diff --git a/emulator/firmware-decomp/edge_verify.py b/emulator/firmware-decomp/edge_verify.py
new file mode 100644
index 0000000..58c57c5
--- /dev/null
+++ b/emulator/firmware-decomp/edge_verify.py
@@ -0,0 +1,60 @@
+"""Numeric verification of the edge decode. The edge SEND payloads carry floats
+~0.1262. Edges are pure screen-space (no z ambiguity), so if 0.1262 matches an
+object edge's line coefficient computed from the captured screen vertices, the
+edge decode is confirmed. Try normalised normal, raw dy/dx, and dx/len forms."""
+import sys, time, struct, pickle, math
+sys.path.insert(0, r'C:\VWE\TeslaRel410\emulator\firmware-decomp')
+import emu860, dis860, emu_main
+emu860.Mem.log = lambda self, *a, **k: None
+S = r'C:\Users\cyd\AppData\Local\Temp\claude\c--VWE-TeslaRel410\4e848c76-6e89-4034-8047-d8d491cb32d8\scratchpad'
+
+snap = pickle.load(open(S + r'\snapv2.pkl', 'rb'))
+r = emu_main.MainRunner(r'C:\VWE\TeslaRel410\dpl3-revive\patha\cap7.raw.bin', fw='capfw7', max_cmds=6000)
+cpu = r.cpu
+cpu.mem.pages = {k: bytearray(v) for k, v in snap['pages'].items()}
+cpu.ctrl.clear(); cpu.ctrl.update(snap['ctrl'])
+cpu.r = list(snap['r']); cpu.f = list(snap['f']); cpu.cr = dict(snap['cr']); cpu.pc = snap['pc']
+cpu._apipe = list(snap['apipe']); cpu._mpipe = list(snap['mpipe']); cpu._fp_pipes()
+cpu._lpipe = list(snap['lpipe']); cpu._gpipe = list(snap['gpipe'])
+cpu._kr, cpu._ki, cpu._t = snap['kr'], snap['ki'], snap['t']
+cpu.lcc = snap['lcc']; r.qi = snap['qi']; r.heap = list(snap['heap'])
+t0 = time.time(); startq = r.qi
+while time.time() - t0 < 60:
+    if r.qi >= startq + 2: break
+    h = r.hooks.get(cpu.pc)
+    if h:
+        if h(cpu) == 'done': break
+        continue
+    if not cpu.step(): break
+def rw(a): return cpu.mem.r32(a & 0xffffffff)
+def asf(w): return struct.unpack('<f', struct.pack('<I', w))[0]
+
+# edge-family payload floats (from SEND(4) + SEND(0x21) headers): the ~0.125 group
+edge_floats = set()
+for base, n in [(0x08015000, 4), (0x08015260, 0x21)]:
+    for i in range(n):
+        f = asf(rw(base + i * 4))
+        if 0.05 < abs(f) < 0.5:
+            edge_floats.add(round(f, 5))
+print("edge-family payload floats:", sorted(edge_floats, key=abs))
+
+# object edges (screen space) from captured verts -> candidate coefficient forms
+objs = pickle.load(open(S + r'\vfull.pkl', 'rb'))['objs']
+allv = [v for o in objs for v in o]
+xs = sorted(set(round(v['mx'], 2) for v in allv)); zs = sorted(set(round(v['mz'], 2) for v in allv))
+grid = {(round(v['mx'], 2), round(v['mz'], 2)): v for v in allv}
+cands = []   # (value, form, edge desc)
+for i in range(len(xs)-1):
+    for j in range(len(zs)-1):
+        tri = [grid[(xs[i],zs[j])], grid[(xs[i+1],zs[j])], grid[(xs[i],zs[j+1])]]
+        for k in range(3):
+            p, q = tri[k], tri[(k+1)%3]
+            dx = q['sx']-p['sx']; dy = q['sy']-p['sy']; L = math.hypot(dx,dy) or 1
+            cands.append((abs(dy/L), 'norm|A|'))     # normalised normal x-comp
+            cands.append((abs(dx/L), 'norm|B|'))     # normalised normal y-comp
+# match each payload edge float to nearest candidate
+print("\nmatches:")
+for ef in sorted(edge_floats, key=abs):
+    best = min(cands, key=lambda c: abs(abs(ef)-c[0]))
+    err = abs(abs(ef)-best[0]) / max(abs(ef), 1e-6) * 100
+    print("  payload %.5f  ~  %.5f (%s)   err %.1f%%" % (ef, best[0], best[1], err))
diff --git a/emulator/firmware-decomp/render-readout.html b/emulator/firmware-decomp/render-readout.html
index a3c3257..b7add28 100644
--- a/emulator/firmware-decomp/render-readout.html
+++ b/emulator/firmware-decomp/render-readout.html
@@ -266,10 +266,11 @@
     line up into clean <b>×2 chains</b> —
     <span class="mono">0.0079 · 0.016 · 0.032 · 0.063 · 0.126 · 0.252 · 0.504 · 1.009</span> —
     a coefficient stored as its binary place values <span class="mono">C·2ᵏ</span>, one per
-    bit-plane, exactly how a bit-serial adder holds a number. The recovered bases match the
-    object's own edge and z slopes computed from the captured vertices — so the coefficients
-    feeding the array simulator (§05) are <b>cross-validated against the compiled stream the
-    hardware actually shipped</b>.</p>
+    bit-plane, exactly how a bit-serial adder holds a number. And the recovered values are the
+    object's own geometry: a payload edge coefficient (<span class="mono">0.12527</span>) lands on
+    the edge normal computed from the captured vertices (<span class="mono">0.12555</span>) to
+    <b>0.2%</b>. The coefficients feeding the array simulator (§05) are
+    <b>the ones the hardware actually shipped</b>.</p>
   </section>
 
   <section>