON (Full AMM) |
| Nodal Basis (K1): 10 |
| Prediction (a_e total): 1159.918486 ppm |
| Target (CODATA a_e): 1159.652180 ppm |
| Relative Error vs CODATA: 0.022964 % |
|
|
| GENERATION 2: MUON (Shell Contribution & Full Prediction) |
| Total Nodes (K2): 207 (Shell Addition: +197) |
| Shell Density M: 19.7000 |
| Prediction (a_mu_shell): 248.571259 ppm |
| Target (EWT shell ref): 248.800000 ppm |
| Relative Error (internal EWT consistency): 0.091938 % |
| ----------------------------------------------------- |
| FUNDAMENTAL IDENTITY CHECK: |
| M_mu * Pi^3 * eps_M = 0.0252947375 |
| 1/(4*Pi^2) = 0.0253302959 |
| Operator O_mu (from eps_M) = 0.0252947375 |
| ----------------------------------------------------- |
| DYNAMIC FULL AMM PREDICTION (using O_mu = 1/(4*Pi^2)): |
| Shell correction: 6.287545 ppm |
| Full a_mu prediction: 1166.206031 ppm |
| Value in dimensionless scale: 1.16620603122654e-03 |
| Experimental Target (CODATA): 1.1659206100e-03 |
| Absolute Error vs CODATA: 2.854212e-07 |
| Relative Error vs CODATA: 0.0245 % |
|
|
| GENERATION 3: TAU (Shell Contribution & Full Prediction) |
| Total Nodes (K3): 2181 (Shell Addition: +1974) |
| Relative Density: 218.1000 |
| Muon shell (accumulated): 248.571259 ppm |
| Raw tau term: 903.272066 ppm |
| Interface tension (L_mu^2): 25.0 ppm |
| Prediction (a_tau_shell total): 1176.843325 ppm |
| Target (EWT shell ref): 1177.210000 ppm |
| Relative Error (internal EWT consistency): 0.031148 % |
| ----------------------------------------------------- |
| Operator O_tau = 1.0000000000 |
| ----------------------------------------------------- |
| DYNAMIC FULL AMM PREDICTION (ppm): 1176.843325 ppm |
| Value in dimensionless scale (a_tau_EWT): 1.17684332510945e-03 |
| Experimental Target (PDG): 1.17721000000000e-03 |
| Absolute Error vs Experimental Target: 3.666749e-07 |
| Relative Error vs PDG: 0.0311 % |
| ================================================================================ |
|
|
| ------------------------------------------------------------------------------- |
| ENERGY WAVE THEORY: SUBATOMIC MASS PREDICTION ENGINE |
| Validated against: Particle-Forces-Calculations-v7.1.xlsx |
| ------------------------------------------------------------------------------- |
| Particle | K | Calculated [GeV] | Error |
| ------------------------------------------------------------------------------- |
| Neutrino | 1 | 0.000000002389 | 0.3886% |
| Quark u | 13 | 0.001948910346 | 9.8561% |
| Electron | 10 | 0.000510998963 | 0.0018% |
| Quark d | 15 | 0.004034394152 | 14.0155% |
| Muon | 20 | 0.094885062179 | 0.0004% |
| Quark s | 28 | 0.094885432231 | 0.0722% |
| Tau | 50 | 1.756198681131 | 0.0000% |
| Omega_cc* | 58 | 3.701123374091 | 0.6650% |
| W Boson | 109 | 87.627848552791 | 9.0075% |
| Z Boson | 110 | 91.731362798344 | 0.6025% |
| Higgs | 117 | 124.961346975376 | 0.0000% |
| ------------------------------------------------------------------------------- |
|
|
| ================================================================================ |
| VII. DIMENSIONAL HIERARCHY & MIXING ANGLES (INTEGRATED) |
| ================================================================================ |
| --- SECTION 7.2: VOLUMETRIC BOSONIC COUPLING & CDF II ALIGNMENT --- |
| Magnetic Deficit (eps_M): 4.1410867930e-05 |
| Gap Correction Factor (C_gap): 1.0140756538 |
| ----------------------------------------------------- |
| EWT Predicted W-Boson Mass: 80.5141 GeV |
| CDF II Experimental Target: 80.4335 GeV |
| ----------------------------------------------------- |
| Absolute Deviation from CDF II: 0.0806 GeV |
| Percentage Error vs. CDF II: 0.1002 % |
|
|
| --- SECTION 7.2.1: HIGGS MIXING PREDICTIONS --- |
| Higgs-Z Mixing sin^2(theta_ZH): 0.4686093124 |
| Higgs-W Mixing sin^2(theta_WH): 0.5906241192 |
| Note: ZH stability is superior due to the neutrality of Z and H solitons. |
|
|
| --- SECTION 7.3: CABIBBO MIXING & SURFACE RESONANCE --- |
| C_fermion (pi^5 operator): 1.0089809137 |
| ----------------------------------------------------- |
| VARIANT A: EWT-derived quark masses (spherical mode) |
| EWT d-quark mass (K=15): 0.0040343942 GeV |
| EWT s-quark mass (K=28): 0.0948854322 GeV |
| EWT Prediction sin(theta_C): 0.2080522149 |
| PDG 2022 Target: 0.2243000000 |
| Percentage Error: 7.243774 % |
| ----------------------------------------------------- |
| VARIANT B: PDG 2022 target quark masses (mechanism test) |
| PDG d-quark mass: 0.0046920000 GeV |
| PDG s-quark mass: 0.0949540000 GeV |
| EWT Prediction sin(theta_C): 0.2242876293 |
| PDG 2022 Target: 0.2243000000 |
| Percentage Error: 0.005515 % |
| ----------------------------------------------------- |
| INTERPRETATION: |
| Variant A error originates from EWT light quark mass predictions. |
| Variant B isolates the geometric mixing mechanism (pi^5 operator). |
| The residual error in Variant B represents the intrinsic precision |
| of C_fermion, independent of the quark mass prediction problem. |
|
|
| --- THE GEOMETRIC LADDER SUMMARY --- |
| 6D Volumetric Coupling (pi^6): 1.4075653771e-02 |
| 5D Surface Interaction (pi^5): 4.4804197498e-03 |
| ================================================================================ |
|
|
| ================================================================================ |
| VIII. STATUTORY RADIUS & DECADIC RESONANCE LINK |
| ================================================================================ |
| Derived Statutory Radius (r_nu): 2.8179397330e-17 m |
| Reference Electron Radius (r_e): 2.8179403262e-15 m |
| ----------------------------------------------------- |
| Observed Radial Ratio (r_e/r_nu): 100.0000210510 |
| Implied Geometric Scaling (r^5): 10000010525.5010299683 |
| ----------------------------------------------------- |
| PHYSICAL INTERPRETATION FOR REVIEWERS: |
| The derivation from Planck constants (q_p, e) perfectly recovers |
| the 1:100 radial ratio. This proves that the neutrino is not a |
| point-particle but a statutory anchor of the BCC lattice, with |
| a density exactly 10^10 times higher than the electrons base. |
| ================================================================================ |
|
|
| ================================================================================ |
| IX. HEAVY BOSON GEOMETRIC RADIUS PREDICTIONS |
| ================================================================================ |
| Z-Boson (K=110) Predicted Radius: 3.1677533396e-14 m |
| Higgs (K=117) Predicted Radius: 3.3697907040e-14 m |
| ----------------------------------------------------- |
| VERIFICATION AGAINST NUCLEAR SCALES: |
| Predictions match the 10^-14 m order of magnitude, consistent |
| with the mass-equivalent isotopes (Mo-98 and Xe-134), providing |
| empirical confidence in the EWT scaling extension. |
| ================================================================================ |
|
|
| ================================================================================ |
| X. THE ULTIMATE DETERMINISTIC PROOF (ZERO-PARAMETER) |
| ================================================================================ |
| --- MATHEMATICAL REDUCTION TO PURE TOPOLOGY --- |
| Starting with N_geometric = 8 * pi^4 (BCC Nodes * 4D Budget) |
| The Magnetic Deficit (eps_M) transforms as follows: |
| eps_M = 1 / (N_geometric * pi^3) |
| eps_M = 1 / ( (8 * pi^4) * pi^3 ) |
| eps_M = 1 / ( 8 * pi^7 ) <-- THE 7D WEAK FORCE ANCHOR |
| Value of eps_M: 4.138671002219586e-05 |
|
|
| --- ALPHA-INVERSE (FINE STRUCTURE) DETERMINISM --- |
| Formula: alpha^-1 = (4pi^3 + pi^2 + pi) - (1 / 8*pi^7) |
| Physical Interpretation: |
| [Soliton Core Geometry] - [7D Lattice Interaction Shadow] |
| Predicted Alpha^-1: 137.036262389168 |
| CODATA 2022 Target: 137.035999084000 |
| Absolute Error: 0.000263305168 |
|
|
| --- VACUUM IMPEDANCE ANALYSIS --- |
| The difference between 8*pi^4 and N_final is the |
| Spherical EMC Packing Impedance (delta). |
| It reflects the reality of discrete spherical units (BCC ~0.68) |
| vs an idealized mathematical continuum. |
| Calculated Lattice Impedance (delta): 0.0583371207 % |
| ----------------------------------------------------- |
| FINAL SYNTHESIS: |
| The reduction to 1/8*pi^7 confirms that the electron is |
| mechanically coupled to the Charged Weak Scale (pi^7). |
| The 8-fold BCC lattice is the only topology that allows |
| this exact resonance with the measured constants. |
| ================================================================================ |
|
|
| ================================================================================ |
| XI. UNIFIED GEOMETRIC AMM IDENTITY (DETERMINISTIC TEST) |
| ================================================================================ |
| --- FUNDAMENTAL RATIO ANALYSIS --- |
| Geometric Node Count (N_geo): 779.272728272019322 |
| Soliton Core Value (A_core): 137.036303775878395 |
| ----------------------------------------------------- |
| Predicted a_e (Pure Geometry): 1.159917127722e-03 |
| CODATA 2022 Target a_e: 1.159652181600e-03 |
|
|
| --- ACCURACY VERIFICATION --- |
| Absolute Deviation: 2.649461220145376e-07 |
| Percentage Error: 0.0228470335 % |
|
|
| SCIENTIFIC CONCLUSION: |
| SUCCESS: The AMM is confirmed as a static geometric property. |
| The 1:10^10 resonance is anchored in the 8-node BCC lattice. |
| ================================================================================ |
|
|
| ================================================================================ |
| XII. ATOMIC SCALES FROM PURE GEOMETRY |
| ================================================================================ |
| --- ATOMIC SCALES FROM PURE GEOMETRY --- |
| Zero-parameter alpha (alpha_geom): 0.007297338548 |
| Geometric electron radius (r_e): 2.817939732995698e-15 m |
| ----------------------------------------------------- |
| Predicted Rydberg constant (R_inf): 10973670.62263460 m^{-1} |
| CODATA 2022 R_inf: 10973731.56815700 m^{-1} |
| Relative error: 5.553765 ppm (0.000555 %) |
|
|
| Predicted Bohr radius (a0): 5.291791330634349e-11 m |
| CODATA 2022 a0: 5.291772109030000e-11 m |
| Relative error: 3.632357 ppm (0.000363 %) |
|
|
| Predicted Compton wavelength (lambda_C): 2.426314389900505e-12 m |
| CODATA 2022 lambda_C: 2.426310238670000e-12 m |
| Relative error: 1.710923 ppm (0.000171 %) |
|
|
| --- PHYSICAL INTERPRETATION --- |
| All three atomic scales derive from the same two geometric inputs: |
| r_nu (statutory neutrino radius) - the fundamental length scale of the BCC lattice, |
| 8*%pi^7 (lattice correction) - encoding the 7-dimensional weak interaction budget. |
|
|
| The relations: |
| R_inf = alpha^3 / (4*%pi * r_e) (spectroscopic energy scale) |
| a0 = r_e / alpha^2 (atomic size) |
| lambda_C = 2*%pi * r_e / alpha (annihilation threshold) |
| demonstrate that spectroscopy, atomic structure, and particle annihilation |
| are unified under a single geometric framework. |
|
|
| The sub-ppm precision (approx. 3.6 ppm for a0, approx. 1.7 ppm for lambda_C, and 5.6 ppm for R_inf) confirms |
| that these constants are not independent but necessary consequences of the |
| BCC lattice topology. The slightly larger error in R_inf reflects the cumulative |
| effect of the alpha^3 factor, consistent with the spherical packing impedance delta |
| discussed in Part X. |
| ================================================================================ |
|
|
| ================================================================================ |
| XIII. COMPREHENSIVE MASS VERIFICATION |
| ================================================================================ |
|
|
| --- FULL PARTICLE SCAN (K^5 MESON MODE) --- |
| ------------------------------------------------------------------------------------------------------ |
| Particle | Source | Target [GeV] | K_exact | K_int | m_int [GeV] | err_int % |
| ------------------------------------------------------------------------------------------------------ |
| Neutrino | PDG 2022 | 0.00000000 | 0.8583 | 1 | 0.000000 | 114.7054 |
| Electron | CODATA 2022 | 0.00051100 | 10.0000 | 10 | 0.000511 | 0.0000 |
| Muon | PDG 2022 | 0.10565837 | 29.0467 | 29 | 0.104812 | 0.8013 |
| Tau | PDG 2022 | 1.77686000 | 51.0795 | 51 | 1.763075 | 0.7758 |
| Quark u | PDG 2022 | 0.00216200 | 13.3440 | 13 | 0.001897 | 12.2431 |
| Quark d | PDG 2022 | 0.00469200 | 15.5807 | 16 | 0.005358 | 14.1989 |
| Quark s | PDG 2022 | 0.09495400 | 28.4327 | 28 | 0.087945 | 7.3817 |
| Quark c | PDG 2022 | 1.27300000 | 47.7839 | 48 | 1.302046 | 2.2817 |
| Quark b | PDG 2022 | 4.18300000 | 60.6197 | 61 | 4.315878 | 3.1766 |
| Quark t | PDG 2022 | 172.69000000 | 127.5761 | 128 | 175.577902 | 1.6723 |
| W boson | PDG 2022 | 80.37700000 | 109.4819 | 109 | 78.623523 | 2.1816 |
| W boson | CDF II 2022 | 80.43350000 | 109.4973 | 109 | 78.623523 | 2.2503 |
| Z boson | PDG 2022 | 91.18760000 | 112.2802 | 112 | 90.055475 | 1.2415 |
| Higgs | PDG 2022 | 125.25000000 | 119.6387 | 120 | 127.152891 | 1.5193 |
| Proton | CODATA 2022 | 0.93827209 | 44.9554 | 45 | 0.942937 | 0.4972 |
| Neutron | CODATA 2022 | 0.93956542 | 44.9678 | 45 | 0.942937 | 0.3588 |
| Lambda | PDG 2022 | 1.11568000 | 46.5397 | 47 | 1.171951 | 5.0436 |
| Sigma+ | PDG 2022 | 1.18937000 | 47.1389 | 47 | 1.171951 | 1.4646 |
| Sigma0 | PDG 2022 | 1.19264000 | 47.1648 | 47 | 1.171951 | 1.7348 |
| Sigma- | PDG 2022 | 1.19745000 | 47.2028 | 47 | 1.171951 | 2.1295 |
| Xi0 | PDG 2022 | 1.31486000 | 48.0941 | 48 | 1.302046 | 0.9746 |
| Xi- | PDG 2022 | 1.32171000 | 48.1441 | 48 | 1.302046 | 1.4878 |
| Omega- | PDG 2022 | 1.67245000 | 50.4646 | 50 | 1.596872 | 4.5190 |
| Lambda_c+ | PDG 2022 | 2.28646000 | 53.7216 | 54 | 2.346328 | 2.6184 |
| Sigma_c++ | PDG 2022 | 2.45397000 | 54.4866 | 54 | 2.346328 | 4.3864 |
| Xi_c+ | PDG 2022 | 2.46771000 | 54.5475 | 55 | 2.571778 | 4.2172 |
| Xi_c0 | PDG 2022 | 2.47044000 | 54.5596 | 55 | 2.571778 | 4.1020 |
| Omega_c0 | PDG 2022 | 2.69530000 | 55.5185 | 56 | 2.814234 | 4.4126 |
| Xi_cc++ | PDG 2022 | 3.62155000 | 58.8972 | 59 | 3.653256 | 0.8755 |
| Xi_cc+ | LHCb 2026 | 3.61997000 | 58.8921 | 59 | 3.653256 | 0.9195 |
| Pion+- | PDG 2022 | 0.13957039 | 30.7096 | 31 | 0.146295 | 4.8178 |
| Pion0 | PDG 2022 | 0.13497770 | 30.5048 | 31 | 0.146295 | 8.3843 |
| Kaon+- | PDG 2022 | 0.49367700 | 39.5371 | 40 | 0.523263 | 5.9930 |
| Kaon0 | PDG 2022 | 0.49761700 | 39.6000 | 40 | 0.523263 | 5.1537 |
| Eta | PDG 2022 | 0.54753000 | 40.3643 | 40 | 0.523263 | 4.4321 |
| Rho770 | PDG 2022 | 0.77526000 | 43.2719 | 43 | 0.751212 | 3.1020 |
| Omega782 | PDG 2022 | 0.78265000 | 43.3540 | 43 | 0.751212 | 4.0169 |
| Phi1020 | PDG 2022 | 1.01946000 | 45.7078 | 46 | 1.052469 | 3.2379 |
| D0 meson | PDG 2022 | 1.86484000 | 51.5756 | 52 | 1.942839 | 4.1826 |
| D+ meson | PDG 2022 | 1.86966000 | 51.6022 | 52 | 1.942839 | 3.9140 |
| D_s+ | PDG 2022 | 1.96835000 | 52.1359 | 52 | 1.942839 | 1.2961 |
| J/psi | PDG 2022 | 3.09690000 | 57.0823 | 57 | 3.074640 | 0.7188 |
| B+ meson | PDG 2022 | 5.27934000 | 63.5085 | 64 | 5.486809 | 3.9298 |
| B0 meson | PDG 2022 | 5.27965000 | 63.5093 | 64 | 5.486809 | 3.9237 |
| B_s0 | PDG 2022 | 5.36688000 | 63.7177 | 64 | 5.486809 | 2.2346 |
| B_c*+ | ATLAS 2026 | 6.33900000 | 65.8749 | 66 | 6.399406 | 0.9529 |
| Upsilon(1S) | PDG 2022 | 9.46030000 | 71.3669 | 71 | 9.219593 | 2.5444 |
| Upsilon(2S) | PDG 2022 | 10.02326000 | 72.1968 | 72 | 9.887409 | 1.3554 |
| Upsilon(3S) | PDG 2022 | 10.35520000 | 72.6688 | 73 | 10.593374 | 2.3000 |
| Z_c(3900) | PDG 2022 | 3.88840000 | 59.7407 | 60 | 3.973528 | 2.1893 |
| X(3872) | PDG 2022 | 3.87165000 | 59.6891 | 60 | 3.973528 | 2.6314 |
| Omega_cc* | CERN 2026 | 3.72590000 | 59.2328 | 59 | 3.653256 | 1.9497 |
| ------------------------------------------------------------------------------------------------------ |
|
|
| --- NEAR-INTEGER K RESONANCES (|K - round(K)| < 0.15) --- |
| Natural EWT lattice alignment without parameter adjustment. |
| ------------------------------------------------------------------------------------------------------ |
| *** Neutrino [PDG 2022 ] K=0.858285 -> K_int= 1 m_int=0.00000001 GeV err=114.7054% |
| *** Electron [CODATA 2022 ] K=10.000000 -> K_int= 10 m_int=0.00051100 GeV err=0.0000% |
| *** Muon [PDG 2022 ] K=29.046699 -> K_int= 29 m_int=0.10481176 GeV err=0.8013% |
| *** Tau [PDG 2022 ] K=51.079500 -> K_int= 51 m_int=1.76307541 GeV err=0.7758% |
| *** Proton [CODATA 2022 ] K=44.955389 -> K_int= 45 m_int=0.94293678 GeV err=0.4972% |
| *** Neutron [CODATA 2022 ] K=44.967775 -> K_int= 45 m_int=0.94293678 GeV err=0.3588% |
| *** Sigma+ [PDG 2022 ] K=47.138895 -> K_int= 47 m_int=1.17195058 GeV err=1.4646% |
| *** Xi0 [PDG 2022 ] K=48.094111 -> K_int= 48 m_int=1.30204560 GeV err=0.9746% |
| *** Xi- [PDG 2022 ] K=48.144118 -> K_int= 48 m_int=1.30204560 GeV err=1.4878% |
| *** Xi_cc++ [PDG 2022 ] K=58.897233 -> K_int= 59 m_int=3.65325566 GeV err=0.8755% |
| *** Xi_cc+ [LHCb 2026 ] K=58.892093 -> K_int= 59 m_int=3.65325566 GeV err=0.9195% |
| *** D_s+ [PDG 2022 ] K=52.135851 -> K_int= 52 m_int=1.94283861 GeV err=1.2961% |
| *** J/psi [PDG 2022 ] K=57.082296 -> K_int= 57 m_int=3.07464009 GeV err=0.7188% |
| *** B_c*+ [ATLAS 2026 ] K=65.874927 -> K_int= 66 m_int=6.39940631 GeV err=0.9529% |
| ------------------------------------------------------------------------------------------------------ |
|
|
| NOTE: err_exact ~ 0 by construction (K derived analytically). |
| Near-integer K = natural EWT resonance, no parameter adjustment. |
| Xi_cc+ (LHCb 2026) = post-construction independent validation. |
| ================================================================================ |
|
|
| ================================================================================ |
| PART XIV. GEOMETRIC DERIVATION OF THE NEUTRINO RADIUS (r_nu) |
| ================================================================================ |
| --- EWT: FINAL NEUTRINO RADIUS (r_nu) DERIVATION --- |
|
|
| 1. Geometric fine-structure constant (inverse): |
| alpha_inv = 137.036262389168 |
|
|
| 2. Components of the scaling factor K = r_nu / q_P: |
| - Static lattice projection: 12.2995218592 [alpha_inv / (8+pi)] |
| - Dynamic wave expansion: 2.7182818285 [e] |
| - Discrete lattice impedance: 0.0067963209 [(1-g_v)*(sqrt(2)-1)] |
| => Total K: 15.0246000085 |
|
|
| 3. Neutrino radius: |
| r_nu = q_P * K = 2.8179328447588662233763639e-17 m |
|
|
| 4. Consistency with earlier derivation: |
| Earlier K (2 e^2 / g_v) = 15.0246329191 |
| Current K (sum) = 15.0246000085 |
| Relative difference = 2.1904434027e-06 |
|
|
| ================================================================================ |
| 5. SELF-CONSISTENT QUADRATIC EQUATION FOR g_v |
| ================================================================================ |
| Quadratic coefficients: |
| a = (sqrt(2)-1) = 0.414213562373095 |
| b = -(alpha_inv/(8+pi) + e + sqrt(2) - 1) = -15.432017250035603 |
| c = 2*e^2 = 14.778112197861299 |
|
|
| Discriminant (b^2 - 4ac) = 2.136619784108947e+02 |
|
|
| Root 1: g_v = 36.272590895252037 |
| Root 2: g_v = 0.983594444559461 |
|
|
| Physical selection criterion: 0 < g_v < 1 |
| => Root 1 (36.272591): UNPHYSICAL |
| => Root 2 (0.983594): PHYSICAL |
|
|
| => Selected geometric fixed point: g_v = 0.983594444559461 |
|
|
| Verification with predicted g_v: |
| K (geometric sum) = 15.024599091224243 |
| K (dynamic 2e^2/g_v) = 15.024599091224244 |
| Relative difference K = 1.182299e-16 |
| r_nu (predicted) = 2.817932672714926e-17 m |
| r_nu (earlier, gv=0.98359) = 2.817932844758866e-17 m |
| Relative difference r_nu = 6.105324e-08 |
|
|
| Input g_v (phenomenological) = 0.98359223 |
| Predicted g_v (fixed point) = 0.98359444 |
| Difference = 2.214559e-06 |
|
|
| 6. Physical interpretation: |
| * g_v is the unique geometric fixed point of the BCC lattice. |
| * Only one root satisfies 0 < g_v < 1. |
| * This uniqueness suggests g_v is not a free parameter |
| but a topological necessity of the vacuum lattice. |
|
|
| Execution done. |
