Conjecture 3: QLDPC Congestion-Dilation Barrier

Big Picture

Conjecture 3 asks for a compiler-native lower bound explaining why expander-style QLDPC syndrome extraction becomes expensive on constrained hardware. The current repo state already proves the minimal static near-square 2D target for theorem-level Quantum Tanner good families, while the broader CD(T_n, G) interpretation remains open.

Current Status

• The publishable core is organized by static-2d-separator-cut-rank-manuscript-package.md.
• The strongest clean theorem is quantum-tanner-good-family-presentation-invariant-2d-barrier.md: theorem-level Quantum Tanner families have depth \(\Omega(n^{3/2}/m)\) for 2D syndrome extraction, hence \(\Omega(\sqrt n)\) in linear space.
• Separator and fixed-minor-free extensions are tracked by weighted-separator-function-to-syndrome-depth.md and fixed-minor-free-hardware-syndrome-depth-barrier.md.
• The compiler-native object is now submodular rather than ordinary packet routing: stabilizer-cut-rank-defines-canonical-submodular-cd-object.md and submodular-cut-congestion-lower-bounds-swap-only-compiler-depth.md.
• The unresolved intrinsic frontier is dense original-matroid connectivity, with dense-tangle-breadth-is-the-canonical-remaining-intrinsic-target.md as the default target if that route reopens.

Default Read Set

Before widening context, read:

1. Research map
2. Graph audit
3. Any node explicitly named by the active question

Next Actions

1. Polish the partial-resolution manuscript package without claiming the full original CD conjecture.
2. Decide whether the next proof effort targets deterministic explicit component codes, dense intrinsic matroid connectivity, or compiler-native submodular semantics.
3. Keep Route-D computational evidence in research/computational/ unless a new theorem-level hidden-vertex or valued-CSP argument is introduced.

Local Files

• Research map
• Graph audit
• Zotero actions report
• Learning corpus
• Manuscript package