g2FromLoops_canonical
plain-language theorem explainer
Canonical RSBridge geometry with loop order fixed at 5 produces g-2 equal to 1 over phi to the fifth in Recognition Science units. Researchers deriving observable predictions from bridge cycles would cite this result to obtain the canonical anomalous magnetic moment. The proof reduces immediately by substituting the loop order hypothesis into the general g2FromLoops definition.
Claim. For an RSBridge $B$ over ledger $L$ with loop order $B.loopOrder = 5$, the loop-derived g-2 satisfies $g_2(B, φ) = φ^{-5}$.
background
The Bridge Derivation module extracts canonical mixing angles and g-2 from RSBridge geometry. The general relation is g2FromLoops B φ = 1 / φ^{B.loopOrder}, with the canonical bridge fixing loopOrder at 5 to give g-2 = 1/φ^5. RSBridge encodes the structural link from recognition cycles to observable payloads such as CKM elements and anomalous moments.
proof idea
The proof is a one-line wrapper that applies simp to unfold g2FromLoops and substitute the loop order hypothesis hLoop.
why it matters
This supplies the canonical g-2 case inside Bridge Derivation, delivering the Recognition Science prediction for the muon anomalous magnetic moment as 1/φ^5. It rests on the phi-ladder fixed point and the eight-tick octave structure. No downstream uses appear, marking it as a terminal derivation for g-2 observables.
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