high_tc_implies_phi_gt_one
plain-language theorem explainer
The theorem isolates the lower bound on the golden ratio from the ledger definition of high-Tc superconductivity. Condensed-matter modelers using the Recognition Science phi-ladder would cite it to fix the scaling rung for critical temperatures. The proof is a direct term projection that extracts the left conjunct of the defining conjunction.
Claim. If high-temperature superconductivity satisfies the ledger condition, then the golden ratio obeys $1 < phi$.
background
Recognition Science places the golden ratio phi as the self-similar fixed point forced at step T6 of the unified forcing chain. The sibling definition high_tc_superconductivity_from_ledger encodes the ledger condition as the conjunction $1 < phi land phi < 2$. This theorem extracts the lower half of that interval, placing high-Tc phenomena inside the phi-ladder mass formula and the eight-tick octave.
proof idea
The term-mode proof applies the first projection to the hypothesis high_tc_superconductivity_from_ledger. No lemmas are invoked; the conjunction is opened directly by the field selector.
why it matters
The result brackets phi inside (1,2) together with its sibling high_tc_implies_phi_lt_two, consistent with the RS-native constants c=1, hbar=phi^{-5} and the alpha band. It supplies the lower edge required by the phi-ladder yardstick for mass and energy scales but does not yet link to a specific high-Tc material realization.
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