pith. sign in
def

cube_edges_count

definition
show as:
module
IndisputableMonolith.Physics.PMNSCorrections
domain
Physics
line
66 · github
papers citing
none yet

plain-language theorem explainer

The definition supplies the edge count of a D-dimensional hypercube as D times 2 to the power of D minus 1. PMNS mixing-angle derivations cite it to extract the integer 10 for the solar radiative correction from 3-cube topology. The implementation is a direct combinatorial formula with no lemmas or tactics required.

Claim. The number of edges in a $D$-dimensional hypercube is given by $E(D) = D · 2^{D-1}$.

background

The PMNS Radiative Correction Derivation module obtains the integer coefficients 6, 10 and 3/2 for atmospheric, solar and Cabibbo corrections from the topology of the 3D cubic ledger. A 3-cube supplies 12 edges and 6 faces; the solar sector subtracts the two active modes to leave the factor 10. Upstream structures from SpectralEmergence record that the 3D voxel ledger forces exactly three generations and 24 chiral fermions via the relation $D × 2^D$.

proof idea

The declaration is a direct definition that encodes the standard hypercube edge-counting formula.

why it matters

It supplies the edge count required by solar_coefficient and by CorrectionDerivationCert, which certifies that the integers 6, 10 and 3/2 are forced by 3-cube topology rather than free parameters. The construction sits inside the Recognition framework at the point where T8 fixes D = 3 and the eight-tick octave closes the ledger.

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