Batching vs speculation: Bar B's cost row is unwinnable as written

[phall1]

Derived result: Bar B's "non-negotiable" cost row is unwinnable with speculation and comfortably winnable with batching — and no invariant forbids batching.

Law 3: cost per landed PR is governed by PRs-per-validation, not by speculation efficiency. Speculation validates one atom per candidate; a batch validates g. This also means M4 (cache) and M5 (affected targets) cannot help — they reduce cost per validation, which applies to the baseline equally, so they cannot move a ratio.

A batch of unrelated atoms replayed as one linear chain is structurally identical to a stack-as-atom: one candidate, one tree, one validation, one CAS, one commit per PR preserved. Invariant 1 satisfied identically. Invariant 2 untouched. The design already implements this — it is the THUNDERDOME cohort — but confines it to an emergency regime and sizes it ~5x wrong (max_atoms: 100 vs n* ~ 1/p ~ 20 at p=5%; at 100 and p=5% it lands 0.59 atoms/run, worse than serial).

The stated reason for rejecting batching (README:25, on Mergify) is factually wrong against Mergify's own documentation — they speculate via max_parallel_checks and bisect on batch failure.

Actions

• Name the invariant that forbids batching unrelated atoms in normal flow. If none exists, make batch size a first-class normal-flow scheduler dial alongside speculation width
• Size it from measured p (n* ~ 1/p single-shot, ~1.4/p with split recovery), bounded by the attribution probe budget
• Replace cohort.max_atoms: 100 with that derived quantity
• Restate Bar B's cost row as Pareto dominance over GitHub's 2-D operating surface — at every latency GitHub achieves, we achieve it at no greater CI cost — recording group_size, build_concurrency, the only-merge-non-failing toggle, and the stack-depth mix

Contested, do not quote yet: four lenses computed the multiple as 5x, 3.0x, 1.43x and ~1.0x because they modelled four different GitHub merge queues. The ordering (batching cheaper per landed PR) is robust; the multiple is not. E3/E5 settle it.

See docs/INVESTIGATION.md §2 Law 3, §6 Q2, §7 R2, §10.

[linear-code]

PHA-310