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Integration: Reading the Research Map

Prerequisites And Diagnostic Checks

Ask the learner to reconstruct this chain:

good QLDPC -> expansion -> cut demand -> hardware separator bottleneck -> syndrome-depth lower bound

Then ask which arrow feels least justified.

Concrete Motivation

The purpose of this course is not to memorize QLDPC vocabulary. It is to make the Conjecture 3 research graph readable enough that the learner can join the frontier.

Current Map Reading

Begin with:

The audit file is crucial because the graph is large. It tells Codex and the learner which nodes are canonical for the current frontier and which are on-demand support.

The Minimal Target Versus The Frontier

The minimal static 2D target is no longer the vague open problem. The graph records strong theorem-backed routes for static 2D and separator-style syndrome-depth barriers.

The frontier is more subtle:

  • make the compiler-native CD story precise
  • understand stabilizer cut-rank as a submodular or matroidal demand object
  • decide whether that demand can be represented by a routing-like object with real compiler semantics

Reading A Node

For any node, ask:

  1. Is this an established theorem, an inferred bridge, a counterexample, or a boundary marker?
  2. What assumptions does it need?
  3. Which earlier nodes does it depend on?
  4. Which gap does it close?
  5. Which gap remains?

This is the correct research-reading unit for this repo.

What This Course Enables

After this course, the learner should be ready for a second, more advanced course on:

  • stabilizer cut rank
  • binary matroid connectivity
  • branchwidth and tangles
  • hidden-vertex graph-cut representability
  • why the CD frontier is not just ordinary graph routing

Active Recall

  • Which source nodes settle the static 2D theorem-level target?
  • What does stabilizer cut rank measure?
  • Why is the remaining CD problem not merely a matter of finding a better graph embedding theorem?

Next-Step Handoff

The recommended next course is a matroid-and-cut-rank frontier course built directly from the canonical spine in ../../../../research/graph-audit.md.