fix(simulation): region baseline latitude — equator-anchored signed rows (T-1186)

region_centre_latitude_deg mapped row 0 to the north pole with lat_frac
clamped [0,1] while the derive core floor-divides equator-anchored signed
world metres — every northern-hemisphere region clamped to +90 (polar
everywhere) and the southern hemisphere read as compressed northern
tropics. Now mirrors the derive core's exact inverse mapping (lat_frac =
centre_y/meridian clamped [-0.5,0.5], lat = -frac*180). The ticket's
in-the-wild datapoint flips as predicted: GJ338Bd region (136,43), old
baseline +13.94N/26.8C -> new -76.06S/10.3C; the 76S district cell now
derives Lake/2.07C/Light glaciation. Goldens regenerated (believability +
window derivation, stable on rerun); two region_profile unit tests
repositioned — their probe coordinates meant different places under the
old convention. step_canvas rung-0 already used the correct signed
convention; layer_proxy's pole-anchored pseudo-grid stays deferred to
T-1181's rung-0 rebuild per D-256(f).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

server/src/atlas/region_profile.rs

@@ -258,11 +258,32 @@ pub fn derive_region_baseline_c(
 
 /// Compute the latitude of a region centre from its grid position.
 ///
-/// The region grid is equirectangular. Row 0 sits at the north pole; the
-/// equator is in the middle. Returns degrees: +90.0 = north pole, −90.0 =
-/// south pole.
+/// **Equator-anchored SIGNED row convention (T-1186 fix)** — this MUST mirror
+/// the canonical derive core's own inverse mapping
+/// (`derive_at_metres_with_riparian`, district_profile.rs: `lat_frac = (wy /
+/// meridian_m).clamp(-0.5, 0.5)`, `lat_deg = -lat_frac * 180.0`, keyed on
+/// equator-anchored signed world metres via `district_to_region`'s
+/// `div_euclid`). `region_pos.1` is therefore SIGNED: negative rows are
+/// north, positive rows are south, row 0 straddles the equator — NOT the
+/// pole-anchored non-negative convention this function used before T-1186
+/// (row 0 = north pole, `lat_frac` clamped to `[0, 1]`), which silently
+/// disagreed with the derive core it feeds (D-256(a): one absolute-metre
+/// derive core, one inverse mapping — this was the second, wrong, mapping).
+///
+/// Returns degrees: +90.0 = north pole, −90.0 = south pole.
 ///
 /// If no body radius is available (tiny test bodies), the region lat is 0.0.
+///
+/// **Convention note (T-1186 audit):** two OTHER call sites in this codebase
+/// still use the old non-negative pole-anchored row convention and do NOT
+/// call this function — `step_canvas::build_step_canvas`'s Global (rung-0)
+/// canvas (deliberately switched to signed-equator rows ahead of this fix,
+/// see its doc comment) and `layer_proxy::build_region_grid` /
+/// `cascade::LayerRegionOutput` (still pole-anchored, non-negative `ry`,
+/// D-256(f)-deferred to T-1181's rung-0 rebuild — its sole reader is the
+/// stale body-view overlay, no consumer disagreement in this ticket's blast
+/// radius). See T-1186's report for the proposed one-convention unification;
+/// this function's fix does not by itself touch either of those call sites.
 pub fn region_centre_latitude_deg(region_pos: RegionPos, body_radius_km: Option<f64>) -> f64 {
     let Some(r_km) = body_radius_km else {
         return 0.0;
@@ -270,13 +291,17 @@ pub fn region_centre_latitude_deg(region_pos: RegionPos, body_radius_km: Option<
     if r_km <= 0.0 {
         return 0.0;
     }
-    // The meridian spans πR km. Each region is REGION_M metres tall.
-    // region_y = 0 maps to the north pole (lat +90), rising y → south.
+    // The meridian spans πR km. Each region is REGION_M metres tall,
+    // equator-anchored: region row 0 straddles the equator, negative rows
+    // are north (mirrors district_to_region's div_euclid on signed,
+    // equator-anchored district positions).
     let meridian_m = std::f64::consts::PI * r_km * 1_000.0;
     let region_centre_y_m = (region_pos.1 as f64 + 0.5) * scale::REGION_M as f64;
-    // Clamp: lat_frac in [0, 1]; 0 = N pole (+90°), 1 = S pole (−90°).
-    let lat_frac = (region_centre_y_m / meridian_m).clamp(0.0, 1.0);
-    90.0 - lat_frac * 180.0
+    // Clamp: lat_frac in [-0.5, 0.5]; -0.5 = N pole, +0.5 = S pole — the exact
+    // inverse of derive_at_metres_with_riparian's `lat_frac = (wy /
+    // meridian_m).clamp(-0.5, 0.5)`.
+    let lat_frac = (region_centre_y_m / meridian_m).clamp(-0.5, 0.5);
+    -lat_frac * 180.0
 }
 
 /// Build a [`RegionProfile`] for the region at `region_pos`.
@@ -611,12 +636,16 @@ mod tests {
 
     #[test]
     fn equatorial_region_is_warmer_than_polar() {
-        // With a body radius, north-pole region vs equatorial region.
+        // T-1186: region rows (RegionPos.1, the Y/row component — RegionPos is
+        // (x, y)) are equator-anchored SIGNED (row 0 straddles the equator;
+        // negative = north, matching the derive core's floor-divide of
+        // equator-anchored world metres). Region (0, 0) is therefore near the
+        // EQUATOR, not the pole — (0, -97) is the genuinely polar region on
+        // this Earth-radius test body (~97.7 regions pole-to-pole).
         let params = earth_params();
         let constants = ClimateConstants::default();
-        // Region (0, 0) is near the north pole; (97, 15) is roughly equatorial.
-        let polar = build_region_profile(body_seed(), &params, &constants, (0, 0));
-        let equatorial = build_region_profile(body_seed(), &params, &constants, (97, 15));
+        let polar = build_region_profile(body_seed(), &params, &constants, (0, -97));
+        let equatorial = build_region_profile(body_seed(), &params, &constants, (0, 0));
         match (polar.clock.mean_temp_c, equatorial.clock.mean_temp_c) {
             (Some(p), Some(e)) => assert!(
                 p < e,
@@ -746,12 +775,23 @@ mod tests {
 
     #[test]
     fn edge_fuzz_varies_with_body_id() {
+        // T-1186: (50, 50) sat right at the equator under the new
+        // equator-anchored-signed row convention (region row 0), where
+        // earth_params()'s ocean/breathable/temperate band saturates at the
+        // 28°C warm ceiling for every neighbour regardless of warp — a
+        // fix-induced false negative, not a real regression (the OLD
+        // pole-anchored convention happened to place row 0 near the pole,
+        // where the band isn't saturated). (50, 2400) — a mid-latitude
+        // district — also turned out to be a coincidental warp collision at
+        // this seed (both bodies landing on the same blend). (73, 2455) is a
+        // confirmed non-degenerate probe: comfortably inside the unsaturated
+        // band with the two bodies' warps genuinely diverging.
         let params = earth_params();
         let constants = ClimateConstants::default();
         let a = region_baseline_at_district(
             42,
             "BodyA",
-            (50, 50),
+            (73, 2455),
             &params,
             &constants,
             body_seed(),
@@ -760,7 +800,7 @@ mod tests {
         let b = region_baseline_at_district(
             42,
             "BodyB",
-            (50, 50),
+            (73, 2455),
             &params,
             &constants,
             body_seed(),