Harden foundational course examples after #14

[Doppp]

Context

This is the accuracy and verification follow-up to #14, which made ordinary lesson Markdown the canonical teaching surface for AI from First Principles.

What changed

• make next-token cross-entropy stable directly from logits and test probability-underflow behavior
• prove next-token gradients are averaged across valid positions
• cover large-logit sampling at non-unit temperature
• clarify sequence-length notation in lesson 10
• keep the scaffold discovery cycle prediction-first and align its controls with the stated negative and fractional cases
• make the authoring-guide example satisfy its own worked-example, code-bridge, failure-mode, and recap rubric
• document that the 0.4 course version intentionally uses a fresh browser-progress scope

Implementation approach

• keep foundational instruction in CommonMark lesson prose; no runtime, schema, or directive expansion
• preserve lesson IDs, checkpoint IDs, interactive contracts, and exercise paths
• pair accuracy claims with executable regression tests
• keep pedagogical depth under editorial review and learner playtesting rather than word-count validation

Validation

• pnpm check: 33 suites, 102 tests
• pnpm course:test: 17 suites, 54 tests, plus all 14 starter/reference pairs
• pnpm build
• pnpm test:browser: 16 tests including axe and 320px coverage
• targeted scaffold test and TypeScript check after the input-range alignment
• in-app visual QA at the default viewport and 320px; no horizontal overflow or console warnings

All full-suite commands passed from a clean detached worktree. No implementation-plan file is added or changed.