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

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. 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.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-30
DOI
https://doi.org/10.5281/zenodo.21703786
Primary Topic
Mental Health Research Topics
Type
preprint
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preprint

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

Hiroaki Aizawa
Zenodo (CERN European Organization for Nuclear Research)
Mental Health Research Topics
preprint

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

Hiroaki Aizawa
preprint en

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. 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.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Mental Health Research Topics
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