release(uncertainty): bind diagonal-Laplace variance to its fitted ALR location #664

Finding

Draft #639 now publishes per-document diagonal-Laplace variances with explicit ALR numerator/reference indexes (#662), but the release contract still omits the fitted ALR location that those variances approximate. topic_measurement::ReferenceTopicModel retains both document_topic_proportions and document_coordinate_variances; ReferenceTopicInput::build_joint_coordinate_precision already derives document-major ALR coordinate means from the fitted topic proportions. tepp.trsl_topic_lineage.v2 currently projects the variances only.

A variance without its fitted coordinate location is not a reconstructable posterior/Laplace coordinate. Two fits can share the same positive diagonal variance while having materially different document topic proportions and therefore different ALR locations. The current artifact cannot distinguish those states from the uncertainty payload alone, cannot reconstruct the local Gaussian approximation it names, and gives a downstream consumer no owner-issued location to pair with the released variance.

This is narrower than #663: #663 binds topic indexes to the fitted topic-term basis. This issue binds each document/ALR uncertainty quantity to the fitted location in that basis. It is also narrower than #658: source/vocabulary provenance remains Evidence-owned and must still be bound separately.

Required RED / contract

Before changing the unreleased v2 wire, prove at least:

1. an actual converged CPU reference fit yields one owner-issued document-coordinate row per admitted modeled document and exactly K-1 ALR coordinates per row;
2. every coordinate carries the fitted ALR location and the existing diagonal-Laplace variance under the same numerator/reference topic coordinate;
3. two otherwise compatible fitted states with equal variance but different topic proportions cannot share the same coordinate posterior state;
4. malformed document count, topic width, non-finite ALR location, missing/reordered coordinate, or non-positive/non-finite variance fails closed;
5. the projection does not manufacture joint covariance, independent plausible values, interval coverage, calibration, or source provenance.

Use an actual fitted/reference-model fixture for the positive path. Hand-authored model states may be used only for malformed-edge coverage.

Minimal owner direction

topic_measurement should first expose a read-only fit-owned document-coordinate posterior summary derived from the admitted ReferenceTopicInput plus converged ReferenceTopicModel: canonical document identity, ALR numerator/reference indexes, fitted ALR location, and the already-retained diagonal variance. Analysis should later project that owner output rather than recomputing ALR coordinates or curvature itself.

The summary is fit-local numerical evidence, not immutable Evidence provenance or semantic topic identity. #658/#527 must still bind source/vocabulary authority, and #663 must still bind topic coordinates to the fitted topic basis before external release authority is complete.

Scientific basis

A Laplace approximation is centered at an estimated posterior location/mode and uses local curvature to approximate uncertainty; retaining curvature/variance while dropping the location does not retain the approximation being claimed. Tierney and Kadane (1986) treat posterior location/moments and local Laplace curvature together, while Aitchison (1982) and Egozcue et al. (2003) establish that log-ratio coordinates are basis/reference dependent.

APA 7th:

• Aitchison, J. (1982). The statistical analysis of compositional data. Journal of the Royal Statistical Society: Series B (Methodological), 44(2), 139–160. https://doi.org/10.1111/j.2517-6161.1982.tb01195.x
• Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barceló-Vidal, C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3), 279–300. https://doi.org/10.1023/A:1023818214614
• Tierney, L., & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81(393), 82–86. https://doi.org/10.1080/01621459.1986.10478240

Boundary

topic_measurement owns the fitted numerical location/variance pair. Analysis owns the digest-bound consumer projection. No LLM inference, semantic topic naming, posterior sampling, tolerance-based repair, or source/vocabulary provenance substitution is authorized.

Keep #639 Draft. Refs #638 #639 #658 #662 #663 ADR 0012.