row_top_quark_in_band
plain-language theorem explainer
The structural top-quark mass prediction, given by phi to the 51st power divided by two million, lies strictly between 10 GeV and 1 TeV. Recognition Science mass-ladder work cites this row to locate the top quark on the phi-ladder at rung 21 before any gap correction. The proof is a direct one-line application of the pre-established order theorem for that explicit phi expression.
Claim. The top-quark structural mass prediction satisfies $10000 < {phi}^{51}/2000000 < 1000000$, where $phi$ is the golden-ratio fixed point of the Recognition Composition Law.
background
The Quark Score Card module consolidates theorem-grade facts for the quark sector as Phase 0 rows P0-Q01 through P0-Q06. It records existing proofs without new physics and notes that charm/up equals phi to the 11, top/charm equals phi to the 6, and all structural quark predictions remain positive. The top-quark prediction itself is defined in the Verification module as the UpQuark sector mass at rung 21.
proof idea
This is a one-line wrapper that invokes the theorem top_quark_pred_order. That upstream result unfolds the definition of top_quark_pred and applies pre-computed bounds on phi to the 51st power obtained from phi_eq_goldenRatio together with Numerics.phi_pow51_gt.
why it matters
The row completes P0-Q06 of the physical derivation plan and is invoked by quarkScoreCardCert_holds to certify the full scorecard collection. It is also referenced directly in row_top_in_band_scorecard of the TopQuarkMassScoreCard module. The result supports the phi-ladder mass formula of the Recognition framework and confirms the top-quark scale before the gap(ZOf f) correction from RSBridge.Anchor.massAtAnchor is applied; the remaining open question is absolute mass agreement inside PDG bands.
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