diff --git a/selfhost/backend/emit_deps.ludic b/selfhost/backend/emit_deps.ludic
index 03c349d6..0a863d34 100644
--- a/selfhost/backend/emit_deps.ludic
+++ b/selfhost/backend/emit_deps.ludic
@@ -279,6 +279,12 @@ var g_dr_find_k: []pointer = new []pointer
 var g_dr_rl_name: []pointer = new []pointer     # a local holding one entry of a registry ...
 var g_dr_rl_reg: []pointer = new []pointer      # ... and which registry
 var g_dr_find_v: []Node = new []Node
+# a ROOT reaches through a table of fn values (a step list, a registry of systems), or calls what does:
+# it reaches every state by definition, so the ratchet's widest_reach and widest_write_reach leave it out
+var g_dr_disp: bool = false                     # the function being walked reads a fn value out of a table
+var g_dr_disp_of: []bool = new []bool
+var g_dr_root: []bool = new []bool
+var g_dr_hf: []int = new []int                  # per node: does a global hold fn values (-1 not yet asked)
 function dr_state_ix(t: pointer) -> int {
   var i = 0
   while i < len(g_state_names) {
@@ -328,7 +334,10 @@ function dr_walk(n: Node, refs: []int) -> void {
     let pre = `ludic_reduce__{n.s}__`
     var ri = 0
     while ri < len(g_dr_name) {
-      if str_starts(g_dr_name[ri], pre) { push(refs, ri) }
+      if str_starts(g_dr_name[ri], pre) {
+        push(refs, ri)
+        push(g_dr_cur2, ri)
+      }
       ri += 1
     }
   }
@@ -337,7 +346,10 @@ function dr_walk(n: Node, refs: []int) -> void {
     while li < len(g_onlisten) {
       if (g_onlisten[li].s == n.s) {
         let lk = dr_index(`@On {n.s}#{itoa(li)}`)
-        if lk >= 0 { push(refs, lk) }
+        if lk >= 0 {
+          push(refs, lk)
+          push(g_dr_cur2, lk)
+        }
       }
       li += 1
     }
@@ -345,9 +357,14 @@ function dr_walk(n: Node, refs: []int) -> void {
   if (n.kind == E_ID or n.kind == E_FNREF) and n.s != null and not (n.kind == E_ID and dr_is_local(n.s)) {
     let k = dr_index(n.s)
     if k >= 0 { push(refs, k) }
+    if k >= 0 and n.kind == E_ID { push(g_dr_cur2, k) }   # a call or a read; a `fn f` written is not one
+    if n.kind == E_ID and k >= 0 and dr_holds_fn(k) { g_dr_disp = true }   # a table of fn values read
     # a registry entry held in a local and handed on whole reaches the whole registry
     let rl = dr_reg_local(n.s)
-    if k < 0 and rl != null and dr_index(rl) >= 0 { push(refs, dr_index(rl)) }
+    if k < 0 and rl != null and dr_index(rl) >= 0 {
+      push(refs, dr_index(rl))
+      push(g_dr_cur2, dr_index(rl))
+    }
   }
   dr_walk(n.a, refs)
   dr_walk(n.b, refs)
@@ -360,6 +377,77 @@ function dr_walk(n: Node, refs: []int) -> void {
     }
   }
 }
+# a global whose value holds `fn f` somewhere (a step list, a registry of systems), asked once
+function dr_holds_fn(k: int) -> bool {
+  while len(g_dr_hf) <= k { push(g_dr_hf, -1) }
+  if g_dr_hf[k] < 0 {
+    let d = g_dr_node[k]
+    g_dr_hf[k] = 0
+    if d.kind == N_VAR and dr_has_fnref(d.a, 0) { g_dr_hf[k] = 1 }
+  }
+  return g_dr_hf[k] == 1
+}
+function dr_has_fnref(n: Node, depth: int) -> bool {
+  if n == null or depth > 6 { return false }
+  if n.kind == E_FNREF { return true }
+  if dr_has_fnref(n.a, depth + 1) or dr_has_fnref(n.b, depth + 1) { return true }
+  if n.kids != null {
+    var i = 0
+    while i < len(n.kids) {
+      if dr_has_fnref(n.kids[i], depth + 1) { return true }
+      i += 1
+    }
+  }
+  return false
+}
+# the roots are the dispatchers: a function that reads fn values out of a table (a step list's walker,
+# a registry of systems) reaches every state by definition. Every other function is also measured
+# WITHOUT going through one, and through its calls only - a `fn f` it writes into a list is supplied its
+# states where the list is walked (g_dr_bits2) - so the frame, the boot and a list's builder count only
+# their own work, and a refactor of them moves the number
+var g_dr_bits2: [][]int = new [][]int
+var g_dr_cur2: []int = new []int                # the function being walked: its calls and reads, no `fn f` written
+var g_dr_refs2: [][]int = new [][]int           # per node: those, the edges the second count follows
+var g_dr_wbits2: [][]int = new [][]int
+function dr_roots(nw: int) -> void {
+  g_dr_root = new []bool
+  g_dr_bits2 = new [][]int
+  g_dr_wbits2 = new [][]int
+  var j = 0
+  while j < len(g_dr_node) {
+    push(g_dr_root, g_dr_disp_of[j])
+    let b = new []int
+    let wb = new []int
+    var w = 0
+    while w < nw {
+      push(b, 0)
+      push(wb, 0)
+      w += 1
+    }
+    dr_own(g_dr_node[j], b, false)
+    dr_own(g_dr_node[j], wb, true)
+    push(g_dr_bits2, b)
+    push(g_dr_wbits2, wb)
+    j += 1
+  }
+  var changed = true
+  while changed {
+    changed = false
+    j = 0
+    while j < len(g_dr_node) {
+      let refs = g_dr_refs2[j]
+      var r = 0
+      while r < len(refs) {
+        if not g_dr_disp_of[refs[r]] {
+          if dr_join(g_dr_bits2[j], g_dr_bits2[refs[r]], nw) { changed = true }
+          if dr_join(g_dr_wbits2[j], g_dr_wbits2[refs[r]], nw) { changed = true }
+        }
+        r += 1
+      }
+      j += 1
+    }
+  }
+}
 # `Port.member` reaches what that member is bound to (or its default), not every member of the port:
 # a port asked for its save is not asked for its load
 function dr_port_member(n: Node, refs: []int) -> bool {
@@ -416,7 +504,10 @@ function dr_reg_field(n: Node, refs: []int) -> bool {
     if e.kind == E_NEW and e.a != null {
       var j = 0
       while j < len(e.a.kids) {
-        if (e.a.kids[j].s == n.s) { dr_walk(e.a.kids[j].a, refs) }
+        if (e.a.kids[j].s == n.s) {
+          if e.a.kids[j].a != null and e.a.kids[j].a.kind == E_FNREF { g_dr_disp = true }   # a step list walked
+          dr_walk(e.a.kids[j].a, refs)
+        }
         j += 1
       }
     }
@@ -497,7 +588,11 @@ function deps_reach(f: pointer) -> void {
     g_dr_locals = new []pointer
     let dn = g_dr_node[j]
     if dn.kind == N_FN or dn.kind == N_SYS or dn.kind == N_BLOCK { dr_collect_locals(dn) }
+    g_dr_disp = false
+    g_dr_cur2 = new []int
     dr_walk(dn, refs)
+    push(g_dr_disp_of, g_dr_disp)
+    push(g_dr_refs2, g_dr_cur2)
     # the generated drain calls every reducer; a reducer is reached from its action's dispatch instead
     if dn.s != null and (dn.s == "drain_actions") {
       let kept = new []int
@@ -542,6 +637,7 @@ function deps_reach(f: pointer) -> void {
       j += 1
     }
   }
+  dr_roots(nw)
   j = 0
   while j < len(g_dr_node) {
     let d = g_dr_node[j]
@@ -549,9 +645,12 @@ function deps_reach(f: pointer) -> void {
       let n = dr_count(g_dr_bits[j])
       var pkg = 0
       if not (pkg_of_file(d.file) == "") { pkg = 1 }
-      if n > 0 { deps_line(f, `reach {itoa(n)} {d.s} {d.file}:{itoa(d.line)} {itoa(pkg)}`) }
+      var root = "0"
+      if g_dr_root[j] { root = "1" }
+      # the reach, whether it is a root, and the reach not going through any dispatcher
+      if n > 0 { deps_line(f, `reach {itoa(n)} {d.s} {d.file}:{itoa(d.line)} {itoa(pkg)} {root} {itoa(dr_count(g_dr_bits2[j]))}`) }
       let wn = dr_count(g_dr_wbits[j])
-      if wn > 0 { deps_line(f, `wreach {itoa(wn)} {d.s} {d.file}:{itoa(d.line)} {itoa(pkg)}`) }
+      if wn > 0 { deps_line(f, `wreach {itoa(wn)} {d.s} {d.file}:{itoa(d.line)} {itoa(pkg)} {root} {itoa(dr_count(g_dr_wbits2[j]))}`) }
     }
     j += 1
   }
diff --git a/tools/ludic-cli/deps.ludic b/tools/ludic-cli/deps.ludic
index ce0f44b7..5d8a8316 100644
--- a/tools/ludic-cli/deps.ludic
+++ b/tools/ludic-cli/deps.ludic
@@ -30,6 +30,9 @@
 # widest_reach: the most states any of them can come to - what it takes, and through calls, `fn f`
 # and globals holding fn values (a step list, a registry of systems) what those take (0.R4);
 # widest_write_reach: of those, the most it can come to change - taken `mut` somewhere down (0.R5).
+# Both leave out the ROOTS - a function that reads fn values out of a table (a dispatcher), which reaches
+# every state by definition - and count every other function without going through one, so the frame
+# and the boot count their own work; the roots are listed on a line of their own.
 var dp_mods: []pointer = null
 var dp_pkg: []int = null
 var dp_uses: []pointer = null
@@ -52,6 +55,12 @@ var dp_fn_at: []pointer = null        # each of the program's own functions: whe
 var dp_fn_w: []int = null
 var dp_fn_r: []int = null
 var dp_fn_x: []int = null             # ... and the states it can come to change
+var dp_fn_root: []bool = null         # ... whether it is a ROOT: reads fn values out of a table (a dispatcher)
+var dp_fn_r2: []int = null            # ... what it reaches and changes NOT going through a dispatcher
+var dp_fn_x2: []int = null
+var dp_root_n: int = 0                # the roots, left out of widest_reach / widest_write_reach, and the widest of them
+var dp_root_reach: int = 0
+var dp_root_at: pointer = ""
 var dp_fallocs: []pointer = new []pointer        # 25.2: `falloc <kind> <file:line> <chain>`, what a frame can allocate
 var dp_frame_allocs: int = 0
 var dp_fkeeps: []pointer = new []pointer          # 25.3: `fkeep <kind> <file:line> <kept at> <chain>`
@@ -98,7 +107,8 @@ function dp_load(path: pointer) -> bool {
   dp_ef = new []int;  dp_et = new []int;  dp_ec = new []int;  dp_en = new []pointer
   dp_wide_n = 0;  dp_wide_at = ""
   dp_reach_n = 0;  dp_reach_at = "";  dp_reach_own = 0
-  dp_fn_at = new []pointer;  dp_fn_w = new []int;  dp_fn_r = new []int;  dp_fn_x = new []int
+  dp_fn_at = new []pointer;  dp_fn_w = new []int;  dp_fn_r = new []int;  dp_fn_x = new []int;  dp_fn_root = new []bool;  dp_fn_r2 = new []int;  dp_fn_x2 = new []int
+  dp_root_n = 0;  dp_root_reach = 0;  dp_root_at = ""
   dp_wreach_n = 0;  dp_wreach_at = ""
   dp_fallocs = new []pointer;  dp_frame_allocs = 0
   dp_fkeeps = new []pointer;  dp_frame_keeps = 0
@@ -143,6 +153,9 @@ function dp_load(path: pointer) -> bool {
     if len(w) >= 5 and (w[0] == "width" or w[0] == "reach" or w[0] == "wreach") and w[4] == "0" {
       let k = dp_fn(`{dp_fn_name(w[2])} ({w[3]})`)
       if w[0] == "width" { dp_fn_w[k] = s_to_int(w[1]) } else if w[0] == "reach" { dp_fn_r[k] = s_to_int(w[1]) } else { dp_fn_x[k] = s_to_int(w[1]) }
+      if len(w) >= 6 and w[5] == "1" { dp_fn_root[k] = true }
+      if len(w) >= 7 and w[0] == "reach" { dp_fn_r2[k] = s_to_int(w[6]) }
+      if len(w) >= 7 and w[0] == "wreach" { dp_fn_x2[k] = s_to_int(w[6]) }
     }
     if len(w) >= 5 and w[0] == "write" {
       push(dp_wowner, w[1])
@@ -160,19 +173,34 @@ function dp_fn(at: pointer) -> int {
   push(dp_fn_w, 0)
   push(dp_fn_r, 0)
   push(dp_fn_x, 0)
+  push(dp_fn_root, false)
+  push(dp_fn_r2, 0)
+  push(dp_fn_x2, 0)
   return len(dp_fn_at) - 1
 }
 # after the load: the widest reach (a function reaches at least what it takes)
+# over the functions that are not roots, each counted without going through a dispatcher: a root (a
+# step list's walker, a registry of systems) reaches every state by definition, and what calls one would
+# only rise with each new state - no split could lower it. The roots are listed on a line of their own.
 function dp_reach_best() -> void {
   for i in 0 .. len(dp_fn_at) {
     if dp_fn_r[i] < dp_fn_w[i] { dp_fn_r[i] = dp_fn_w[i] }
-    if dp_fn_r[i] > dp_reach_n {
-      dp_reach_n = dp_fn_r[i]
+    if dp_fn_r2[i] < dp_fn_w[i] { dp_fn_r2[i] = dp_fn_w[i] }
+    if dp_fn_root[i] {
+      dp_root_n += 1
+      if dp_fn_r[i] > dp_root_reach {
+        dp_root_reach = dp_fn_r[i]
+        dp_root_at = dp_fn_at[i]
+      }
+      continue
+    }
+    if dp_fn_r2[i] > dp_reach_n {
+      dp_reach_n = dp_fn_r2[i]
       dp_reach_at = dp_fn_at[i]
       dp_reach_own = dp_fn_w[i]
     }
-    if dp_fn_x[i] > dp_wreach_n {
-      dp_wreach_n = dp_fn_x[i]
+    if dp_fn_x2[i] > dp_wreach_n {
+      dp_wreach_n = dp_fn_x2[i]
       dp_wreach_at = dp_fn_at[i]
     }
   }
@@ -195,7 +223,9 @@ function dp_top(n: int, by: int) -> void {
   for i in 0 .. len(order) {
     let k = order[i]
     if shown < n and (dp_fn_w[k] > 0 or dp_fn_r[k] > 0) {
-      print(`{dp_pad(string(dp_fn_w[k]), 5)}  {dp_pad(string(dp_fn_r[k]), 7)}  {dp_pad(string(dp_fn_x[k]), 7)}  {dp_fn_at[k]}`)
+      var mark = ""
+      if dp_fn_root[k] { mark = "  (root)" }
+      print(`{dp_pad(string(dp_fn_w[k]), 5)}  {dp_pad(string(dp_fn_r[k]), 7)}  {dp_pad(string(dp_fn_x[k]), 7)}  {dp_fn_at[k]}{mark}`)
       shown += 1
     }
   }
@@ -369,6 +399,7 @@ function dp_print_numbers() -> void {
   if dp_reach_n > dp_reach_own { print(`the widest reach: {dp_reach_at}, {string(dp_reach_n)} states ({string(dp_reach_n - dp_reach_own)} through calls and fn values it does not take)`) }
   if dp_wreach_n == 1 { print(`the widest write reach: {dp_wreach_at}, 1 state it can come to change`) }
   if dp_wreach_n > 1 { print(`the widest write reach: {dp_wreach_at}, {string(dp_wreach_n)} states it can come to change`) }
+  if dp_root_n > 0 { print(`roots, left out of the reaches (they walk a table of fn values; the rest are counted without going through one): {string(dp_root_n)}, the widest {dp_root_at}, {string(dp_root_reach)} states`) }
   let layers = dp_layers()
   if layers != "" {
     print(`layers: {layers}`)
diff --git a/tools/ludic-cli/test.ludic b/tools/ludic-cli/test.ludic
index 2bca1f10..b6076ea1 100644
--- a/tools/ludic-cli/test.ludic
+++ b/tools/ludic-cli/test.ludic
@@ -621,14 +621,15 @@ function actions_deps_case() -> void {
   let got = capture(`bin/ludic deps examples/actions/modules.ludic 2>&1`)
   if s_contains(got, "largest_cycle: 1") and s_contains(got, "dependencies: 0") and s_contains(got, "the widest function: reducer Bag on PickUp (") { ok(lbl) } else { bad2(lbl, s_trim(got)) }
 }
-# 0.R4: a step list takes no state and reaches every state its steps take; --widest and --reach
-# list the functions by what they take and by what they reach
+# 0.R4: a step list takes no state and reaches every state its steps take - a ROOT, left out of
+# widest_reach and listed on its own line, and what calls it (one) is counted without going through
+# it; --widest and --reach list the functions by what they take and by what they reach, a root marked
 function deps_reach_case() -> void {
-  let lbl = "ludic deps: the reach through fn values, --widest N and --reach N"
+  let lbl = "ludic deps: the reach through fn values, the roots apart, --widest N and --reach N"
   let got = capture(`bin/ludic deps examples/state/reach.ludic 2>&1`)
-  if not s_contains(got, "widest_reach: 3") or not s_contains(got, "the widest reach: one (examples/state/reach.ludic:13), 3 states (2 through calls and fn values it does not take)") { bad2(lbl, s_trim(got));  return }
+  if not s_contains(got, "widest_reach: 1") or not s_contains(got, "roots, left out of the reaches (they walk a table of fn values; the rest are counted without going through one): 1, the widest run_steps (examples/state/reach.ludic:10), 2 states") { bad2(lbl, s_trim(got));  return }
   let top = capture(`bin/ludic deps examples/state/reach.ludic --reach 2 2>&1`)
-  if not s_contains(top, "    1        3        3  one (examples/state/reach.ludic:13)\n    0        2        2  run_steps (examples/state/reach.ludic:10)") { bad2(lbl, s_trim(top));  return }
+  if not s_contains(top, "    1        3        3  one (examples/state/reach.ludic:13)\n    0        2        2  run_steps (examples/state/reach.ludic:10)  (root)") { bad2(lbl, s_trim(top));  return }
   let wide = capture(`bin/ludic deps examples/state/reach.ludic --widest 1 2>&1`)
   if s_contains(wide, "takes  reaches  changes  function") and s_contains(wide, "one (examples/state/reach.ludic:13)") and not s_contains(wide, "step_a") { ok(lbl) } else { bad2(lbl, s_trim(wide)) }
 }