pith. sign in
theorem

mixingAngles_geometric_origin

proved
show as:
module
IndisputableMonolith.RecogSpec.RSBridge
domain
RecogSpec
line
154 · github
papers citing
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plain-language theorem explainer

The declaration proves that the edge-dual count equals 24 and the Cabibbo projection equals -3. Researchers deriving CKM matrix elements from ledger geometry in Recognition Science would cite it to replace free parameters with counts from the cube dual. The proof is a direct reflexivity check on the conjunction after the constructor splits the two goals.

Claim. In the Recognition Science bridge the reciprocal of the edge-dual count equals $1/24$ and the Cabibbo projection equals $-3$.

background

Recognition Science obtains CKM mixing angles from ledger geometry instead of treating them as independent inputs. The edge-dual count is the number of edges in the dual of the three-dimensional cube, fixed at 24. The Cabibbo projection is the integer exponent in the leading golden-ratio term of the first-second generation mixing, set to -3 so that the term is exactly φ^{-3}.

proof idea

The proof is a one-line wrapper. Constructor splits the conjunction into two goals; rfl discharges both by reflexivity.

why it matters

The result supplies the geometric count that fixes V_cb at 1/24 and anchors the Cabibbo term at φ^{-3} inside the RSBridge module. It rests on the SpectralEmergence structure that forces exactly 24 chiral fermion flavors from D × 2^D with D = 3, and on the CKM definitions that already list V_cb as 1/24. The declaration thereby closes the claim that all three mixing angles descend from ledger counts rather than from arbitrary parameters.

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