The Floor-Receipt: α = 2 as Threshold-Crossing, Not Residence

The coupling coefficient α(d,β) = 1 + d/(d+β), β = 6/23, reframed as a floor-structure: a ladder of discrete floors (φ ground, 48/25 attractor, 2 ceiling) over a continuous complexity coordinate d. The cascade gap telescopes — from any floor it sums to exactly 2 − α. Since α ∈ (1,2) strictly, 2 is a threshold-receipt, never a residence; exceeding it requires a sign-flip. Two crossings (graceful climb / catastrophic drop) with the branch set by a measurable selector (NASA Li-ion: interphase sign-flip at DoD×C-rate ≈ 25). Fork-structured prediction — precise at the coordinate, probabilistic at the outcome; the at-chance cardiac forward-test reported as a negative. Author: James E. Dunn — Independent Researcher, Hydrogen Lifecycle Research ProgrammeORCID: https://orcid.org/0009-0005-2679-6574Corpus: zenodo.org author search · SciX · ADSLicense: CC BY 4.0 International