Spin(2,3) / Efimov Bridge

Purpose

This document houses the Level 5 Spin(2,3) -> Efimov bridge. It keeps the useful comparison while preventing the bridge from being treated as established core structure.

Claim level: 5, plausible but future work.

Safe Statement

The Spin(2,3) transport framework contains threshold surfaces where the reduced dynamics linearize in a scale-covariant way. Standard Efimov physics also arises from a scale-covariant, supercritical inverse-square problem after the Faddeev and hyperradial reductions.

The proposed bridge is that a three-state Spin(2,3) threshold collective mode may realize the same SO(2,1) Casimir structure that controls the Efimov exponent.

This is not yet derived.

Starting Point

The core framework supplies:

  • a T1 + T2 split under J^{01};
  • a reduced two-branch transport system;
  • persistence and locking thresholds;
  • a plausible SO(2,1) scaling sector near threshold;
  • a conjectural route from three near-boundary transport states to a three-body collective mode.

The Efimov derivations in derivations/ supply:

  • Faddeev channel decomposition;
  • Bethe-Peierls boundary conditions at unitarity;
  • hyperspherical reduction;
  • the symmetric channel eigenvalue;
  • eigenvalue-flow language for universality classes.

Bridge Map

Spin(2,3) object Efimov/Faddeev object Current level
Three near-boundary transport states Symmetric Faddeev channel triplet Level 5 embedding
Threshold SO(2,1) Casimir Supercritical inverse-square strength Level 5 equality
dot R ~= epsilon R Hyperradial scaling law Level 5 structural analogy
omega/kappa_u threshold data Unitarity-limit scaling data Level 5 quantitative test
Collective eigenvalue flow Efimov universality class Level 5 shared language

Main Gaps

  • Embed the Faddeev channel basis into Spin(2,3) transport-sector data.
  • Derive the SO(2,1) Casimir matrix from the Spin side.
  • Match the Faddeev recoupling kernel normalization without fitting.
  • Decide whether the Spin-side calculation recovers s_0 ~= 1.00624.
  • Determine what finite T1/T2 mixing means for range corrections or new universality classes.

Working Rule

Use this track as a quantitative test of the framework. Do not move its claims into the core documents or papers until the proof obligations are complete or explicitly marked as partially complete with limits.