predicted_tc_ratio
plain-language theorem explainer
The definition states that the critical temperature ratio between phi-ladder rungs n and m equals phi raised to the power (n-m). Materials scientists scaling predicted Tc values for high-temperature superconductors would cite it when mapping observed transitions near 130-160 K to rungs 20-22. The definition is a direct power expression with no lemmas or tactics applied.
Claim. The ratio of critical temperatures on phi-ladder rungs $n$ and $m$ equals $phi^{n-m}$, where $phi$ is the golden ratio and the rungs label quantized coherence levels.
background
Recognition Science places superconductivity on the phi-ladder with pairing energies $E_n = E_{coh} phi^n$, where $E_{coh} = phi^{-5}$ eV exceeds room-temperature thermal energy. The module EN-002 derives ambient superconductivity conditions from this structure, requiring coherent ledger states so that binding energy overcomes $k_B T$ at 300 K. Upstream interfaces ensure collision-free programs and simplicial edge lengths that keep the ladder well-defined.
proof idea
Direct definition that sets the ratio to the power expression $phi^{(n-m)}$. No lemmas are invoked and no tactics are used; the body is the literal exponentiation.
why it matters
The definition supplies the scaling factor used by the downstream theorem tc_ratio_formula, which unfolds both sides and applies the zpow subtraction rule to obtain the ratio identity. It completes step EN-002.14 in the room-temperature superconductivity derivation and connects to the phi-ladder monotonicity result and the foundational eight-tick octave. It leaves open the material-specific assignment of rungs at ambient pressure.
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