working on todo.md features

docs/claude/invariants-math-channels.md

@@ -233,3 +233,19 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
     `MathNodeRt` was measured and bought **nothing** -- at six nodes the whole runtime is
     L1-resident either way. It was kept for the shape, not for a number; do not expect a cache
     argument to pay at this size.
+
+## A gap is a gap in a filter's output, never the end of its state
+
+A reserved hole is NaN in the source channel, and a biquad that integrates it poisons `z1`/`z2`
+for ever: every later sample comes out NaN, so a filtered trace died at the first drop and never
+came back. Relative time made it systematic — a counter gap reserves NaN slots by construction,
+where a stream-time gap is often absorbed by the stamps — but EMI caused it in both modes, and
+the reading was unambiguous: the memoryless channels held 95% finite samples while every
+`LowPass`/`HighPass`/`BandPass` channel held `finite=0`.
+
+`biquad_step()` therefore returns NaN **without touching the state words** when its input is not
+finite. The hole stays visible in the filtered trace (the gap is the truth about the data), the
+filter's history remains the last *real* samples it saw, and the trace resumes after the hole
+with at most the transient a re-start costs. The exit dump's `math '<name>': finite=N/M` line is
+the assertion: `finite` must be about `M` minus the hole share, and `finite=0` beside non-zero
+`hole_slots` is this defect returned.