IndisputableMonolith.StandardModel.JarlskogInvariant
Module packages the Jarlskog invariant of the CKM matrix from RS geometry: Gray-code chirality on the 3-cube plus the Berry-phase CP angle δ = π/2. It proves J is structurally positive and hierarchically small, so CP violation exists but is weak. Cosmology cites it for the sign of baryon asymmetry. Arguments reduce to the fixed phase, sine nonvanishing, and the standard Jarlskog combination of mixings.
claimWith CP phase $\delta=\pi/2$ from the directed Gray-code Berry phases on $Q_3$, the Jarlskog invariant $J\propto s_{12}s_{13}s_{23}c_{12}c_{13}^2 c_{23}\sin\delta$ is strictly positive and small. Hence CKM CP violation exists and is hierarchically suppressed.
background
Recognition Science places quark mixing on the 3-cube $Q_3$. The Cabibbo–Kobayashi–Maskawa matrix is built from cube geometry, generation torsion ${0,11,17}$, and the directed Gray-code walk with hop pattern $[4,2,2]$. GrayCodeChirality shows that walk is chiral: clockwise and counterclockwise face traversals are inequivalent, which is the geometric seed of CP violation.
CPPhaseDerivation accumulates a Berry phase for each generation eigenstate around the eight-tick cycle. The module’s working angle is the difference $\delta=\gamma(\mathrm{gen}_1)-\gamma(\mathrm{gen}_2)=4(\pi/4)-2(\pi/4)=\pi/2$. The classical Jarlskog invariant $J$ is the unique (up to convention) rephasing-invariant measure of CP violation in the three-generation CKM matrix; its sign tracks $\sin\delta$ and its magnitude tracks the product of the small mixing angles.
Constants supplies the RS tick and related units; the present file does not re-derive mixings, only the CP-sensitive scalar built from them and $\delta$.
proof idea
The module is a short theorem stack, not a definition dump. It fixes cpAngle to the Berry difference $\pi/2$, then shows $\sin\delta\neq 0$. Structural lemmas assemble the standard Jarlskog monomial in sines and cosines of the CKM angles with that $\sin\delta$, prove $J>0$, and record the hierarchy (product of small angles). Existence and “small but nonzero” CP violation are corollaries. A certificate bundle (JarlskogCert / jarlskogCert) packages the proved facts for downstream import. No deep new analysis: the work is wiring CKMFromCube and CPPhaseDerivation into the classical $J$ formula and discharging sign and nonvanishing.
why it matters in Recognition Science
Sakharov’s second condition needs C and CP violation. Downstream, SakharovFromLedger imports this module as the RS source of that violation. BaryonAsymmetryDerivation states explicitly that the structural theorem $\eta_B>0$ follows from $J_{\mathrm{CP}}>0$ (Jarlskog from Gray-code chirality) plus the Sakharov conditions; the sign of the asymmetry is derived content, while the numerical size remains scaffolded. BaryogenesisStaging keeps honest targets so the baryogenesis lane cannot fake a missing CP mechanism.
In the forcing picture this sits after the eight-tick octave and $D=3$ cube geometry: chirality of the Gray cycle on $Q_3$ forces a nonzero $\delta$, hence $J\neq 0$, hence a preferred matter sign once B violation and out-of-equilibrium dynamics are in place. Without a positive Jarlskog lemma, the cosmology chain would only have a hypothesis-level CP input.
scope and limits
- Does not compute numerical CKM angles or fit PDG Jarlskog magnitude.
- Does not derive baryon asymmetry η_B or sphaleron dynamics.
- Does not prove uniqueness of δ beyond the Berry-phase difference used here.
- Does not address leptonic CP violation or the PMNS matrix.
- Does not replace experimental extraction of J; it only gives the RS structural sign and hierarchy.