g2FromLoops
g2FromLoops supplies the structural expression for the muon g-2 anomaly in terms of the Recognition Science bridge geometry. Researchers deriving particle constants from the phi-ladder and loop structures would reference it to obtain the canonical result 1/phi^5. The definition reduces directly to the reciprocal of phi raised to the loopOrder integer carried by the RSBridge record.
claim$g_2(B, phi) = 1 / phi^{B.loopOrder}$ where $B$ is an RSBridge instance over ledger $L$ and $phi$ is a real parameter.
background
The Bridge Derivation module extracts canonical CKM mixing angles and the g-2 anomaly from RSBridge geometry. RSBridge carries a structural loopOrder field (default 5) together with cycle and defect data. Upstream, L is the unit ledger with debit and credit both equal to 1, while canonicalRSBridge constructs the default bridge instance used in the downstream theorems.
proof idea
One-line definition that directly returns the reciprocal of phi raised to the power of the bridge's loopOrder field.
why it matters in Recognition Science
The definition is invoked by canonical_g2FromLoops and g2FromLoops_canonical to prove that the canonical bridge yields g-2 = 1/phi^5. It supplies the g-2 step inside the Bridge Derivation module, linking the loop-order integer to the phi fixed point of the forcing chain and the eight-tick octave.
scope and limits
- Does not derive g-2 from first principles beyond the bridge loop structure.
- Does not incorporate experimental measurements of the muon anomaly.
- Does not fix loopOrder outside the canonical case of 5.
formal statement (Lean)
48def g2FromLoops (B : RSBridge L) (φ : ℝ) : ℝ :=
proof body
Definition body.
49 1 / (φ ^ B.loopOrder)
50
51/-- For the canonical bridge, V_cb = 1/24. -/