Phase 1: Implement Eq. 24-style Newton-Schulz inner momentum variant (muon_ns)

[georgepullen]

Purpose

Implement Newton-Schulz nonlinearity path for inner momentum updates to align with Eq. 24-style formulation.

Mandatory Reading (blocking)

First comment must summarize:

• reports/NL_IMPLEMENTATION_ORACLE.md section 6.1.1 and optimizer gap notes
• reports/paper/NL-print.extracted.clean.txt Eq. (24)
• src/nested_learning/optim/m3.py Newton-Schulz implementation

Required Code Anchors

• src/nested_learning/optim/deep.py
• src/nested_learning/optim/m3.py
• src/nested_learning/optim/factory.py

Scope

• Add inner variant muon_ns using Newton-Schulz output transform.
• Clarify difference between outer Muon optimizer and inner muon_ns memory rule in docs.
• Keep backward compatibility with current muon configs.

Test Requirements

• Unit tests for NS path shape/stability.
• Deterministic toy-case checks.

Deliverables

• Variant implementation + docs + ablation config.

Acceptance Criteria

• No regression in outer optimizer behavior.
• 5k run finite with expected telemetry keys.
• First issue comment contains mandatory reading summary.