jarlskog_pred
plain-language theorem explainer
The geometric prediction for the Jarlskog invariant is assembled as the product of edge-dual ratio, fine-structure leakage, torsion overlap, and sine of the CKM CP phase. Particle physicists studying CP violation in weak interactions would cite this for its topological derivation from the cubic ledger. The definition directly composes the factors without invoking further theorems.
Claim. The Jarlskog invariant is predicted by $J = r · ℓ · o · sin δ$, with $r$ the edge-dual ratio, $ℓ$ the fine-structure leakage, $o$ the torsion overlap, and $δ$ the CP phase. Equivalently, $J ≈ (1/24) · (α/2) · φ^{-3}$.
background
Phase 7.2 derives the CKM and PMNS mixing matrices geometrically from the cubic ledger, replacing numerical fits with topological arguments. Edge-dual coupling is set by 8-tick window overlaps. Topological ratios yield |V_cb| = 1/24 from single-edge to double-vertex coverage and |V_ub| = α/2 from fine-structure leakage between non-adjacent vertices. Unitarity is enforced by 8-tick closure. Upstream, the SpectralEmergence structure forces SU(3) × SU(2) × U(1) gauge content, exactly three particle generations from face-pair count, and 24 chiral fermion flavors. PhiForcingDerived supplies the J-cost structure, while LedgerFactorization calibrates the J functional from the positive reals under multiplication.
proof idea
This definition directly multiplies the edge-dual ratio by the fine-structure leakage, the torsion overlap, and the sine of the CKM CP phase. No additional lemmas or proof steps are required; the expression assembles the geometric components as defined in the mixing geometry.
why it matters
The definition feeds the jarlskog definition and the jarlskog_match theorem, which verifies that the prediction agrees with the observed 3.08 × 10^{-5} within 20 percent, establishing the geometric origin of CP violation. It draws on the eight-tick octave and three spatial dimensions from the forcing chain. The match theorem requires transcendental bounds on α and φ.
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