pith. sign in
module module moderate

IndisputableMonolith.Materials.BCSPairingFromPhiLadder

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This module defines the reference BCS pairing strength as the RS-native dimensionless unit 1 and supplies scaling functions for pairing strength along the phi-ladder. Condensed matter researchers applying Recognition Science to superconductors would cite these definitions when computing pairing energies. The module is definitional, establishing positivity, monotonicity, and ratio properties for the sequence without complex proofs.

claimThe reference BCS pairing strength is the RS-native dimensionless constant equal to 1. The pairing strength at phi-ladder rung $r$ is a positive, strictly increasing function of $r$ with adjacent ratios fixed by the self-similar structure.

background

The module sits in the Materials domain and imports Constants, whose doc-comment states that the fundamental RS time quantum is the RS-native quantity with value 1 tick. It introduces the reference BCS pairing strength as the dimensionless unit 1 together with the pairingStrength function that maps rungs on the phi-ladder to pairing values. The setting draws on the phi-ladder mass formula and the eight-tick octave from the upstream forcing chain.

proof idea

This is a definition module, no proofs. It sets the reference value at 1, defines the pairing strength sequence, and records elementary lemmas establishing positivity, strict increase, and adjacent ratios.

why it matters in Recognition Science

The module supplies the foundational definitions for BCS pairing strengths that feed into broader materials theorems in the Recognition Science framework. It links pairing to the phi-ladder structure from T6 (phi fixed point) and T7 (eight-tick octave). No downstream uses are recorded yet, but the definitions support derivation of physical constants in the alpha band.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (8)