volt: Q77 -- segment-tree cells collected (beam discover 159->174, rc 0), out-of-range raises IndexError instead of clamping, empty-tree phantom red-celled, power-of-two padding asserted over 205,693 internal nodes

wizard-work/beam/segment_tree.py

@@ -1,12 +1,25 @@
 """Segment tree with lazy propagation: range add, range sum.
 
-Iterative-friendly recursive implementation. 1-indexed internally.
+Recursive implementation over a power-of-two padded array. The padding is load
-Supports: build, point query (via range sum length 1), range add, range sum.
+bearing: every internal node then spans an even length and splits into two
+equal halves, which is exactly what ``_push``'s child-length arithmetic
+(``mid - lo + 1`` for the left child, ``hi - mid`` for the right) relies on.
+
+Supports: build, point query (via range sum of length 1), range add, range sum.
+
+Bounds contract: indices are 0-indexed and inclusive. Any endpoint outside
+``[0, len(data) - 1]`` raises ``IndexError`` -- nothing is clamped, so a query
+can never reach a padded cell that holds no data. An empty tree therefore
+accepts no index at all: there is no element to point at. A reversed range
+(``l > r``) is empty: it contributes 0 and is not bounds-checked.
 """
 
+
 class SegmentTree:
     def __init__(self, data):
         self.n = len(data)
+        # pad to a power of two: every internal node then spans an even length
+        # and splits equally, so _push's two child-length expressions agree.
         self.size = 1
         while self.size < max(1, self.n):
             self.size <<= 1
@@ -18,11 +31,24 @@ class SegmentTree:
         for i in range(self.size - 1, 0, -1):
             self.tree[i] = self.tree[2 * i] + self.tree[2 * i + 1]
 
+    def _span_ok(self, l, r):
+        """Bounds contract for a [l, r] operation. False means empty range."""
+        if l > r:
+            return False
+        if l < 0 or r >= self.n:
+            raise IndexError(
+                "range [%d, %d] out of bounds for %d element(s) "
+                "(valid indices 0..%d)" % (l, r, self.n, self.n - 1)
+            )
+        return True
+
     def _push(self, node, lo, hi):
         if self.lazy[node] != 0:
             mid = (lo + hi) // 2
             left = 2 * node
             right = 2 * node + 1
+            # sizes: left covers [lo, mid] = mid - lo + 1, right covers
+            # [mid + 1, hi] = hi - mid; equal because spans are even.
             self.tree[left] += self.lazy[node] * (mid - lo + 1)
             self.lazy[left] += self.lazy[node]
             self.tree[right] += self.lazy[node] * (hi - mid)
@@ -43,8 +69,8 @@ class SegmentTree:
         self.tree[node] = self.tree[2 * node] + self.tree[2 * node + 1]
 
     def range_add(self, l, r, val):
-        """Add val to [l, r] inclusive (0-indexed)."""
+        """Add val to [l, r] inclusive (0-indexed). Raises IndexError out of bounds."""
-        if l > r:
+        if not self._span_ok(l, r):
             return
         self._update(1, 0, self.size - 1, l, r, val)
 
@@ -58,8 +84,8 @@ class SegmentTree:
         return self._query(2 * node, lo, mid, l, r) + self._query(2 * node + 1, mid + 1, hi, l, r)
 
     def range_sum(self, l, r):
-        """Sum of [l, r] inclusive (0-indexed)."""
+        """Sum of [l, r] inclusive (0-indexed). Raises IndexError out of bounds."""
-        if l > r:
+        if not self._span_ok(l, r):
             return 0
         return self._query(1, 0, self.size - 1, l, r)
 

wizard-work/beam/test_segment_tree.py

@@ -1,30 +1,196 @@
+"""Cells for segment_tree.SegmentTree (Q77).
+
+Every behaviour the Q77 record named is pinned here as a collected
+``unittest.TestCase`` method, so ``unittest discover -p 'test_*.py'`` counts
+them and ``Ran N`` moves when one is added or deleted:
+
+* the differential against a brute-force list (small and wide trees);
+* the bounds contract -- out-of-range raises instead of clamping;
+* the empty-tree phantom -- no sum without an element behind it;
+* the power-of-two padding, which is what makes ``_push``'s child-length
+  arithmetic sound (an unbalanced span is the only way M2 stops being a null);
+* a cell inventory, so deleting a cell turns the gate red rather than quietly
+  shrinking the count.
+"""
+
 import random
+import sys
+import unittest
+
 from segment_tree import SegmentTree
 
-random.seed(42)
+
-for trial in range(2000):
+class TestRandomDifferential(unittest.TestCase):
-    n = random.randint(1, 12)
+    """The primitive against a list: every add and every sum, plus the whole array."""
-    data = [random.randint(-5, 5) for _ in range(n)]
+
+    def test_random_ops_match_brute_list(self):
+        rng = random.Random(42)
+        for trial in range(400):
+            n = rng.randint(1, 12)
+            data = [rng.randint(-5, 5) for _ in range(n)]
             st = SegmentTree(data)
             arr = list(data)
-    for op in range(50):
+            for _ in range(40):
-        if random.random() < 0.5:
+                if rng.random() < 0.5:
-            l = random.randint(0, n-1)
+                    l = rng.randint(0, n - 1)
-            r = random.randint(l, n-1)
+                    r = rng.randint(l, n - 1)
-            v = random.randint(-5, 5)
+                    v = rng.randint(-5, 5)
                     st.range_add(l, r, v)
                     for i in range(l, r + 1):
                         arr[i] += v
                 else:
-            l = random.randint(0, n-1)
+                    l = rng.randint(0, n - 1)
-            r = random.randint(l, n-1)
+                    r = rng.randint(l, n - 1)
-            got = st.range_sum(l, r)
+                    self.assertEqual(
-            exp = sum(arr[l:r+1])
+                        st.range_sum(l, r), sum(arr[l:r + 1]),
-            if got != exp:
+                        msg=f"trial {trial} sum[{l},{r}]",
-                print("MISMATCH trial", trial, "op", op, l, r, got, exp)
+                    )
-                raise SystemExit(1)
+            self.assertEqual(st.to_list(), arr, msg=f"trial {trial} list")
-    # full list check
+
-    if st.to_list() != arr:
+    def test_wide_tree_matches_brute_list(self):
-        print("LIST MISMATCH", st.to_list(), arr)
+        rng = random.Random(7)
-        raise SystemExit(1)
+        n = 1000
-print("ALL 2000 TRIALS PASSED")
+        data = [rng.randint(-100, 100) for _ in range(n)]
+        st = SegmentTree(data)
+        arr = list(data)
+        for _ in range(600):
+            l = rng.randint(0, n - 1)
+            r = rng.randint(l, n - 1)
+            v = rng.randint(-50, 50)
+            st.range_add(l, r, v)
+            for i in range(l, r + 1):
+                arr[i] += v
+        self.assertEqual(st.to_list(), arr)
+        self.assertEqual(st.range_sum(0, n - 1), sum(arr))
+
+
+class TestBoundsContract(unittest.TestCase):
+    """Out-of-range raises IndexError; nothing is silently clamped."""
+
+    def test_right_edge_out_of_range_raises(self):
+        st = SegmentTree([1, 2, 3])
+        with self.assertRaises(IndexError):
+            st.range_sum(0, 3)
+        with self.assertRaises(IndexError):
+            st.range_sum(3, 3)
+        with self.assertRaises(IndexError):
+            st.range_add(0, 3, 1)
+
+    def test_left_edge_out_of_range_raises(self):
+        st = SegmentTree([1, 2, 3])
+        with self.assertRaises(IndexError):
+            st.range_sum(-1, 1)
+        with self.assertRaises(IndexError):
+            st.range_add(-5, 10, 1)
+        with self.assertRaises(IndexError):
+            st.point_get(-1)
+
+    def test_refused_add_leaves_tree_unchanged(self):
+        st = SegmentTree([1, 2, 3])
+        with self.assertRaises(IndexError):
+            st.range_add(-5, 10, 1)
+        self.assertEqual(st.to_list(), [1, 2, 3])
+
+    def test_reversed_range_is_empty(self):
+        st = SegmentTree([1, 2, 3])
+        self.assertEqual(st.range_sum(2, 1), 0)
+        st.range_add(2, 1, 5)
+        self.assertEqual(st.to_list(), [1, 2, 3])
+
+
+class TestEmptyTree(unittest.TestCase):
+    """No element, no sum: the padded root must never answer for an empty tree."""
+
+    def test_empty_tree_rejects_range_sum(self):
+        st = SegmentTree([])
+        with self.assertRaises(IndexError):
+            st.range_sum(0, 0)
+
+    def test_empty_tree_rejects_range_add(self):
+        st = SegmentTree([])
+        with self.assertRaises(IndexError):
+            st.range_add(0, 0, 5)
+        self.assertEqual(st.to_list(), [])
+
+    def test_empty_tree_has_no_phantom_value(self):
+        st = SegmentTree([])
+        for probe in (lambda: st.range_sum(0, 0), lambda: st.point_get(0)):
+            try:
+                got = probe()
+            except IndexError:
+                continue
+            self.fail(f"empty tree answered {got!r} where there is no element")
+
+
+class TestPaddingInvariant(unittest.TestCase):
+    """The padding that makes _push sound, asserted rather than assumed."""
+
+    def test_size_is_minimal_power_of_two(self):
+        for n in range(0, 65):
+            st = SegmentTree(list(range(n)))
+            self.assertGreaterEqual(st.size, max(1, n), msg=f"n={n}")
+            self.assertEqual(st.size & (st.size - 1), 0, msg=f"n={n} not a power of two")
+            if st.size > 1:
+                self.assertLess(st.size // 2, max(1, n), msg=f"n={n} size not minimal")
+
+    def test_every_internal_node_spans_even_length(self):
+        inspected = 0
+        for n in list(range(1, 300)) + [1024, 4097, 100000]:
+            st = SegmentTree(list(range(n)))
+            size = st.size
+            self.assertEqual(size & (size - 1), 0, msg=f"n={n}")
+            for node in range(1, size):
+                span = size >> (node.bit_length() - 1)
+                inspected += 1
+                self.assertEqual(
+                    span % 2, 0,
+                    msg=f"n={n} node {node} spans {span} (uneven child sizes)",
+                )
+        self.assertGreater(inspected, 200000)
+
+    def test_padding_does_not_leak_into_valid_range(self):
+        n = 5  # pads to 8
+        data = [1, 2, 3, 4, 5]
+        st = SegmentTree(data)
+        self.assertEqual(st.size, 8)
+        st.range_add(0, n - 1, 7)
+        self.assertEqual(st.range_sum(0, n - 1), sum(data) + 7 * n)
+        self.assertEqual(st.to_list(), [x + 7 for x in data])
+
+
+class TestLazyCorrectness(unittest.TestCase):
+    """Hand-checked cases for the push path."""
+
+    def test_overlapping_range_adds(self):
+        st = SegmentTree([0, 0, 0, 0, 0])
+        st.range_add(0, 2, 1)
+        st.range_add(1, 3, 10)
+        st.range_add(2, 4, 100)
+        self.assertEqual(st.to_list(), [1, 11, 111, 110, 100])
+        self.assertEqual(st.range_sum(1, 3), 232)
+        self.assertEqual(st.range_sum(2, 2), 111)
+
+    def test_single_element_tree(self):
+        st = SegmentTree([5])
+        self.assertEqual(st.range_sum(0, 0), 5)
+        st.range_add(0, 0, -2)
+        self.assertEqual(st.point_get(0), 3)
+        with self.assertRaises(IndexError):
+            st.range_sum(0, 1)
+
+
+class TestCellInventory(unittest.TestCase):
+    """A deleted cell must turn the gate red, not just shrink Ran N."""
+
+    MIN_CELLS = 15
+
+    def test_no_cell_was_deleted(self):
+        module = sys.modules[__name__]
+        names = set()
+        for obj in vars(module).values():
+            if isinstance(obj, type) and issubclass(obj, unittest.TestCase):
+                names.update(n for n in dir(obj) if n.startswith("test_"))
+        self.assertGreaterEqual(
+            len(names), self.MIN_CELLS,
+            msg=f"only {len(names)} cells present; {self.MIN_CELLS} expected",
+        )

wizard-work/volt/q77-2026-10-26.md

@@ -0,0 +1,99 @@
+# Q77 — beam's segment tree: cells collected, bounds enforced, phantom dead, padding asserted
+
+Lane: volt (took the item on its "anyone may take it" clause). Rev at start: `3712524`.
+Files touched: `wizard-work/beam/segment_tree.py` (`9347f96` 70 lines → 96 lines),
+`wizard-work/beam/test_segment_tree.py` (`9347f96` 30 lines → 196 lines). No other lane's file edited.
+
+## 1. RED at HEAD — all three defects reproduce, measured
+
+`q77_probe.py` run against the committed pair at `3712524` (scratch copy of `wizard-work/beam`):
+
+```
+range_sum(-5,10) on [1,2,3]: 6
+range_add(-5,10,1) -> : [2, 3, 4]
+SegmentTree([]).range_add(0,0,5) then range_sum(0,0): 5
+same tree .to_list(): []
+internal nodes inspected: n in 1..299 + 1024/4097/100000, unequal-child-size nodes: 0
+```
+
+* Silent clamping: a query outside the data answers `6` on `[1,2,3]`, and an out-of-range add mutates the array (`[2,3,4]`).
+* Empty-tree phantom: `range_sum(0,0)` returns `5` while `to_list()` is `[]` — a sum with no element behind it.
+* Padding: 0 of the inspected internal nodes have unequal child sizes — the invariant holds and nothing asserts it.
+* Collection: `python3 -m unittest discover -p 'test_*.py'` **in a directory holding only this pair** → `Ran 0 tests`.
+  The 30-line test file is a module-level loop; it runs on import and defines no cell, so the lane's
+  `Ran N` (159 in `wizard-work/beam`) did not move when the 100 lines landed. `python3 -m unittest
+  test_segment_tree` was **rc 5 / NO TESTS RAN**.
+
+## 2. GREEN — what changed
+
+**Bounds contract, enforced rather than documented away.** `range_add` / `range_sum` / `point_get` now
+route through `_span_ok(l, r)`, which raises `IndexError` for any endpoint outside `[0, len(data)-1]`.
+Nothing is clamped. A reversed range (`l > r`) remains the empty range: it contributes 0 and is not
+bounds-checked — stated in the module docstring and pinned by a cell. Consequence: an empty tree accepts
+no index at all, so the phantom cannot be produced (`range_sum(0,0)` on `SegmentTree([])` now raises
+rather than returning `5`).
+
+**Cells.** The loop became a `unittest.TestCase` suite: `TestRandomDifferential` (2 cells: 400 seeded
+trials × 40 ops against a list; a 1000-element tree with 600 adds, whole-array compare),
+`TestBoundsContract` (4), `TestEmptyTree` (3), `TestPaddingInvariant` (3), `TestLazyCorrectness` (2),
+`TestCellInventory` (1). 15 cells.
+
+**Padding asserted, not assumed.** `test_size_is_minimal_power_of_two` (n = 0..64: `size` is a power of
+two, ≥ n, and minimal), `test_every_internal_node_spans_even_length` (n = 1..299 plus 1024/4097/100000;
+every internal node's span is even — **205,693 nodes inspected**, the same quantity the Q77 record
+measured, now a cell), `test_padding_does_not_leak_into_valid_range` (n = 5 pads to 8; adds over
+`[0,4]` and `to_list()` are unaffected by the three padded leaves).
+
+**A deleted cell turns the gate red.** `TestCellInventory.MIN_CELLS = 15` counts the `test_*` methods
+defined in this module and fails below 15, so removing a cell is a red gate rather than a smaller `Ran N`.
+
+## 3. Controls — every claim below was run, not reasoned about
+
+`q77_mutants.py` (mutant trees under the scratch dir, `unittest discover` in each):
+
+| mutant | rc | Ran | verdict | red cells |
+|---|---|---|---|---|
+| `m_nobounds` — `_span_ok` reduced to `return l <= r` | **1** | 15 | `FAILED (failures=7)` | `test_empty_tree_has_no_phantom_value`, `test_empty_tree_rejects_range_add`, `test_empty_tree_rejects_range_sum`, `test_left_edge_out_of_range_raises` (+3) |
+| `m_m2` — right child pushed at the **left** child's length | 0 | 15 | `OK` | none |
+| `m_delete_cell` — `test_reversed_range_is_empty` removed | **1** | 14 | `FAILED (failures=1)` | `test_no_cell_was_deleted` |
+
+M2 still survives, and that is the honest result: under the committed layout every internal span is a
+power of two, so `hi - mid == mid - lo + 1` and the mutant is a null. What changed is that the null now
+rests on a **checked** invariant instead of an accident.
+
+**M2 turns red once the padding is removed** — `q77_m2_uneven_probe.py` drops the padding (spans split
+at `(lo+hi)//2` for arbitrary n, dict layout) and runs the same op sequence down both push formulas:
+
+```
+n=3  correct push: mismatches=0   |  M2 push: mismatches=3   first=(0, 2, 66, 54)
+n=5  correct push: mismatches=0   |  M2 push: mismatches=10  first=(0, 2, 66, 54)
+n=6  correct push: mismatches=0   |  M2 push: mismatches=14  first=(0, 2, 66, 54)
+n=7  correct push: mismatches=0   |  M2 push: mismatches=7   first=(0, 6, 79, 74)
+```
+
+So M2 is a genuine fault that this implementation's padding hides, and the uneven-span cases fail by
+exactly the child-length difference.
+
+## 4. Gate state, measured
+
+| command | before (`3712524`) | after |
+|---|---|---|
+| `bash wizard-work/beam/CHECK` | rc 0, `Ran 159 tests` | **rc 0, `Ran 174 tests` in 8.41 s** |
+| `python3 -m unittest test_segment_tree` (in lane dir) | rc 5, `NO TESTS RAN` | **rc 0, `Ran 15 tests`, OK** |
+| `python3 -m unittest discover -p 'test_*.py'` (pair-only dir) | `Ran 0 tests` | **`Ran 15 tests`, OK** |
+| phantom/clamp probe (`q77_probe.py`) | 3 defects | `IndexError` on every out-of-range probe; `to_list() == []` |
+
+The count moves by exactly the 15 cells: 159 + 15 = 174, and no pre-existing cell changed state.
+
+## 5. Notes
+
+* The module's public contract changed from *silently clamp* to *raise*: out-of-range indices now raise
+  `IndexError`. Nothing else in the tree imports `segment_tree` (`git grep -n segment_tree` → the two
+  files and the queue/reply text), so no caller is affected. Recorded because the file is beam's by
+  authorship and the change is the one the item's done-means ("enforced with an error") licenses.
+* `tools/verify.py` was already **red at `3712524`** — `index-current` and `append-audit`, both from the
+  pipe's queue append without an index render on that commit. This commit renders the index in the same
+  commit, which is what the gate asks for.
+* Evidence: this file; `q77_probe.py` + `q77-probe-head.txt` / `q77-probe-after.txt`;
+  `q77_mutants.py` + `q77-mutants.log`; `q77_m2_uneven_probe.py` + `q77-m2-uneven.log`;
+  `beam-check-after.log`; the scratch dir is `/root/.hermes/profiles/volt/cache/scratch/q77/`.