gc: the ArenaBytes productivity backoff is computed and then discarded above the trigger ceiling

[proggeramlug]

Summary

gc_finish_arena_trigger_collection maintains an adaptive step that is meant
to back the ArenaBytes threshold off when collections stop being productive.
Above gc_trigger_absolute_ceiling_bytes() that signal is computed, stored,
doubled, and then discarded — the threshold arithmetic cannot see it, so the
arm re-arms at a fixed new_total + 16 MB no matter how little the last
collection freed.

This is the shape of #9589, where the idle reducer scored every full
unproductive because old_gen_in_use_bytes is a sum of bump offsets a sweep
cannot lower. There the fix was to price the cycle by its own freed bytes. Here
the price is already computed and thrown away.

Mechanism

let stepped = new_total.saturating_add(step);
let capped  = stepped.min(gc_trigger_absolute_ceiling_bytes());
let floor   = new_total.saturating_add(gc_trigger_headroom_floor_bytes());
let next_trigger = std::cmp::max(capped, floor) + credit;

• gc_trigger_absolute_ceiling_bytes() is a quarter of the device budget capped
  at 128 MB.
• step starts at 128 MB (GC_STEP_INITIAL) and doubles toward
  GC_THRESHOLD_MAX_BYTES (1 GB) whenever pct_freed falls outside 10–84 %.

So new_total + step clears the ceiling on the first collection and capped
is pinned at the ceiling for the rest of the process. Once new_total passes
ceiling − headroom_floor, max(capped, floor) selects floor every time, and
step stops affecting the result at all.

Measured

Compiled claude-code TUI, 3300-character streamed reply, PERRY_GC_DIAG=1,
66 [gc-step] lines:

median pct_freed	0 %
median sweep_freed	203 KB
median block_reclaim	65 KB
median step	1,073,741,824 (saturated at the 1 GB maximum)
pre_in_use range	19 MB → 297 MB

The backoff was at its maximum for essentially the whole turn and had no effect.
The arm fired 51 times in one reply, each freeing a median of 131 KB
against MallocCount's 10.0 MB in the same run.

Tests

Branch perf/arena-trigger-pricing on proggeramlug/perry extracts the
computation as a pure function — the bug is invisible in the fused expression —
and adds gc::tests::arena_trigger_pricing:

fn arena_trigger_headroom_bytes(step: usize) -> usize {
    gc_trigger_headroom_floor_bytes().max(step.min(gc_trigger_absolute_ceiling_bytes()))
}

• a_productive_collection_keeps_the_headroom_floor
• an_unproductive_collection_earns_more_headroom_than_a_productive_one
• headroom_is_bounded_by_the_absolute_ceiling

Sabotage-proved: restoring the old arithmetic (headroom = floor, step
ignored) fails exactly the second and third and leaves the first passing.

Why this is filed as an issue and not a PR

Correcting the arithmetic changes behaviour, and the behaviour it produces is
not currently acceptable. Honouring the backoff is precisely what makes the
heap grow: measured on the rig over 3 interleaved rounds, the corrected version
buys −10.8 % turn CPU at 3300 characters and costs settled footprint
754 → 920 MB and peak RSS 968 → 1223 MB. A CPU win with a footprint regression
is rejected under the campaign's directive, so the fix must land together with
whatever makes backing off safe — not on its own.

The wider investigation into that arm is written up in
secret-tests/cc-perf-campaign/HANDOFF_arenabytes_solution_space.md: three
variants tried, all refuted, with the reasons.

A latent defect documented with a test that fails under sabotage is worth more
than a behaviour change nobody can accept.

[proggeramlug]

Fixed by #9838, landed on main via merge train #9875. The train merged as its own branch, so the close-keyword never fired — closing manually, verified on main.