api_throughput_guidelines: disambiguate the two sync/batch crossover figures (200k balanced vs 20k dispatcher constant) + state precedence vs CLAUDE.md

Provenance

workflow_fix_target: docs/api_throughput_guidelines.md

Surfaced by the #2329 q35_ladder_decay post-approval critique panel (round 1), where it caused a full Claude-vs-Codex lens disagreement that consumed a binding reconciler spawn to resolve.

The bug

docs/api_throughput_guidelines.md contains TWO different sync/batch crossover numbers describing two different objects:

• ~200k — the Sonnet-4.5 balanced crossover (around line 75).
• 20k — the recommended dispatcher constant SYNC_BATCH_CROSSOVER_N (around line 132).

Nothing in the document flags that these are different quantities. In the #2329 round-1 panel, the Claude efficiency critic cited ~200k and the Codex efficiency twin cited 20k, each in support of an OPPOSITE verdict on the same plan (PASS vs REVISE) — Codex additionally proposed a mechanical check that would "reject forced Batch when passes exceed 3 or N < 20,000", which would have contradicted CLAUDE.md's standing Batch mandate had it been implemented.

The reconciler's finding was that neither reviewer misread the document: both figures are really there, for different objects, and the document does not distinguish them. That is a documentation defect, not a reviewer defect — and it cost a reconciler spawn plus two rounds of critic reasoning.

Secondary gap in the same document

The reconciler also had to establish the document's own AUTHORITY from a self-description buried at lines 10-12 ("RECOMMENDATIONS, not hard API limits") in order to rule that CLAUDE.md's Batch mandate and the user's scope directive both outrank it. That precedence is correct but should not require excavation: the document should state its standing relative to CLAUDE.md's Critical Rules up front.

Proposed fix

1. Rename or qualify each figure at its site so they cannot be cited interchangeably — e.g. "balanced-cost crossover (Sonnet 4.5): ~200k" vs "dispatcher routing constant SYNC_BATCH_CROSSOVER_N = 20k (a conservative default, not the cost-balance point)" — and cross-reference each from the other.
2. Add a short precedence header near the top: this document is recommendations; CLAUDE.md Critical Rules and an explicit user directive in a task's scope marker both outrank it; the wedge-pass guidance is a general default that a calendar-tolerant zero-GPU phase may legitimately override.
3. State explicitly that the wedge-pass rule (>2-3 passes => prefer sync) applies to GPU-coupled or latency-coupled waves, and that a phase holding no compute may take Batch above that pass count — the exact case the #2329 reconciler had to reason out from first principles.

Acceptance criteria

1. Each crossover figure carries a distinguishing name at its definition site, and neither can be read as "the" crossover.
2. A precedence statement appears before the decision table.
3. The wedge-pass rule states its scope (compute-coupled vs zero-GPU calendar-tolerant waves).
4. No numeric recommendation CHANGES in this task — it is a disambiguation and precedence edit only. Any actual threshold change is a separate task with its own grounding.
5. Grep the repo for existing citations of either figure and update any that are now ambiguous.