feat(skirt-weights): back pin zone, seam tie ramp, ride t-gate, spatial smoothing

Wrap final recipe + pugu arc (pairs with ariki-game b8c439d6c):
- SKIRT_PIN_BACK: the pin/snap/seam zone now mirrors to the BACK centerline —
  the back hem wedged open at full split exactly like the front did.
- Seam is a RAMP (own thigh at the zone edge -> 50/50 at the centerline):
  a flat 50/50 band stepped 1.0->0.5 and read as a cut at full split.
- SKIRT_RIDE_T_LO: keeps the belly rope pure pelvis (ride skips the top band).
- SKIRT_SMOOTH_W/K: same-side kNN Laplacian weight smoothing — kills the
  stretch-notch triangles at the hem at run; centerline snap stays crisp,
  rope band skipped.

clothing/skirt_garment_weights.py

@@ -209,6 +209,10 @@ RIDE_T_LO = _envf("SKIRT_RIDE_T_LO", 0.0)
 # that is already there" (Ozan: "can you just put the bone where the error
 # persists"). 0 (default) = off.
 PIN_FRONT = _envf("SKIRT_PIN_FRONT", 0.0)
+# BACK half of the pin zone (2026-08-23, wrap run-from-behind: back hem wedges
+# opened at full split). Same window/snap/seam as the front, measured off the
+# BACK centerline. 0 (default) = back unpinned (approved-garment safe).
+PIN_BACK = _envf("SKIRT_PIN_BACK", 0.0)
 PIN_AZ_LO = _envf("SKIRT_PIN_AZ_LO", 20.0)
 PIN_AZ_HI = _envf("SKIRT_PIN_AZ_HI", 70.0)
 PIN_T_LO = _envf("SKIRT_PIN_T_LO", -0.4)
@@ -231,6 +235,16 @@ PIN_SNAP = _envf("SKIRT_PIN_SNAP", 0.0)
 # between the legs, and parks at the midpoint BETWEEN them (never inside a
 # leg). 2026-08-23: flat 50/50 band → ramp (its 1.0→0.5 step read as a cut).
 PIN_SEAM = _envf("SKIRT_PIN_SEAM", 0.0)  # degrees each side of front center
+# SPATIAL WEIGHT SMOOTHING (2026-08-23, Ozan run review: "running creates too
+# many small triangles at the bottom — can't we smooth those stretch
+# triangles"): stretch notches are NEIGHBOURING verts with divergent weight
+# vectors shearing apart mid-stride. Laplacian pass after the main loop: each
+# vert blends SMOOTH_W toward the mean of its SMOOTH_K nearest rest-position
+# neighbors — SAME snap side only (the centerline snap/tie discontinuity must
+# survive) and the top band is skipped (rope stays pure pelvis). 0 = off
+# (default; approved recipes reproduce bit-identical).
+SMOOTH_W = _envf("SKIRT_SMOOTH_W", 0.0)
+SMOOTH_K = int(_envf("SKIRT_SMOOTH_K", 4.0))
 MAX_INFLUENCES = 4
 
 COMP_FMT = {5120: "b", 5121: "B", 5122: "h", 5123: "H", 5125: "I", 5126: "f"}
@@ -514,7 +528,7 @@ def main():
         # pants/SOLID4 branches — those pack and `continue`, so a post-pass after
         # them never sees the hem verts (first attempt changed nothing, measured).
         pinned = False
-        if PIN_FRONT > 0.0 and tube_fwd is not None:
+        if (PIN_FRONT > 0.0 or PIN_BACK > 0.0) and tube_fwd is not None:
             fwd_ang = math.atan2(tube_fwd[1], tube_fwd[0])
             rel = abs((math.atan2(v[2] - pelvis[2], v[0] - pelvis[0])
                        - fwd_ang + math.pi) % (2 * math.pi) - math.pi)
@@ -523,25 +537,32 @@ def main():
             # the left while walking"): a HARD pin boundary tears a wedge where
             # the pinned sector hugs the leg and the free midline hangs. Fade
             # the share to 0 across PIN_AZ_FADE degrees on both sides instead.
+            # 2026-08-23 BACK zone (Ozan, run from behind: "the back side has
+            # triangles, extra stuff laying around — back of leg pushes
+            # cloth"): the same wedge opened at the BACK hem center at full
+            # split. d = angular distance to the NEAREST centerline (front or
+            # back); the back half pins with PIN_BACK, ties with the same seam.
             fade = math.radians(PIN_AZ_FADE)
-            strength = (smoothstep((rel - (math.radians(PIN_AZ_LO) - fade)) / fade)
+            d = rel if rel <= math.pi / 2 else math.pi - rel
-                        * (1.0 - smoothstep((rel - math.radians(PIN_AZ_HI)) / fade)))
+            zone = PIN_FRONT if rel <= math.pi / 2 else PIN_BACK
-            if strength > 0.0 and PIN_T_LO <= t_rel <= PIN_T_HI:
+            strength = (smoothstep((d - (math.radians(PIN_AZ_LO) - fade)) / fade)
-                share = PIN_FRONT * strength
+                        * (1.0 - smoothstep((d - math.radians(PIN_AZ_HI)) / fade)))
+            if strength > 0.0 and zone > 0.0 and PIN_T_LO <= t_rel <= PIN_T_HI:
+                share = zone * strength
                 hip_half = max(0.02, abs(origin["thigh_l"][0] - pelvis[0]))
                 side = max(-1.0, min(1.0, (v[0] - pelvis[0]) / hip_half))
                 sign_l = 1.0 if origin["thigh_l"][0] >= pelvis[0] else -1.0
                 f_l = 0.5 + 0.5 * side * sign_l
                 if PIN_SNAP > 0.0:
                     f_l = smoothstep((side * sign_l + 0.05) / 0.10)
-                if PIN_SEAM > 0.0 and rel < math.radians(PIN_SEAM):
+                if PIN_SEAM > 0.0 and d < math.radians(PIN_SEAM):
                     # TIE the flap ends (2026-08-23, Ozan: "a sharp cut, two
                     # separate lines at full split — tie those end surfaces"):
                     # a FLAT 50/50 seam band steps 1.0→0.5 at its boundary and
                     # the step reads as a cut. Ramp f_l from the flap's own
                     # thigh at the zone edge to 0.5 at the centerline instead —
                     # the stretch distributes across the whole seam, no step.
-                    u = rel / math.radians(PIN_SEAM)
+                    u = d / math.radians(PIN_SEAM)
                     f_own = 1.0 if (side * sign_l) >= 0.0 else 0.0
                     f_l = 0.5 + (f_own - 0.5) * u
                 w[slot["pelvis"]] = 1.0 - share
@@ -802,6 +823,36 @@ def main():
         out_j.append(tuple(j for j, _ in top4))
         out_w.append(tuple(x for _, x in top4))
 
+    # ── spatial weight smoothing post-pass (see the SKIRT_SMOOTH_W header) ──
+    if SMOOTH_W > 0.0:
+        dense = [{j: x for j, x in zip(js, ws) if x > 0.0}
+                 for js, ws in zip(out_j, out_w)]
+        side_of = [1.0 if p[0] >= pelvis[0] else -1.0 for p in pos]
+        t_rel_of = [(y_top - p[1]) / span if span > 1e-9 else 0.0 for p in pos]
+        for i in range(len(pos)):
+            if t_rel_of[i] < PIN_T_LO:      # rope / top band: keep pure pelvis
+                continue
+            d2 = sorted(((pos[i][0] - pos[j][0]) ** 2
+                         + (pos[i][1] - pos[j][1]) ** 2
+                         + (pos[i][2] - pos[j][2]) ** 2, j)
+                        for j in range(len(pos))
+                        if j != i and side_of[j] == side_of[i])[:SMOOTH_K]
+            acc = {}
+            for _, j in d2:
+                for b, x in dense[j].items():
+                    acc[b] = acc.get(b, 0.0) + x / SMOOTH_K
+            blended = {b: (1.0 - SMOOTH_W) * dense[i].get(b, 0.0) + SMOOTH_W * acc.get(b, 0.0)
+                       for b in set(dense[i]) | set(acc)}
+            top4 = sorted(blended.items(), key=lambda kv: -kv[1])[:MAX_INFLUENCES]
+            total = sum(x for _, x in top4) or 1.0
+            top4 = [(j, x / total) for j, x in top4]
+            while len(top4) < MAX_INFLUENCES:
+                top4.append((0, 0.0))
+            out_j[i] = tuple(j for j, _ in top4)
+            out_w[i] = tuple(x for _, x in top4)
+        log(f"spatial smooth: W={SMOOTH_W} K={SMOOTH_K} "
+            f"(same-side only, top band skipped)")
+
     # ── gates FIRST: never leave a broken garment on disk ──
     n = len(pos)
     log(f"waistband (pelvis only): {stats['waistband']} verts")