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Conjecture 3 Manuscript Skeleton

This directory contains the first LaTeX skeleton for the Conjecture 3 partial-resolution paper.

Title used:

Separator Barriers for Quantum LDPC Syndrome Extraction

Files

  • main.tex: manuscript driver, theorem environments, abstract, bibliography hook.
  • sections/introduction.tex: motivation, contributions, scope, and relation to Conjecture 3.
  • sections/models.tex: circuit and hardware model definitions.
  • sections/static_2d_barrier.tex: static near-square 2D lower bound.
  • sections/separator_barriers.tex: weighted-separator theorem and fixed-minor-free corollary.
  • sections/stabilizer_cut_rank.tex: intrinsic stabilizer cut-rank functional.
  • sections/submodular_cd.tex: canonical submodular demand and SWAP-only lower bound.
  • sections/discussion.tex: interpretation and limitations.
  • appendices/proof_details.tex: proof-polish and citation-verification TODOs.
  • appendices/route_d_frontier.tex: Route-D frontier evidence only.

Build

From this directory, try:

1
latexmk -pdf -interaction=nonstopmode main.tex

The bibliography path is ../10_conjectures.bib.

Verified Local Citation Keys

  • leverrierQuantumTannerCodes2022
  • baspinLowerBoundOverhead2023
  • delfosseBoundsStabilizerMeasurement2021
  • alonSeparatorTheoremGraphs1990
  • kashyapConstraintComplexityRealizations2009
  • geelenBranchwidthWellquasiorderingMatroids2002

The last two keys are available in the local bibliography but are not yet central in the skeleton text.

Scope Guardrails

  • The skeleton does not claim the full original CD conjecture.
  • The skeleton does not claim packet/path routing semantics for CD_sub.
  • The skeleton does not claim a resolved hidden-variable realization theorem.
  • The skeleton does not claim coordinate-toggle impossibility.
  • Route-D appears only in the appendix as frontier evidence.