CorrectionDerivationCert
plain-language theorem explainer
The certificate asserts that PMNS radiative correction coefficients 6, 10, and 3/2 are forced by the face and edge counts of a 3-cube. Neutrino physicists would cite it when grounding mixing angle corrections in geometry instead of treating the integers as free parameters. It packages the four equalities that link each coefficient to its topological expression and verify the matches.
Claim. Let $a$ denote the atmospheric correction coefficient, $s$ the solar correction coefficient, and $c$ the Cabibbo correction coefficient. The certificate requires $a$ equals the number of faces of the 3-cube, $s$ equals the number of edges of the 3-cube minus 2, $c$ equals (number of faces of the 3-cube) divided by 4, and the conjunction $a=6$ and $s=10$ and $c=3/2$.
background
The module derives the integer coefficients appearing in PMNS mixing angle predictions from the topology of the three-dimensional cubic ledger. Atmospheric mixing receives a correction proportional to the six faces of the cube, each contributing one unit of vacuum polarization to the mu-tau sector. Solar mixing uses an effective count of ten obtained by subtracting two from the twelve edges to isolate the passive modes. The Cabibbo coefficient is obtained as six faces divided by four vertex-edge slots, yielding 3/2.
proof idea
This is a structure definition that directly records the four required equalities. No tactics or lemmas are applied beyond the construction of the fields themselves; the numerical identities follow immediately from the definitions of the coefficient functions.
why it matters
This declaration grounds the correction terms used in the PMNS predictions, supplying the parent structure for the verification theorem that confirms the derivation. It realizes the claim that the integers 6, 10, and 3/2 are forced by the cubic topology rather than introduced as free parameters, aligning with the Recognition Science requirement that D equals 3 spatial dimensions.
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