thermal_ratio_lt_one
The declaration proves that the room-temperature thermal ratio k_B T_room over the RS coherence quantum E_coh is strictly less than one. Materials scientists exploring ambient superconductivity would cite this bound to confirm coherence energy exceeds thermal fluctuations at 300 K. The proof is a one-line wrapper that unfolds the constant definition of the ratio and reduces it by numerical normalization.
claim$k_B T_{room} / E_{coh} < 1$, where $E_{coh} := phi^{-5}$ is the RS coherence quantum in native units.
background
In the Recognition Science setting of module EN-002, the coherence quantum is defined as E_coh = phi^(-5), the fundamental pairing energy scale on the phi-ladder. The thermal ratio at room temperature is supplied as the explicit constant 0.289, equal to k_B T_room / E_coh at T = 300 K. The module derives superconductivity conditions from the phi-ladder energy structure, requiring binding energy at least k_B T for Cooper pair formation.
proof idea
The proof is a one-line wrapper that unfolds the definition of thermal_ratio_room_temp and applies norm_num to confirm the numerical inequality.
why it matters in Recognition Science
This theorem completes EN-002.2 and feeds directly into the en002_certificate definition, which lists it among the verified conditions for room-temperature superconductivity. It supports the claim that phi-coherent pairing can overcome thermal fluctuations at ambient temperature, consistent with the phi-ladder hierarchy where E_n = E_coh * phi^n and E_coh = phi^{-5}.
scope and limits
- Does not establish existence of materials satisfying the coherence condition.
- Does not compute explicit critical temperatures for given phi-rungs.
- Does not address pressure tuning of the phi-ladder.
- Does not prove experimental observability of the predicted effect.
formal statement (Lean)
65theorem thermal_ratio_lt_one : thermal_ratio_room_temp < 1 := by
proof body
Term-mode proof.
66 unfold thermal_ratio_room_temp
67 norm_num
68
69/-- **THEOREM EN-002.3**: Room temperature thermal ratio is positive. -/