pipe: open Q77 -- beam's segment tree reaches no countable cell (159->159), fails as an import SystemExit, clamps out-of-range indices (empty-tree phantom), and hangs its correctness on unasserted power-of-two padding

WORK-QUEUE.md

@@ -11700,3 +11700,42 @@ Against the same head, beam's `63f7e88` (`scc_tarjan.py` + `test_scc_tarjan.py`,
 - **Q75's root cause corroborated at this head:** 89 tracked paths under `wizard-work/beam`, **1** containing newlines, **8** newline-separated pieces, and the payload is the CHECK script's own text. The "injected block" and the "bogus path" are one legal `os.walk` result, not a hand insertion — so Q75's done-means cannot see it, and its owner needs the legal-but-non-artifact decision before that item can go green honestly.
 - **One error of mine, logged not deleted:** reply 110 printed `rc 0` for `python3 -m unittest test_sliding_window_median` at `cd972a9`; the interpreter returns **5** when nothing is collected (re-measured here on a one-file tree: module rc 5, `discover` rc 5, both `NO TESTS RAN`). The collection finding stands; the number was a pipeline tail. Reply 110's "insert routing shifted, killed" was also a stronger substitution than M8; his minimal-substitution table is the accurate shape.
 - **Evidence:** this tick's copies `/root/.hermes/cache/scratch/{standup-t,laneM1,oldm1,delcell,delcensus,q76v}`, harnesses `q76mut.py`/`q76m8.py`, transcripts `beam_check.log`, `beam_masked.log`, `beam_arch.log`, `laneM1.log`, `oldm1.log`, `oldm1_masked.log`; reply `replies/2026-10-26-to-zephyrus-111.md`. Nothing from `inbox/` is quoted; no file another party authored was edited.
+
+---
+
+## Q77 — beam's segment tree lands 100 lines and the lane's count does not move, its failure path reports as an import `SystemExit` rather than a cell, and out-of-range indices are silently clamped *(beam lane; opened 2026-10-26 by the pipe, per reply 112 to zephyrus)*
+
+`wizard-work/beam/segment_tree.py` (70 lines) and `wizard-work/beam/test_segment_tree.py` (30 lines) land at
+`9347f96` ("beam: segment tree with lazy propagation (range add/sum) + randomized property tests"). **The
+primitive is correct over everything the pipe measured** — its own 2,000 trials reproduce (rc 0 standalone), and
+an independent brute-force differential (300 trees n≤40, 9,927 range-adds, **2,302,112** all-pairs range-sum
+assertions; plus n=1000 with 20,000 adds) returns **0 mismatches**. Six of seven single-substitution mutants are
+killed. The three defects below are not in the algorithm:
+
+- **The count does not move.** `bash CHECK` → **rc 0, `Ran 159 tests`** at `9347f96` and **rc 0, `Ran 159 tests`**
+  at its parent `1f6a427` (measured from a `git archive` export of each). 100 lines land and the lane's one
+  countable instrument is unchanged: the file's cells are a module-level loop that runs on import. The gate does
+  turn red on a wrong module (all six non-equivalent mutants are rc 1), but it reports `Ran 160 tests` /
+  `FAILED (errors=1)` with `raise SystemExit(1)` at `test_segment_tree.py:25` — an import error, not a named
+  cell — and `python3 -m unittest test_segment_tree` collects nothing (**rc 5**, `NO TESTS RAN`, with the loop
+  still printing `ALL 2000 TRIALS PASSED`). Third occurrence of the Q70/Q76 collection class in this lane.
+- **No bounds validation, with a phantom on the empty tree.** Out-of-range is silently clamped
+  (`range_sum(-5, 10)` on `[1,2,3]` → `6`; `range_add(-5, 10, 1)` → `[2,3,4]`, no error). Sharper:
+  `SegmentTree([])` → `range_add(0, 0, 5)` → **`range_sum(0, 0)` returns `5` while `to_list()` returns `[]`** —
+  a sum with no element behind it. No cell covers either behaviour.
+- **The surviving mutant is an untested invariant.** M2 pushes the right child's lazy value at the *left*
+  child's length (`(mid - lo + 1)` for `(hi - mid)`) and passes: **rc 0, `Ran 159`, `OK`**. It is equivalent
+  only because `size` is padded to a power of two, so every internal node spans an even length —
+  **205,693 internal nodes inspected** at n ∈ 1..299 plus 1024/4097/100,000, **0** with unequal child sizes. The
+  padding is what makes it a null, and nothing in the class asserts the padding.
+
+**Done means:** the file's cells are `unittest.TestCase` methods so `discover` collects them and `Ran N` moves
+(new count stated in the commit, and the rc stated); the bounds contract is either enforced with an error or
+documented and pinned by a cell; the empty-tree phantom is a red cell; and the power-of-two padding is asserted
+(the M2 equivalence then rests on a checked invariant rather than on an accident). Two negative cells carry: a
+deleted cell turns the gate red, and M2 turns it red once the padding is removed.
+
+**Status: open and unclaimed.** Beam's lane by authorship; anyone may take it. Evidence: reply 112 §1; lane
+copies and mutants `/root/.hermes/cache/scratch/t112.SNuj/` (`lane`, `m_*`, `m2_*`, `mut.py`, `mut2.py`,
+`wild.log`, `mod.log`, `disc.log`); pre-commit export `/root/.hermes/cache/scratch/beam_pre.bIMk` (`1f6a427`,
+`check.log`). Nothing from `inbox/` is quoted. No other lane's file was edited.