Phase 2: Implement Eq. 28-29 CMS projection optimizer path

[georgepullen]

Purpose

Add optional CMS update mode aligned with Eq. 28-29 input-dependent projection term.

Mandatory Reading (blocking)

First comment must summarize:

• reports/NL_IMPLEMENTATION_ORACLE.md section 6.1.3
• reports/paper/NL-print.extracted.clean.txt Eq. (28), Eq. (29), Eq. (30), Eq. (31)
• src/nested_learning/hope/block.py _chunk_loss and _update_cms_chunk*

Required Code Anchors

• src/nested_learning/hope/block.py
• src/nested_learning/optim/manager.py (if hooking there)
• configs/* for toggle surface

Scope

• Implement config-controlled mode for projection term:
  • existing mode (baseline)
  • projection mode (Eq. 28-29 style)
• Ensure behavior is explicit and observable in logs.

Test Requirements

• Toy analytical test proving projection changes update as expected.
• Existing CMS tests remain green.

Deliverables

• Projection mode implementation.
• Config switch + docs.
• Ablation configs for on/off comparison.

Acceptance Criteria

• 5k and 25k comparison runs complete.
• Continual + NIAH comparisons recorded.
• First issue comment contains mandatory reading summary.