rational plan v0.2: the ten open questions decided

[tap]

What this changes

rational/PLAN.md goes from v0.1 (draft, ten open questions) to v0.2: every section 9 question is decided by the maintainer as recommended and folded into the decisions it touches (new R13–R16, amended R3/R6/R7/R11), with sections 3.3–3.6 regenerated under the settled rules and stale file:line citations refreshed. One row of the family PLAN.md (the illustrative 48 → 88.2 chain) is corrected to match. No code.

Why

The plan's "Next" entry needs a reviewed plan before M0 lands in DspTap; v0.1 left the ten decisions to the maintainer. Decided (2026-10-01):

1. bridge at the lowest k (R13): 48 → 88.2 is bridge k = 0 → ↑2 at 62 % of the MACs of ↑2 → bridge k = 1, same (f_pass, A); the family plan's row corrected; transparent needs no exception.
2. Fewer stages when within 10 % — precisely, 10 % of the rational stages' MACs per output, with bridge's identical stage excluded from the comparison so a bridge-dominated total cannot absorb a worse rational factorization (R3). 17 rows change: 3/1 is one ↑3 (12.0 vs 11.0), 16 → 44.1 is ↑3 · bridge↓ (71.1 vs 70.0), and so on; 8 → 11.025 stays ↑2 · ↑3 · bridge↓ · ↓2 · ↓2.
3. Dipping rows flagged ⚑ "covered, not recommended" when the bridge stage runs at ≥ 2× the chain's output rate (R14): 38 rows; risk S4 mitigated.
4. chain<> in DspTap confirmed (R6), proven on decimate.h in M0.
5. 384 kHz stays (R15).
6. ↑4 / ↓4 is two half-bands; no single 4th-band stage ships until a latency-first consumer asks (R3). The 1/16 and 1/24 rows it would improve are named, with the cost (1/16 at 133 vs 113 est.).
7. bridge's four profile names reused, edges as fractions of the pair's lower rate (R5).
8. Latency as the exact rational plus latency_seconds() (R7); bridge keeps its double.
9. The C ABI exposes the 34 named within-family chains (R16).
10. Family version 0.5.0 at M6 (R11).

Verification

Prose only. The matrix tables were regenerated by the scratch generator described in section 3 (Dijkstra over the 2^a·3^b lattice with the harris length estimate, the fewer-stages selection on the rational part around the minimal chain's own bridge stage, the flag, and no 4th-band stage); every ordered pair of the 14 rates is still covered (none excluded). Every number remains labelled est. and owed to M2/M4. pre-commit has no Markdown hook; CI's style and book jobs are the first gate.

Notes for the reviewer

• Two things the regeneration surfaced, both recorded in the plan rather than hidden: without a single 4th-band stage, long ↓16/↓24 chains cost up to 18 % more (est.) than v0.1's ↓4-first chains, which is exactly the latency-first consumer's reopening point; and the first cut applied the 10 % to the whole chain, which let bridge-dominated rows take worse rational stages (8 → 11.025 would have gone 297 → 326) — hence the precise form in decision 2.
• No open questions remain; the next step is M0, the DspTap substrate PR (tap/dsp/nyquist.h, tap/dsp/chain.h).

🤖 Generated with Claude Code

https://claude.ai/code/session_015VR1VC4SDGxHZQQsQvPBaA

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