No alternative stable state at beep scale in one long ESM affect series: a frozen drift-field transition-type assignment, its measured power, and a retracted positive finding

Abstract

A pre-registered quantitative test for alternative stable states in experience-sampling (ESM) mood series, and what came back. Result: no second attractor at beep scale. In the one series long enough for nonparametric drift estimation (1,476 observations, one participant, ten items plus a composite), every unit returned a single stable fixed point and no barrier - at both bandwidths, under both increment definitions, and in each of six contiguous windows (66/66 window fits). The null is informative rather than indeterminate: at this series length the instrument recovers two attractors in 80% of synthetic deep-well cases and 92.5-100% of 4-6 SD separations, against a 2.5% false-alarm rate. It is uninformative in principle, for any finite series, about barriers deep enough that the second state is never visited. v0.4 CORRECTS v0.3 ON THIS CLAIM. The power figures above were measured with no response-style distortion. Under a 20% central-tendency compression - an ordinary property of Likert self-report - detection of a 6 SD separation falls from 100% to 5%, while false alarms stay at zero, so compression is a pure false-negative mechanism. The null is therefore informative about series whose respondent used the scale without substantial compression and uninformative about series whose respondent did not, and which describes this participant is not established. Relatedly, four of the ten items deliver only 1.4-2.8 effective response levels, and an item yielding about two distinguishable values cannot resolve attractors 2 SD apart whatever produced the concentration. v0.4 also examines three further catastrophe flags. Reading the primary source (Gilmore 1981, via van der Maas & Molenaar 1992) established that there are eight, of which only three are anticipatory. Inaccessibility is negative with 93% power against a real barrier; anomalous variance is non-stationary but moves in the direction opposite to its own mechanism, under a specification committed to version control before its code was written. All three anticipatory flags are now accounted for and none supports anticipation here. Section 1's claim that the cusp-catastrophe literature was unsurveyed was false about this project's own operating frame and is replaced. The four-type transition classification tested here - bifurcation-induced, noise-induced and rate-induced tipping, and noise-induced diffusion - and its clinical assignment tree are published by Cui et al. (2025, doi:10.1037/abn0000991), in the Ashwin lineage, and are not claimed here. The contribution is a quantitative, frozen-before-execution version of one of their questions, run on observed rather than simulated series, with the instrument's power measured. Note for anyone using their decision tree: the openly accessible preprint prints its last two terminals reversed, and the erratum (doi:10.1037/abn0001061) is authoritative. This note includes a retraction, deliberately. A positive secondary finding survived four calibrated nulls before being explained by response degeneracy: the three items concerned are 67-84% a single Likert level, so the drift-field root flips between the gaps either side of the modal level while the mean stays pinned by the mass. The recommendation that follows - report the modal share of every series analysed, and treat it as a screening variable - is the part of this note most likely to be useful to others. Two further transferable results: the generators this project had calibrated on were themselves in the barrier-free regime at every separation ever tested; and detection power is in tension with its target, since seeing two attractors requires a series many dwell times long while a deep barrier is what makes the dwell long (empirically T >= 20-30 x dwell). Code, frozen specifications, calibration tables and all result documents, including the retraction: https://github.com/onsenojisan/esm-transition-type-assignment No participant data is redistributed; the deposited tables are derived summary statistics.