row_anchor_top_charm_ratio_exp
plain-language theorem explainer
The ratio of Recognition Science anchor masses for the top and charm quarks equals exp(6 log phi). Researchers checking quark mass hierarchies against PDG 2024 values would cite this when validating the phi-ladder spacing for up-type fermions. The tactic proof applies the general anchor_ratio lemma after a decide step on equal Z values and a simp-norm_num reduction showing the rung difference is exactly 6.
Claim. The ratio of the anchor mass for the top quark to the anchor mass for the charm quark equals $e^{6 log phi}$.
background
In this module the anchor mass of a fermion f is the native expression M0 * exp(((rung f - 8 + gap(ZOf f)) * log phi)), where rung assigns the integer level on the phi-ladder and phi is the self-similar fixed point. The QuarkAbsoluteBridgeScoreCard module deepens the earlier QuarkScoreCard by proving exact agreement on within-family ratios for u/c/t using the equal-Z anchor bridge; the absolute MeV calibration remains a residual open question. The key upstream result is the anchor_ratio theorem, which states that when ZOf f = ZOf g the ratio massAtAnchor f / massAtAnchor g reduces to exp(((rung f - rung g) * log phi)).
proof idea
The tactic proof begins with a decide tactic establishing ZOf .t = ZOf .c. It then invokes the anchor_ratio lemma on .t and .c with that hypothesis. A subsequent simp [rung] followed by norm_num confirms the rung difference equals 6. The final simpa substitutes the difference into the exponential to obtain the target.
why it matters
This supplies the exponential form of the top-to-charm ratio that the downstream row_anchor_top_charm_ratio_rpow immediately rewrites as phi^6. It completes one of the Phase 0 quark rows (P0-Q01..P0-Q06) in the physical derivation plan by confirming the six-rung spacing on the phi-ladder between charm and top. The absolute MeV bridge to PDG values stays open pending a future SI/display mapping.
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