row_top_charm_structural_anchor_agree
plain-language theorem explainer
row_top_charm_structural_anchor_agree establishes that the structural top-to-charm quark mass ratio equals the anchor mass ratio for those flavors. Researchers verifying quark mass hierarchies and within-family consistency in Recognition Science would cite this result. The term proof rewrites the equality by substituting the structural top-charm ratio theorem and the anchor top-charm ratio theorem.
Claim. $m_t^{pred} / m_c^{pred} = M_{anchor}(t) / M_{anchor}(c)$, where the left side is the structural rs_mass_MeV prediction ratio and the right side is the native anchor expression with gap-corrected phi-ladder exponent.
background
The Quark Absolute Bridge Score Card module deepens QuarkScoreCard by proving agreement between the structural rs_mass_MeV formula and the equal-Z anchor bridge on within-family ratios for u/c/t. rs_mass_MeV is the sector yardstick in displayed MeV that includes the 10^6 reporting divisor; massAtAnchor is the native RSBridge.Anchor expression yardstick * phi^(rung - 8 + gap(ZOf f)). The module states that the absolute MeV bridge remains a partial theorem because the two anchors differ in display handling. Upstream, row_anchor_top_charm_ratio_rpow gives massAtAnchor .t / massAtAnchor .c = phi^6 after rewriting the exponential form and applying Real.rpow_def_of_pos.
proof idea
The term proof is a direct rewrite that substitutes row_structural_top_charm_ratio_rpow on the structural side and row_anchor_top_charm_ratio_rpow on the anchor side, equating the two ratios without additional computation or case analysis.
why it matters
This supplies the top_charm_ratio_agrees field to quarkAbsoluteBridgeScoreCardCert_holds, which constructs the full Nonempty QuarkAbsoluteBridgeScoreCardCert. It fills Phase 0 row P0-Q06 in the physical derivation plan. In the Recognition Science framework the result confirms the phi^6 ratio on the phi-ladder for the top-charm pair, consistent with the self-similar fixed point phi and the eight-tick octave. The absolute calibration to PDG MeV values stays open pending resolution of the SI/display bridge.
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