-- The metadata column (meta_version 1, docs/mvp-design.md section 4) carries
-- everything predict_glm() will need to rebuild the design matrix. jsonb
-- normalizes key order, so jsonb_pretty() and -> / ->> output are stable.
CREATE TEMP TABLE t_meta (
    y      double precision,
    x1     double precision,
    gender text
);
INSERT INTO t_meta VALUES
    (1.2, 0, 'F'), (2.3, 1, 'M'), (3.1, 2, 'Other'),
    (1.8, 3, 'F'), (2.9, 4, 'M'), (3.7, 5, 'Other'),
    (2.1, 6, 'F'), (3.3, 7, 'M'), (4.2, 8, 'Other');
-- DISTINCT proves every coefficient row carries the identical metadata.
SELECT DISTINCT jsonb_pretty(metadata) AS metadata
FROM fbsql.fit_glm(
    relation => $$ SELECT y, x1, gender FROM t_meta $$,
    formula  => 'y ~ x1 + gender',
    family   => 'gaussian');
              metadata               
-------------------------------------
 {                                  +
     "xlevels": {                   +
         "gender": [                +
             "F",                   +
             "M",                   +
             "Other"                +
         ]                          +
     },                             +
     "response": "y",               +
     "contrasts": {                 +
         "gender": "contr.treatment"+
     },                             +
     "intercept": true,             +
     "coef_terms": [                +
         "(Intercept)",             +
         "x1",                      +
         "genderM",                 +
         "genderOther"              +
     ],                             +
     "term_labels": [               +
         "x1",                      +
         "gender"                   +
     ],                             +
     "data_classes": {              +
         "y": "numeric",            +
         "x1": "numeric",           +
         "gender": "factor"         +
     },                             +
     "meta_version": 1              +
 }
(1 row)

-- Individual field access, as predict_glm() will consume it.
SELECT DISTINCT
       metadata ->> 'meta_version' AS meta_version,
       metadata ->> 'response'     AS response,
       metadata -> 'term_labels'   AS term_labels,
       metadata -> 'coef_terms'    AS coef_terms
FROM fbsql.fit_glm(
    relation => $$ SELECT y, x1, gender FROM t_meta $$,
    formula  => 'y ~ x1 + gender',
    family   => 'gaussian');
 meta_version | response |   term_labels    |                   coef_terms                    
--------------+----------+------------------+-------------------------------------------------
 1            | y        | ["x1", "gender"] | ["(Intercept)", "x1", "genderM", "genderOther"]
(1 row)

SELECT DISTINCT
       metadata -> 'data_classes' AS data_classes,
       metadata -> 'xlevels'      AS xlevels,
       metadata -> 'contrasts'    AS contrasts
FROM fbsql.fit_glm(
    relation => $$ SELECT y, x1, gender FROM t_meta $$,
    formula  => 'y ~ x1 + gender',
    family   => 'gaussian');
                     data_classes                      |             xlevels             |           contrasts           
-------------------------------------------------------+---------------------------------+-------------------------------
 {"y": "numeric", "x1": "numeric", "gender": "factor"} | {"gender": ["F", "M", "Other"]} | {"gender": "contr.treatment"}
(1 row)

-- Numeric-only model: xlevels and contrasts must be empty objects.
SELECT DISTINCT
       metadata -> 'xlevels'    AS xlevels,
       metadata -> 'contrasts'  AS contrasts,
       metadata -> 'coef_terms' AS coef_terms
FROM fbsql.fit_glm(
    relation => $$ SELECT y, x1 FROM t_meta $$,
    formula  => 'y ~ x1');
 xlevels | contrasts |      coef_terms       
---------+-----------+-----------------------
 {}      | {}        | ["(Intercept)", "x1"]
(1 row)