feat(psychometric): recover Driver p.16 DIFFUSIONstd after positive asymDIFFUSION

[seonghobae]

Stacked on #188 (444304d) / #187 (6afd048) / #185 (69ffec6) / #184 (6b93147) / #183 (c10097be) / #182 (2d4d6bf) / #181 (542806b) / #49 (6f95142). ADR 0005 executable slice stays inside psychometric_core. This is not a second invariance crate and does not recreate #78 or #80.

psychometric_core recovers the Driver, Oud, and Voelkle (2017, p. 16 DIFFUSIONstd; Eq. 4, p. 5; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T13:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised continuous DIFFUSION. Page 16 prints continuous-time parameters (e.g., DRIFT, DIFFUSION) and, when appropriate, standardised matrices with the suffix std. Footnote 4: standardisations use only the relevant variance, not the total. Process noise is within-subject stochastic input, so that relevant variance is within-subject asymDIFFUSION -q / (2 a), the same footnote 4 variance used for DRIFT.

Form strictly positive asymDIFFUSION first, then q / (-q / (2 a)). In the scalar stationary case that ratio equals -2 a and does not depend on q once q > 0.

• Unstandardised q is defined for growing a ≥ 0 and for zero diffusion; standardised DIFFUSION is not.
• Zero asymDIFFUSION has no positive SD and fails closed (StandardisedContinuousDiffusionRequiresPositiveWithinSubjectVariance).
• a ≥ 0 cannot form finite asymDIFFUSION and fails closed (StationaryVarianceRequiresStableDrift).
• The discrete standardisation Q_Δt / (-q / (2 a)) = 1 - exp(2 a Δt) depends on the event interval and is not DIFFUSIONstd.
• Section 7.1 warns that omitting trait variance confounds between- and within-person information. q / (trait + p + added) uses the total, not asymDIFFUSION, and is not DIFFUSIONstd when TRAITVAR is nonzero.
• TRAITVAR is not the footnote 4 standardisation variance.

Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation. Meredith (1993) remains unread (Unpaywall 2026-08-23T13:19Z: is_oa: false; title Measurement Invariance, Factor Analysis and Factorial Invariance). Mislevy (1991, Psychometrika, 56, 177–196) remains unread (Unpaywall 2026-08-23T13:19Z: is_oa: false; title Randomization-Based Inference about Latent Variables from Complex Samples).

Do not merge, self-approve, or request Copilot.

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[seonghobae]

Folded into the consolidation vehicle #231; this draft stays open until the vehicle merges, then closes as superseded-by-consolidation.