[Burntgogi]

Problem

A valid placement with no selected host experts reaches 0 / 0 in the predicted-ratio column. A valid window size that fits no chunk also divides by zero in slots/window, even with positive predicted host work.

Change

• Keep the existing undefined-ratio convention: nan, not a fabricated ratio of zero.
• Keep actual zero work at 0.0; report undefined measured means as nan when no complete window exists.
• Add numeric report regressions for zero-host windows, empty windows, and pooling zero-work and positive-work sets.
• Document these boundaries in the tool's reference header.

No placement/parser changes; this is independent of #659.

Verification

• New report regression failed before the fix with ZeroDivisionError; python3 tools/ref/window-union.py --self-test passes afterward.
• Actual CLI: the issue's full-card placement, only selected experts resident, full-card strata, and empty-window cases with/without predicted host work all exit 0.
• Four positive-work CLI reports are unchanged before/after, including a placement with one idle layer and a strata placement.
• LC_ALL=C bash tools/contrib-check.sh --tier t0 --only '^(fmt|check-recipes|check-comments|check-arch|check-levers)$': 5 checks, 0 red (160 s).

CPU tooling only; no GPU/model validation claimed. Local just pre-review is unavailable because the Claude CLI is not installed.

Closes #656.

[github-actions]

Verdict: CLEAN: Both report divisions handle zero denominators, and the regression assertions distinguish undefined measurements from zero work.

Checked

Duplicates: 0 new functions, types or constants; manual search found no new duplicate owner.
Complexity: report gains two guards for independent denominators.
Silent failure: 2 guarded divisions followed to printed columns; undefined values print nan, while measured zero work remains zero.
Tests: the new report assertions pass with in-memory router sets and fail on the base with ZeroDivisionError. Removing either guard at tools/ref/window-union.py:246 and tools/ref/window-union.py:247 raises ZeroDivisionError; replacing either nan fallback with zero fails an assertion.
Boundaries: full-card and selected-only residency, empty windows and mixed-set pooling checked; three positive-work reports match the base output.
Gates: no existing pins or assertions relaxed; the PR reports FAIL-first evidence for the regression.
Escape catalog: no patterns matched.

Notes

No Rust file changed; dryer and crapper did not run.
Validation used in-memory router sets; the full self-test was not rerun.

_{🔨 Shingler, bloomery's review bot: approves a clean pull request and requests changes on a must-fix (how it works)}

[juliankang4]

@Burntgogi Thanks for the contribution. The review is done, so I'm merging this.