vectorized_mlp_skill: per-absolute-index MLP init seeding (chunk-invariant fits)

Goal

Make fit_batched_split_mlp (src/explore_persona_space/analysis/vectorized_mlp_skill.py) partition-invariant: seed each group's MLP init from the group's ABSOLUTE index/key rather than its batch position, so any chunking/partitioning of a group list across calls yields bit-identical per-group inits; update the documented determinism contract and the assert_matches_reference-style exactness gates (#658/#722 lineage) accordingly.

Problem (surfaced by #841 fu-r1 v15)

fit_batched_split_mlp seeds inits as torch.manual_seed(seed) followed by one _MLPMulti init per group in BATCH order (member g gets draw g; docstring "SEEDING" paragraph). Splitting the same group list across separate calls therefore changes every member's init: measured maxdiff 0.82 between a 5-group call and 2-group calls over the same groups. The docstring documents this as "Deterministic + reproducible across runs" without flagging the partition sensitivity.

Contrast: fit_batched_loco_mlp / fit_batched_loco_mlp_multihead (on main) draw ONE shared n-fold init block reused by every group, so they are partition-invariant by construction, and the existing exactness gate already asserts internal chunk-invariance for them. The bug class is specific to the split variant's per-group draws.

Proposed change

1. Derive each group's init deterministically from (seed, group absolute identity) — e.g. a per-group torch.Generator seeded from seed + a stable per-group key (caller-supplied absolute index, or a stable non-salted hash of SplitMLPGroup.key). Exact mechanism is a plan decision; the requirement is: bit-equal per-group inits under any partition (and ideally any reordering) of the same group list across calls.
2. Update the docstring SEEDING contract to state the partition-invariance guarantee.
3. Extend the exactness/self-check gate to assert partition-invariance for the split variant (e.g. one 5-group call vs 2+3-group calls, bit-identical per-group results), mirroring the existing chunk-invariance gate for the LOCO variants.
4. Unit test pinning the new contract.

Acceptance criteria

1. fit_batched_split_mlp(groups, ...) and any partition of groups across calls produce bit-identical per-group inits (hence identical trained results at matched settings) — asserted by a new gate/test.
2. Documented determinism contract (docstring + any doc/rule text referencing it) updated.
3. Existing #658/#722 exactness gates still PASS (LOCO variants' contract unchanged).
4. ruff + touched-scope pytest PASS.

Constraints / dependencies

• The target function is NOT on main — it exists on TWO unmerged live branches: issue-841 (origin commit 404046fefe; 21 commits ahead of main; #841 live at followups_running) and issue-922 (carries a copy plus consumers experiments/issue_922/maps922.py, scripts/issue922_fit_maps.py; #922 live at planning). Branch-local consumers of the function: experiments/issue_841/maps.py, scripts/issue841_scaling_common.py / _stage0.py (issue-841), and the issue-922 files above. main's copy of vectorized_mlp_skill.py carries only the LOCO variants. The plan MUST pick a landing strategy (wait-for-branch-merges vs port-the-function-to-main-with-fix and accept reconciliation cost at each branch's eventual merge vs another option) and must NOT write into #841's or #922's live worktrees.
• Forward-only contract change: the new seeding changes numerical outputs relative to the old batch-order inits. Committed artifacts produced under the old contract (e.g. #841's eval results) are NOT retro-invalidated; the plan states how any reproduce-check referencing old outputs is handled.

Compute

0 GPU-h — CPU-only src/analysis change + tests. No pod.

References

• src/explore_persona_space/analysis/vectorized_mlp_skill.py (main: LOCO variants + exactness gate; issue-841 branch ~line 785: fit_batched_split_mlp)
• .claude/rules/vectorize-many-cell-fits.md (determinism / Supersede-contract lineage, #658/#722)
• Origin prompt (verbatim, from task frontmatter): "#841 fu-r1 v15 finding: fit_batched_split_mlp seeds each group's MLP init in BATCH ORDER (vectorized_mlp_skill.py:809), so chunking a group list changes every member's init (measured maxdiff 0.82 between 5-group and 2-group calls). Proposed: seed by the group's ABSOLUTE index/key so any chunking is bit-equivalent; update the documented determinism contract + assert_matches_reference gates (#658/#722) accordingly. Out of workflow-fix scope (src/analysis) — ordinary infra change, full review pipeline."