bert-compose: proportional-release buffer mode (first-order decay → unlocks Lotka-Volterra)

[rsthornton]

The gap (found by the Troncale sweep, verified)

Buffering's release is zeroth-order: a constant amount per tick (min(stock, release_rate)), not a fraction of stock. The Troncale sweep verified (by probe) that this is a hard floor — a Sensing→Modulating loop on the release only sheds downstream mass, it cannot make the STOCK itself drain proportional to its level.

Consequences, all confirmed in troncale-sweep/:

• Exponential (first-order) decay is not expressible. decay rung shows a straight line to zero, not an exponential.
• Lotka-Volterra / predator-prey is not expressible. 05-coupled-predator-prey runs away — the predator grows unbounded because constant-rate death can't balance a growing inflow.

Proposal

A per-buffer release mode, mirroring the gradient/pushed flow-mode pattern already shipped:

• fixed (current): release = min(stock, rate) — zeroth-order, constant amount.
• proportional: release = rate · stock (rate now a fraction/tick, 0..1) — first-order, exponential drain.

This is the conservative-physics analogue of the gradient flow mode, and it's small (one buffer attribute + a branch in circuit.rs step, same shape as the FlowMode work). It must stay conservation-faithful (the ledger already guards this).

Payoff

• Exponential decay becomes atomic → the decay rung gets a true first-order variant.
• Lotka-Volterra / predator-prey becomes constructible → closes the sweep's sharpest boundary (bucket d? → a), and gives the lens packs a real Ecology/Odum population-dynamics demo.
• First-order kinetics generally (radioactive decay, drug clearance, RC discharge) — the other half of the dynamics vocabulary.

Context: Troncale sweep landed this session (src/sweep.rs); conservation ledger fec49c9; gradient flow-mode 65edd87. On feature/bert-core, main untouched.

[rsthornton]

Resolved. time_constant (shipped in #87) is the proportional-release buffer mode this asked for: a Buffer with τ>0 releases ≈ stock/τ per tick — first-order/exponential drain instead of the zeroth-order release_rate.

That unlocks Lotka-Volterra, as predicted:

• predator_prey_first_order() (ladder.rs, sweep rung 05b, bucket "a") — a damped, mass-conserving LV. The predation term βxy is realized as a genuine product: the prey's first-order release (∝ prey) gated by a Sensing read of the predator level (∝ predator), (x/τ)·clamp(k·y) — verified in sweep_sensing_modulating_is_a_product_not_a_sum. A back-pressured predation valve keeps uneaten prey in the stock, so the loop stays conservative. Result: prey peaks, predator peaks a quarter-cycle later, winding to a fixed point (trophic inefficiency dissipates — closed orbits are LV's idealization). Also shipped as the Ecology example "Predator and prey" beside the meadow.
• predator_prey_alpha_growth() — true exponential prey growth (αx) realized conservatively (grass Source gated by Sensing(prey)). Produces a sustained, mass-conserving limit cycle (Rosenzweig-MacArthur), where constant immigration only damped.
• sweep_predator_prey_basin (#[ignore]) — k×η basin over both growth models; conservation asserted across every cell (worst residual ~1e-5). The αx grid shows limit cycles plus predator-extinction collapse at high predation×efficiency (the paradox of enrichment).

The old runaway rung 05-coupled-predator-prey is kept as the before-picture. Sweep narration updated. Commits: 0930415 (damped LV + boundary lift), d657ffc (αx variant + basin harness).

Known limit (not chased): dt=1 Euler gets stiff near the bifurcation boundary.