Mass-Level Taxonomy — 5 механизмов массы

Master DD-принцип: масса — не один объект. Это спектральный инвариант оператора продолжения на соответствующем уровне carrier closure. NO один operator не покрывает все 5 уровней.

Это страница доказывает, что charged-lepton hierarchy выводится из substrate ~1% через единственный параметр δ. Покрути слайдер ниже и увидишь сам.

Level A — Elementary Fermion Yukawa

Operator: D_F + Yukawa + scalar bridge

Mass formula: m_f = Y_f · v / √2

🔬 Live Koide / Z₃-uniform calculator (charged leptons)

Z₃-uniform parametrization на normalized x_k = √m_k / Σ√m_j:

x_k = (1/3) + (√2/3) · cos(2π·k/3 + δ), k ∈ {0, 1, 2}

Σ x_k = 1 trivially (Z₃ identity). Σ x_k² = 2/3 = Koide ratio (automatic).

Mass m_k = K · x_k² где K = (Σ √m_j)² scale factor.

δ (degrees): 12.71°

Mass ratio	DD prediction	Observed	Match factor

Try δ = 12.71° — match ~1%. Try δ = 15° (boundary) — m_e becomes 0.

Single parameter δ fixes BOTH ratios. Three masses → one degree of freedom.

Result: charged lepton hierarchy derived ~1% accurate via 3 ingredients:

Block XXII: β₁(K_3) = 1 forces 3 generations
iter 248: Z₃-uniform parametrization on normalized √m
iter 298: Koide ceiling Q = 2/3 structurally

+ single δ ≈ 12.71° fits both observable ratios m_e/m_τ + m_μ/m_τ.

Open at level A:

Why δ = 12.71° specifically (1 free param)
Up/down quark Z₃-deviation mechanism (Q grows с hierarchy: lep 0.667 < d 0.733 < u 0.854)
CKM matrix specific values

Level B — Broken Gauge Boson

Operator: scalar vacuum orbit Hessian on broken generators

m_W = g · v / 2 ; m_Z = v · √(g² + g'²) / 2 ; m_γ = 0

Result: Tree-level exact:

m_W / m_Z = cos(θ_W) — observed: 80.379 / 91.188 = 0.8815 = cos(28.17°) ✓
m_γ = 0 guaranteed (unbroken U(1)_em, orthogonal to Z)
W± degenerate (J_F particle-antiparticle symmetry)
Higgs eats 3 of 4 doublet components → 3 broken generators get mass

Open at level B: g, g', v numerical (3 free params, pending Block XXVII gauge couplings + Block XXX scalar vacuum closures).

Level C — Confined Hadron

Operator: QCD bound-state Hamiltonian / stress-energy tensor

Λ_QCD = μ · exp(−2π / (b₀ · α_s(μ))) ; b₀ = 11 − (2/3)·N_f

m²_hadron = ⟨H | T^μ_μ | H⟩ / (2 · m_hadron)

Result: dimensional transmutation generates Λ_QCD от dimensionless coupling. Hadron mass decomposition (lattice QCD, μ = 2 GeV):

Quark kinetic energy: ~33%
Gluon field energy: ~37%
Trace anomaly: ~23%
Quark scalar condensate: ~9%
Bare quark sum (m_u + m_u + m_d) ≈ 9 MeV vs proton 938 MeV → ~99% от QCD dynamics

Hierarchy decomposition: m_p / m_e = 1836 = (Λ_QCD / m_e) × (m_p / Λ_QCD) = 391 × 4.7.

Open at level C:

α_s scale (Block XXVII g_3 closure)
O(1) factor m_p / Λ_QCD = 4.7 (lattice QCD non-perturbative)
Specific hadron spectrum

Level D — Neutrino (Dirac vs Majorana)

2 closure routes:

D1 Dirac: ν_R ordinary singlet, m_ν = Y_ν · v / √2. Requires Y_ν / Y_e < 10⁻⁶ — extreme hierarchy без mechanism.
D2 Majorana / type-I seesaw: m_ν ≈ (Y_ν · v)² / M_R. Light if M_R ≫ v. Lepton number violated by 2.

Empirical observed:

Δm²_21 ≈ 7.42×10⁻⁵ eV²
|Δm²_31| ≈ 2.51×10⁻³ eV²
Σm_ν < 0.12 eV (Planck+BAO)
PMNS large mixing (θ_12 ≈ 33°, θ_23 ≈ 49°, θ_13 ≈ 8.5°)

Open at level D:

Dirac vs Majorana — decisive observable: 0νββ search (KamLAND-Zen, nEXO, LEGEND)
Mass ordering NO/IO — empirical pending
CP phase δ_CP — hint of −π/2, не conclusive
Free params: D1 = 4, D2 = 9

Level E — Composite Atom / Molecule

Operator: many-body bound-state Hamiltonian + Einstein E = m·c²

m_composite = Σ m_constituents − E_binding / c²

Hierarchy:

Nucleon: ~99% от QCD binding (level C)
Nucleus: ~8 MeV/nucleon strong nuclear binding (Bethe-Weizsäcker semi-empirical)
Atom: dominated by nucleus (~99.95%, electron mass total ~0.05%)
Molecule: chemical bonds eV scale (negligible на mass)
Bulk: lattice cooperative effects emergent от EM

Mass-defect ratio: ~10⁻⁸ atom level (electron binding), ~10⁻² nuclear level.

Cross-level scoreboard

Quantity	DD prediction	Observed	Status
Koide Q (charged leptons)	2/3 exact	2/3	structural
m_e / m_τ	0.000284	0.000288	1.4% off
m_μ / m_τ	0.0598	0.0596	0.3% off
m_W / m_Z	cos(θ_W)	0.8815	tree-level exact
m_γ photon	0	0	guaranteed
Generation count	3 (β₁=1)	3	topological
Q monotone (lep<d<u)	predicted	0.667<0.733<0.854	confirmed
m_p ≈ Λ_QCD × O(1)	structural	~99% от QCD	confirmed
δ_lepton specific value	≈12.71° fits	12.71°	1 free param remains
Quark Q-deviation mechanism	structural exists	—	specific form open
Numerical g, g', v, α_s	—	SM values	Block XXVII pending

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