Conjecture 3 Frontier Alignment

This course starts after Coding and Expansion Foundations. Its job is different from the foundations course: it aligns the learner with the current proof frontier for Conjecture 3 as represented in the local graph.

The course assumes the learner can already explain CSS codes, Tanner graphs, expansion, QLDPC, and the static 2D bottleneck at the level of the foundations course. It then teaches the live research spine:

1. what is already theorem-backed;
2. what is presentation-dependent versus presentation-invariant;
3. what CD(T_n, G) still means after the naive routing interpretation fails;
4. where the intrinsic matroid and compiler-native routes currently stop.

Course Outcome

After this course, the learner should be able to state the current Conjecture 3 frontier without collapsing solved and open parts. In particular, the learner should be able to say:

• the minimal static near-square 2D lower bound is already solved for theorem-level Quantum Tanner families;
• the remaining frontier is not "prove any 2D lower bound" but refine the result toward compiler-native CD(T_n, G) semantics, explicit deterministic families, and intrinsic balanced cut-rank mechanisms;
• stabilizer cut rank is the right invariant cut object, but ordinary graph-cut or path-routing semantics do not automatically follow;
• dense tangle breadth, local quotient-image accumulation, and Route-D semantic separation are current frontier formulations, not established closure theorems.

Lessons

• Lesson 01 - Frontier Status and How to Read the Spine
• Lesson 02 - Static 2D Theorem and Separator Meta-Theorem
• Lesson 03 - Explicit Quantum Tanner Family Stack
• Lesson 04 - Stabilizer Cut Rank and Matroid Connectivity
• Lesson 05 - Submodular CD and SWAP-Only Service
• Lesson 06 - Why Classical Routing Semantics Fail
• Lesson 07 - Intrinsic Matroid Frontier
• Lesson 08 - Local-Block Rank Accumulation
• Lesson 09 - Route-D Hidden-Vertex Frontier
• Lesson 10 - Alignment Capstone and Research Handoff

Textbook Chapters

• 01 - Current Frontier and Static 2D Barrier
• 02 - Quantum Tanner Explicit-Family Stack
• 03 - Stabilizer Cut Rank and Submodular CD
• 04 - Intrinsic Matroid and Route-D Frontier

Progress

• Course Progress

Assessment

• Conjecture 3 Frontier Assessment Rubric

Source Trace

This course is generated from the local Conjecture 3 graph, not from Heptabase prose. Its source map is here.

When using this course in live tutoring, do not mark alignment complete merely because these files exist. Alignment requires the learner to pass the diagnostics and capstone checks in Lesson 10, graded with the assessment rubric.