pith. sign in
def

referenceStrength

definition
show as:
module
IndisputableMonolith.Materials.BCSPairingFromPhiLadder
domain
Materials
line
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plain-language theorem explainer

The declaration fixes the base BCS pairing strength at the dimensionless value 1 in RS-native units. Materials physicists modeling superconductor gap ratios on the phi-ladder cite it to anchor rung-zero predictions for conventional BCS compounds. It is a direct constant definition requiring no lemmas or reduction steps.

Claim. The reference pairing strength is defined by $1$ (dimensionless) at rung zero of the phi-ladder, so that the strength at rung $k$ equals $1$ times $phi^k$.

background

The module sets out BCS Cooper-pair binding on the phi-ladder: the dimensionless ratio sits at integer rungs with adjacent material classes differing by exactly phi. Conventional BCS (Sn, Pb, Nb) occupy rung 0 with empirical ratio near 1.76; intermediate and strong-coupling classes occupy rungs 1 and 2. The reference value normalizes the ladder base before scaling by phi^k. Upstream rung definitions supply the integer indices for sectors and material classes but are not invoked in this constant.

proof idea

Direct constant definition assigning the real number 1; no lemmas, tactics, or reductions are applied.

why it matters

The constant anchors pairingStrength, which scales by phi^k to generate the predicted gap ratios across BCS classes and high-Tc materials at rungs 3-4. It supplies the structural base for the Recognition Science phi-ladder prediction in the materials domain, consistent with the self-similar fixed point forced in the T0-T8 chain. No open scaffolding questions are attached to this definition.

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