[Scientific Gap] Implement the shared-latent temporal topic CPU f64 reference estimator

[seonghobae]

Buyer problem

TEPP has accepted topic-model requirements, compositional coordinate work in #48, model-selection gates in #67, and many surrounding temporal/relation/membership contracts. Protected main still lacks the production estimator that turns a cutoff-safe corpus into posterior topic measurements with structural covariates and uncertainty. Without that engine, TEPP cannot substantiate its central product claim.

Required estimator

Implement the CPU f64 reference for the approved Temporal Relational Shared-Latent Topic Measurement family. The first release must be deliberately bounded but scientifically complete for its stated model:

• one global topic identity set across the analysis window;
• logistic-normal document/topic coordinates;
• prevalence covariates;
• explicit time, relation, and weighted cross-classified/multiple-membership effects;
• shared-concept channel plus native lexical evidence where admitted by validated profiles;
• posterior uncertainty and deterministic/reproducible fitting controls;
• activation, dormancy, and reactivation without identity reminting.

Existing related work

• feat(topic): logistic-normal ALR coordinates with true-parameter RMSE #48 provides ALR/ILR/logistic-normal coordinate contracts, not fitting.
• feat(concept): language-profile gates with shared-space RMSE #53 provides language-profile/concept gates, not semantic preprocessing or estimation.
• feat(model): statistical Pareto K gates refuse LLM numerical authority #67 provides admissibility/Pareto selection, not candidate fitting.
• feat(topic): keep one identity across dormancy and reactivation #73 provides topic activity identity, not a topic posterior.
• tepp_simulation and validation_core provide known-truth and metric foundations.

This issue owns the estimator vertical and should consolidate compatible fragments rather than introduce another façade crate with no production arithmetic.

Acceptance criteria

• The model likelihood/objective and estimands are fixed in an accepted ADR/TRD update with equation-to-source traceability and APA 7 references.
• Production arithmetic is Rust CPU f64; Python/R may be independent oracles only.
• Sparse CSR/CSC inputs and bounded fixed worker pools are used; deterministic reduction mode is available.
• The estimator accepts only validated cutoff-safe snapshots and explicit relation/membership design matrices.
• Raw topic proportions, TF-IDF, BM25, stopword-deletion weights, LLM labels, and retrieval scores cannot enter the estimator as inferential coordinates.
• Multiple initializations and seeds produce explicit convergence diagnostics; failed convergence is a typed failure.
• Posterior topic coordinates, prevalence/content parameters, covariance, uncertainty, and model-fit diagnostics are emitted in versioned artifacts.
• Known-truth simulations recover topic identities after identified matching and report computed RMSE, bias, interval coverage, convergence, and collapse rates across corpus size, sparsity, overlap, imbalance, time, and membership conditions.
• Relation-aware split and rolling-origin tests prove no future-availability or revision/translation/episode leakage.
• A comparison against a verified independent implementation or analytically tractable fixtures is documented; discrepancies fail closed.
• Production statement/branch coverage and public docs remain 100%; property/fuzz/numerical edge tests cover singular, empty, nonfinite, extreme, and label-switching cases.
• The estimator is wired to model_selection so candidate K evaluation executes real fitted models rather than metadata-only candidates.

Explicit non-claims

The first implementation need not claim every neural/polylingual backend, topic birth/split/merge, full Bayesian sampling, or GPU acceleration. It must not call a coordinate transformation or OLS gate a topic estimator.

Authority

Follow ADR 0012, the approved PRD, TRD, and the repository research register.