row_top_order_MeV
plain-language theorem explainer
The declaration establishes that the structural top-quark mass prediction lies between 10000 and 1000000 MeV. A physicist checking the Recognition Science phi-ladder mass scorecard would cite this row to confirm the order-of-magnitude placement at rung 51. The proof is a direct reference to the pre-established bounds on phi^51 in the Verification module.
Claim. Let $m_t^pred = phi^{51}/2000000$ (in MeV) where $phi$ is the golden ratio. Then $10000 < m_t^pred < 1000000$.
background
In the Recognition Science framework structural quark masses sit on the phi-ladder via the mass formula yardstick times phi to a power set by rung and gap(Z). The top-quark prediction is defined as phi^51 divided by 2000000 MeV and belongs to the UpQuark sector. The module supplies Phase 2 P2-t, the order-of-magnitude row for this mass; the upstream top_quark_pred_order theorem states that phi^51/2000000 lies in the multi-GeV range even without the full gap correction.
proof idea
The proof is a one-line wrapper that applies the top_quark_pred_order theorem from the Verification module. That theorem unfolds the definition of the prediction and invokes the precomputed bounds phi^51 in (45537548334, 45537549354) together with the Numerics.phi_pow51_gt lemma.
why it matters
This result populates the order_MeV field inside the TopQuarkMassScoreCardCert certificate. It supports the partial theorem status for the top quark, confirming the wide MeV interval on the phi-ladder without claiming sub-percent agreement with the PDG anchor 172690 MeV. The placement aligns with the self-similar fixed point forced in the T0-T8 chain and the Recognition Composition Law.
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