Max 20x weekly cap does not scale proportionally with session multiplier

Description

On Max 20x ($200/month), the 5-hour session limit scales as advertised — burst throttling essentially disappeared compared to 5x. But the weekly cap does not scale proportionally. At 87% weekly utilization on Wednesday with a Saturday reset, practical weekly capacity is ~7 full sessions regardless of plan tier.

This matches the math reported in #52135 and #59525: one session consumes ~14% of the weekly cap on 20x, identical to the ratio on lower tiers. The "20x" multiplier widens the per-session pipe but the weekly reservoir doesn't grow proportionally, so heavier sessions just drain the week faster.

Evidence

Data collected via ccburn (utilization snapshots) and codeburn (token/cost ledger) across plan transitions on the same account:

ccburn — ceiling pressure (% of each plan's own cap)

| Period | Plan | Avg 5h | 5h ≥80% | 5h =100% | Avg 7d | 7d ≥80% | 7d =100% |
|--------|------|--------|---------|----------|--------|---------|----------|
| 4/3–4/5 | Pro | 57.5% | 23.5% | 2.2% | 50.0% | 0.0% | 0.0% |
| 4/6–5/5 | 5x | 35.0% | 8.3% | 3.1% | 46.0% | 17.4% | 0.0% |
| 5/6–6/3 | Pro | 54.5% | 24.5% | 14.2% | 41.7% | 10.9% | 0.0% |
| 6/4–6/15 | 5x | 38.3% | 9.7% | 4.4% | 45.2% | 13.5% | 0.4% |
| 6/16–7/1 | 20x | 12.9% | 0.9% | 0.8% | 46.4% | 19.9% | 0.0% |

5h session cap-hit dropped from 9.7% → 0.9% on 20x — working as expected.
7d weekly cap-hit rose from 13.5% → 19.9% on 20x — despite a nominally 4x larger weekly cap.

codeburn — actual consumption (5x vs 20x)

| Metric | 5x (6/4–6/15) | 20x (6/16–7/1) | Ratio |
|--------|---------------|-----------------|-------|
| Cost/day (API-equiv) | $276.55 | $350.40 | 1.27x |
| API Calls/day | 2,933 | 3,159 | 1.08x |
| Sessions/day | 77 | 126 | 1.64x |
| Output Tokens/day | 1,667,543 | 2,169,289 | 1.30x |

Actual consumption increased ~1.3x from 5x → 20x. The cap increased 4x. Yet weekly ceiling contact got worse, not better.

Model mix shift

On 20x, Opus 4.8 consolidated from 53% to 82% of spend — the wider session pipe enables heavier model usage per session, which then eats the weekly cap faster. This is the core mechanism: 20x encourages heavier sessions that deplete a weekly cap that didn't scale 20x.

Current state

Right now (July 1, Wednesday): weekly utilization at 87–88%, reset on Saturday. On the highest-cost consumer plan available.

Expected behavior

If "20x" means 20x the usage capacity, the weekly cap should scale such that 20x session usage doesn't exhaust the week in ~7 sessions — the same count achievable on lower tiers.

Related issues

• #52135 — Max 20x weekly limit depletes disproportionately (51% mid-week, ~17% per session)
• #59525 — Max 20x: neither 2x session nor 1.5x weekly increases applied
• #50742, #47587, #51715, #51219, #41174 — similar reports

Environment

• macOS Darwin 25.5.0
• Claude Code (current)
• Max 20x plan
• Account has been on Pro, 5x, and 20x at various points — data covers all transitions