The 168 Monads: Walk-States on the Fano Plane, Frobenius Orbits, and the Standard Model Spectrum

We construct 168 discrete walk-states on the Fano plane PG (2, ₂), the minimal projective geometry underlying octonionic multiplication. Beginning with three fluxions \-1, 0, +1\ and seven axioms extending Peano arithmetic with triadic closure and totality, exactly 42 computational operators (glyphs) emerge from combinatorial necessity: 7 lines 3 Frobenius strides 2 orientations = 42. These glyphs generate 168 walk-states through four topologically distinct walk types, organizing into 14 Frobenius orbits of 12 states each. The total 168 = |PSL (2, ₇) | coincides with the order of the automorphism group of the Klein quartic, the unique genus-3 surface achieving the Hurwitz bound. The dimensional ratio 168/42 = 4 equals the codimension of the 8D 4D octonionic projection. Physical constants appear as geometric eigenvalues of this structure: the fine-structure constant ^-1 137 at row 137, the gravitational boundary at row 168, with ratio 168/137 /2 bridging circular and discrete projection basins. The correction term in the expansion involves the factor 20, which we identify as |M₂₁| - 1, where M₂₁ PSL (3, 4) is the Mathieu group acting on 21 points of PG (2, 4), with the identity (projection origin) removed. This framework maps Standard Model particles to specific walk-state addresses, with mass ratios and mixing angles reproduced to median accuracy of 0. 32\% via transforms involving, , and structural integers---all with zero free parameters. Unmapped orbits provide dark matter candidates. We present the complete glyph tables, orbit assignments, and falsifiability conditions.