[P0] Synthesize phase-continuous pitch and volume envelopes #11

Parent plan: #1
Priority / gate: P0 / M2
Requirement: F14 in the PRD
Design: Technical design
Depends on: #7, #8, #10, #9

Outcome

Produce sound and reusable functions from the drawn carrier, pitch curve, and gain curve without pitch errors or lost dynamics.

Scope

• Implement per-oscillator accumulated phase θ(t) = θ0 + integral of f(t) in cycles and source s(t) = g(t)·p(frac(θ(t))).
• Use stable analytic integration of log-linear pitch segments, phase-prefix values at knots, and linear gain interpolation.
• Compare the chosen native-node or custom renderer against the analytic reference, including fast modulation and sideband bandwidth behavior.
• Remove carrier DC before modulation; apply headroom once over the completed mix and preserve intentional gain dynamics/silent intervals.
• Integrate revision/cancellation, loop-seam policy, actual sample-rate handling, and shared preview/offline/code-export settings.
• Expose phase/state and pre-final-output rendering interfaces that [P1] Modulate sounds with imported audio or saved clips #20 can extend with an effective-frequency stream or sampled carrier; retain the analytic log-linear reference for unmodified drawn lanes. Full clip-driven integration belongs to F18.

Acceptance criteria

• Constant pitch/gain reproduce the equivalent unmodulated oscillator; sine-carrier sweeps match the declared integrated phase.
• Phase is continuous across pitch knots and render chunks; near-equal frequency endpoints use a numerically stable constant-frequency limit.
• The implementation never substitutes f(t)·t for integrated phase, and exported JS/Python evaluators use the same interpolation/integration contract.
• All-zero gain renders exact silence; silent spans have only the explicitly documented finite filter/transition tails, without post-envelope mean subtraction or normalization refilling them.
• Fast pitch/gain changes and near-Nyquist harmonics pass spectral tests against the oversampled reference under the recorded bandwidth policy.
• Maximum four-voice compositions preserve relative gain envelopes, obey peak/resource limits, and meet the measured render budget or an explicitly revised requirement.
• Loop boundaries and finite initial phase are explicit in preview and exported metadata; stale jobs cannot restart stopped audio.

Validation

Constant/octave/log-frequency sweep fixtures, near-zero slope and knot-boundary integrals, chunked-versus-whole evaluation, zero-gain and attack/decay tests, modulation spectrum comparisons, and preview/export parity.

Boundaries

Unbounded modulation bandwidth and bit-identical device output are not promised; any rendered changes must be visible and reproducible.

Implementation evidence

Phase-integrated pitch/gain rendering and complete source functions are implemented. Analytic sweeps, zero gain, octave and mixing fixtures pass. Maximum-workload performance qualification remains open in #16.

Merged work: #23, #28, #29.

Validated CI run · Validation report. The report arrives with the final documentation PR; numerical/browser logs already exist. Release-wide human acceptance and the recorded performance/memory gaps remain explicit in #15 and #16.