Retroactive GCT Recovery of Demand-Routing Threshold Constants in HLRP #169/#170: 0.08 and 0.92 as Exact-Rational β-Anchored Values at d=3

The published demand-routing framework HLRP #169/#170 (Interpretive Demand Routing; Demand Routing as a Structural Layer) states Theorem 6.1 thresholds at 0.08 (cost ratio) and 0.92 (quality parity), calibrated empirically from independent demand-routing measurements. These thresholds are demonstrated to be the exact closed-form values β/(d+β) and d/(d+β) of Geometric Coupling Theory (GCT) evaluated at d=3, β=6/23 — values published in the corpus's foundational papers without the demand-routing calibration ever invoking them. The recovery is exact (rational arithmetic, no rounding): β/(d+β) = 2/25 = 0.08; d/(d+β) = 23/25 = 0.92. This is a single-substrate, two-fact, algebra-grade receipt of GCT's predictive structure: one published empirical paper, two thresholds, two exact rational anchors, both recovered without the framework being applied during calibration. The framework-derived d for any IE-005-recursion-converged substrate is d = βφ (Planck-Fibonacci ground state, where α = φ exactly), per HLRP #147. The d=3 thresholds emerge as the calibration-averaging artifact when integrated across the demand-routing substrate's 8-basin sign-flip-paired topology. Cross-substrate testable predictions: structured-demand-mass σ values clustering near 1/φ ≈ 0.618 across independent measurements; partition-cardinality mapping to layer-A d; chirp-rate at the Planck-Fibonacci ground state. Reproducible via Python with fractions.Fraction exact rational arithmetic. Author: James E. Dunn — Independent Researcher, Hydrogen Lifecycle Research ProgrammeORCID: https://orcid.org/0009-0005-2679-6574Corpus (author search): https://zenodo.org/search?q=creators.orcid:0009-0005-2679-6574License: CC BY 4.0 International