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Coding and Expansion Foundations

This course builds the five foundations needed to read the Conjecture 3 research map fluently:

  1. classical linear codes over GF(2)
  2. Tanner graphs and LDPC structure
  3. expander graphs and graph cuts
  4. CSS and QLDPC constructions
  5. syndrome extraction under hardware constraints

It is intentionally not a general coding-theory textbook. It is a personalized bridge from stabilizer/surface-code intuition into the QLDPC barrier research program.

Course Outcome

After this course, the learner should be able to explain why expander-style QLDPC codes create a routing bottleneck on static near-square 2D hardware, identify which pieces of the Conjecture 3 program are already theorem-backed, and locate the remaining open gaps around compiler-native CD(T_n, G) semantics.

The follow-on course is Conjecture 3 Frontier Alignment. Start it only after completing this course or passing the completion diagnostic.

Fresh-Start Lessons

Use these files as the learner-facing course. They regenerate the Heptabase material from scratch, correct loose or broken parts, and add the missing final course material.

The old sessions/ files remain as compact historical plans. They are not the fresh-start learner path.

Progress

Assessment

Use the rubric after the lesson path, or as a placement test if the learner wants to skip directly into the frontier course.

Textbook Chapters

Source Trace

The historical Heptabase source map is here. Use it as provenance and teaching-style evidence, not as the authoritative mathematical source. The lesson mismatch is explained there: Heptabase had seven AI Tutor sections, but each section contained multiple finer lesson parts.