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feat(psychometric): recover Driver p.16 asymCINTstd after positive p - #216

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feat(psychometric): recover Driver p.16 asymCINTstd after positive p#216
seonghobae wants to merge 1 commit into
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Stacked on #213 (discreteCINTstd). Next unique licensed map on this ancestry is footnote-4 standardisation of 2017-era asymCINT. Do not duplicate #195 CINTstd. TDPREDVARstd is commented out in the 2017-era source and is not recovered.

Driver, Oud, and Voelkle (2017, p. 16; Eq. 3, p. 4; footnote 4; Table 2, p. 12; JSS PDF re-opened 2026-08-24T09:05Z) print standardised matrices with the suffix std when appropriate. Footnote 4 standardises using only the relevant variance. CINT is the process intercept of individual, or average individual, dynamics, so that relevant variance is within-subject asymDIFFUSION p = −q / (2 a). The 2017-era summary.ctsemFit.R forms asymCINT whenever verbose = TRUE:

asymCINT <- -solve(DRIFT) %*% CINT

That source does not form an asymCINTstd matrix. The scalar map here is the footnote 4 standardisation of that named asymptotic intercept: (-κ / a) / √p.

Recovery

  • recover_standardised_asymptotic_continuous_intercept(κ, q, a, clock) forms strictly positive p first, then the asymptotic intercept, then divides by √p.
  • A zero intercept is exactly zero.
  • A later event interval changes discreteCINTstd and not this map.
  • Zero q fails closed. Unstandardised asymCINT is defined for a zero process; standardised asymCINT is not.
  • Non-event clock fails closed.
  • a ≥ 0 fails closed (lasting asymDIFFUSION requires stable drift).

Claim boundary

  • Unstandardised asymCINT is not asymCINTstd.
  • κ / √p is the continuous intercept standardisation and is not this total-change map.
  • A^{-1}[e^{A Δt} − I] κ / √p depends on the event interval and is not this Δt → ∞ map.

Meredith (1993) and Mislevy (1991) remain closed (Unpaywall 2026-08-24T08:02Z: is_oa: false, 0 locations).

Do not merge without an independent APPROVE plus exact-head required-check success. Do not self-approve. Do not request Copilot.

Form strictly positive asymDIFFUSION, then (−κ/a) / √p.
Distinct from κ/√p and from discreteCINTstd. The 2017-era source forms
asymCINT and does not form an asymCINTstd matrix.
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@seonghobae

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

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Superseded by consolidation: this slice's Driver et al. (2017) standardization recovery landed on protected main through the integration vehicles (#231/#232), and its contract coverage is carried by the reconciled suites (multilevel_event_time_recovery_contract, rubin_and_mean_gate_contract) with test-signature repair tracked in #234. The stacked-draft form is retired to keep the delivery queue at review-ready work only; no capability is lost — the exact-head provenance remains in the vehicle PR descriptions and CHANGELOG.

@seonghobae seonghobae closed this Aug 25, 2026
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