Static 2D Separator Cut-Rank Manuscript Package

Claim/Theorem

The graph now supports a publishable manuscript package centered on the solved static-2D and separator lower-bound core, with Route-D hidden-variable realization relegated to appendix/frontier evidence.

The package should be organized around five parts.

1. Static near-square 2D lower bound.

   The presentation-invariant theorem is already on disk: [[quantum-tanner-good-family-presentation-invariant-2d-barrier.md]] gives an Omega(sqrt(n)) depth lower bound in linear space for theorem-level Quantum Tanner good families. The proof route is parameter-based, via [[2d-syndrome-depth-from-code-parameters.md]], and therefore avoids the unresolved intrinsic cut-rank route.

2. Fixed-minor-free and weighted-separator extension.

   [[weighted-separator-function-to-syndrome-depth.md]] packages the separator mechanism as a hardware meta-theorem, and [[fixed-minor-free-hardware-syndrome-depth-barrier.md]] specializes it to bounded-degree fixed-minor-free hardware. This gives the natural generalization beyond square grids.

3. Stabilizer cut-rank functional.

   [[stabilizer-cut-rank-functional.md]] and [[cross-cut-stabilizer-rank-rank-formula.md]] provide the presentation-invariant cut-rank language needed to state the stronger CD-like objective without committing to a specific Tanner presentation.

4. SWAP-only compiler lower bound through submodular cut congestion.

   [[submodular-cut-congestion-lower-bounds-swap-only-compiler-depth.md]] and [[stabilizer-cut-rank-defines-canonical-submodular-cd-object.md]] give the compiler-native cut-functional theorem in the measurement-free SWAP-only regime. This is the cleanest rigorous CD_{\mathrm{sub}} statement currently available.

5. Route-D hidden-variable realization as appendix/frontier evidence.

   The Route-D auxiliary-variable program should be summarized as boundary evidence, not as the manuscript's main theorem route. [[coordinate-toggle-finite-branch-demoted-to-computational-frontier.md]] records that the most recent finite coordinate-toggle obstruction branch returned Outcome D and should now be appendix/computational frontier material unless a new exact generator theorem or closed sparse dual appears.

The active manuscript pivot is therefore:

Present the solved static near-square 2D barrier and its separator/cut-rank/compiler-native extensions as the main story; keep dense intrinsic tangle breadth and hidden-variable realization as frontier discussion rather than proof-critical dependencies.

Dependencies

• [[quantum-tanner-good-family-presentation-invariant-2d-barrier.md]]
• [[2d-syndrome-depth-from-code-parameters.md]]
• [[weighted-separator-function-to-syndrome-depth.md]]
• [[fixed-minor-free-hardware-syndrome-depth-barrier.md]]
• [[stabilizer-cut-rank-functional.md]]
• [[cross-cut-stabilizer-rank-rank-formula.md]]
• [[stabilizer-cut-rank-defines-canonical-submodular-cd-object.md]]
• [[submodular-cut-congestion-lower-bounds-swap-only-compiler-depth.md]]
• [[coordinate-toggle-finite-branch-demoted-to-computational-frontier.md]]

Conflicts/Gaps

• This node is a manuscript-planning node, not a new proof.
• The static-2D theorem is already solved in a parameter-based presentation-invariant form, but the sharper intrinsic dense-breadth and full classical-routing realization programs remain open.
• The SWAP-only CD_{\mathrm{sub}} theorem is cut-functional and submodular; it does not recover packet/path/guest-graph semantics.

Sources

• local graph synthesis from the dependency nodes listed above