[qmc] frustration-free: authenticated long-range percolation pilot

.superpowers/sdd/final-fix-report.md

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+# Challenge #194 Final Fix Report
+
+## Scope
+
+Applied the requested final Day-0 fix wave on branch `challenge/194` with no scope expansion.
+
+## Root Cause
+
+`ModelSpec` previously accepted positive finite `sigma` values so small that `1.0 + sigma` rounded back to exactly `1.0`. Downstream Hurwitz-zeta and reference-tail formulas assume exponent strictly greater than `1.0`, so that boundary admitted pole and division-by-zero behavior.
+
+## RED -> GREEN
+
+### RED tests added first
+
+- `tests/test_model.py`
+  - rejects a positive `sigma` with `1.0 + sigma == 1.0`
+  - accepts `math.ulp(1.0)`, `0.8`, `1.0`, and `1.1`, and checks `periodic_kernel()` stays finite
+  - adds direct invalid-input tests for `distance_classes()` and `canonical_edge()`
+- `tests/test_kernel.py`
+  - checks `kernel_weight_sum()` equals the multiplicity-weighted `periodic_kernel()` table
+  - adds a regression proving the periodic-image kernel differs from bare minimum-image `r^-(1+sigma)` while matching the Hurwitz-zeta expression
+- `tests/test_oracle.py`
+  - checks oracle public symbols are exported from the package root and listed in `__all__`
+
+### RED command
+
+```bash
+./.venv/bin/python -m pytest tests/test_model.py tests/test_kernel.py tests/test_oracle.py -q
+```
+
+Result:
+
+```text
+.F...........................                                            [100%]
+=================================== FAILURES ===================================
+___ test_model_spec_rejects_positive_sigma_when_one_plus_sigma_rounds_to_one ___
+
+E       Failed: DID NOT RAISE <class 'ValueError'>
+
+1 failed, 28 passed in 5.48s
+```
+
+### GREEN implementation
+
+- Updated `src/long_range_percolation/model.py` to reject `sigma` unless:
+  - `sigma` is finite
+  - `sigma > 0.0`
+  - `math.isfinite(1.0 + sigma)`
+  - `(1.0 + sigma) > 1.0`
+- Removed the unused `math` import from `src/long_range_percolation/kernel.py`
+
+### GREEN command
+
+```bash
+./.venv/bin/python -m pytest tests/test_model.py tests/test_kernel.py tests/test_oracle.py -q
+```
+
+Result:
+
+```text
+.............................                                            [100%]
+29 passed in 11.27s
+```
+
+## Full Verification
+
+### Full suite
+
+```bash
+./.venv/bin/python -m pytest -q
+```
+
+Result:
+
+```text
+........................................................................ [100%]
+72 passed in 40.84s
+```
+
+### Diff formatting
+
+```bash
+git diff --check
+```
+
+Result:
+
+```text
+[no output]
+```
+
+### Working tree artifact check before report/commit
+
+```bash
+git status --short
+```
+
+Result:
+
+```text
+ M tracks/qmc/solutions/frustration-free/challenge-194/src/long_range_percolation/kernel.py
+ M tracks/qmc/solutions/frustration-free/challenge-194/src/long_range_percolation/model.py
+ M tracks/qmc/solutions/frustration-free/challenge-194/tests/test_kernel.py
+ M tracks/qmc/solutions/frustration-free/challenge-194/tests/test_model.py
+ M tracks/qmc/solutions/frustration-free/challenge-194/tests/test_oracle.py
+```
+
+No unrelated untracked artifacts were produced by this fix wave.
+
+## Files Changed
+
+- `tracks/qmc/solutions/frustration-free/challenge-194/src/long_range_percolation/model.py`
+- `tracks/qmc/solutions/frustration-free/challenge-194/src/long_range_percolation/kernel.py`
+- `tracks/qmc/solutions/frustration-free/challenge-194/tests/test_model.py`
+- `tracks/qmc/solutions/frustration-free/challenge-194/tests/test_kernel.py`
+- `tracks/qmc/solutions/frustration-free/challenge-194/tests/test_oracle.py`
+- `.superpowers/sdd/final-fix-report.md`