Conjecture 3 Graph Audit

Purpose

This file is the maintenance layer for the Conjecture 3 graph. It does not replace index_conjecture_3.md; it tells future runs which nodes should be treated as the canonical active spine, which nodes are only on-demand support, and which nodes are historical or boundary markers that should not be loaded by default.

Current recommendation: do not delete or merge nodes aggressively yet. The atomic-node discipline is still paying off. The right way to control context size at the current stage is to keep the graph intact but narrow the default read set.

Default Read Set

Future Conjecture 3 runs should, by default, read:

• index_conjecture_3.md
• the nodes in the Canonical Spine section below
• any node directly named in the current local frontier question

Do not load the full 60+ node neighborhood unless the active proof attempt explicitly needs it.

Canonical Spine

These are the nodes currently closest to the live mathematical frontier. They are the ones future runs should load first.

• quantum-tanner-good-family-presentation-invariant-2d-barrier.md
• 2d-syndrome-depth-from-code-parameters.md
• weighted-separator-function-to-syndrome-depth.md
• stabilizer-cut-rank-functional.md
• swap-only-compiler-extraction-reduces-cd-to-stabilizer-cut-rank.md
• token-crossing-extraction-fails-for-swap-only-compilation.md
• cross-cut-gate-service-lower-bounds-stabilizer-cut-rank.md
• stabilizer-cut-rank-is-not-a-graph-cut-function.md
• stabilizer-cut-rank-defines-canonical-submodular-cd-object.md
• submodular-cut-congestion-lower-bounds-swap-only-compiler-depth.md
• generic-submodular-demand-does-not-force-classical-routing-realization.md
• matroid-connectivity-does-not-force-hypergraph-approximation.md
• binary-matroid-connectivity-equals-fundamental-graph-cut-rank.md
• fundamental-graph-edge-cuts-are-basis-unstable.md
• basis-robust-fundamental-graph-loads-must-be-pivot-invariant.md
• local-incidence-lifts-of-fundamental-graphs-are-not-pivot-robust.md
• pivot-class-best-incidence-load-still-overestimates-connectivity.md
• simple-binary-connectivity-violates-nonnegative-hypergraph-cut-condition.md
• four-qubit-stabilizer-cut-rank-is-hidden-vertex-graph-cut-representable.md
• five-qubit-stabilizer-cut-rank-satisfies-fsep.md
• boolean-network-generalization-adds-no-nonmonotone-power-for-stabilizer-cut-rank.md
• five-qubit-stabilizer-cut-rank-is-hidden-vertex-graph-cut-representable.md
• six-qubit-stabilizer-cut-rank-escapes-modular-plus-fan-cone.md
• six-qubit-witness-survives-all-four-ary-exact-minors.md
• six-qubit-witness-satisfies-direct-fsep.md
• six-qubit-witness-is-hidden-vertex-graph-cut-representable.md
• parallel-class-affine-basis-family-is-hidden-vertex-graph-cut-representable.md
• parallel-extension-of-binary-circuit-gives-threshold-lift-cut-rank.md
• direct-sums-of-threshold-lift-pieces-stay-hidden-vertex-representable.md
• low-order-gluing-does-not-explain-high-intrinsic-width.md
• threshold-lift-plus-direct-sum-class-never-reaches-connectivity-three-core.md
• multiple-parallel-classes-on-one-circuit-give-connected-cut-rank-at-least-three-family.md
• multi-parallel-circuit-connected-family-reduces-to-selected-or-selector.md
• minimizing-hidden-binary-submodular-energy-preserves-submodularity.md
• selected-or-selector-is-not-hidden-vertex-graph-cut-expressible.md
• selector-quotient-is-not-a-submodular-minor-of-connected-family.md
• branch-min-route-for-connected-family-fails-at-local-submodularity.md
• smallest-connected-multi-parallel-circuit-member-survives-all-four-ary-exact-minors.md
• cross-cut-stabilizer-rank-rank-formula.md
• quantum-tanner-expander-anchor.md
• quantum-tanner-diagonal-expansion-structure.md
• quantum-tanner-incidence-spectral-gap.md
• regular-graph-expansion-to-incidence-expansion.md
• quantum-tanner-local-generator-blowup.md
• incidence-expansion-to-parity-tanner-expansion.md
• quantum-tanner-theorem17-parity-expander.md
• quantum-tanner-theorem17-static-2d-barrier.md
• dual-distance-gives-generator-puncture-rank.md
• small-side-local-cut-gives-full-local-cross-rank.md
• cross-cut-rank-not-monotone-under-stabilizer-extension.md
• tangle-breadth-gives-k-connected-set.md
• tangle-independent-set-gives-connected-set.md
• high-tangle-order-gives-large-connected-set.md
• robust-tangle-tree-displays-all-nonsequential-separations.md
• every-k-flower-is-anemone-or-daisy.md
• reduced-partial-3-tree-is-unique.md
• sequential-matroid-has-canonical-left-right-ends.md
• good-codes-admit-logarithmic-width-lean-decomposition.md
• large-k-connected-set-gives-balanced-cut-rank.md
• dense-k-connected-set-forces-balanced-cut-rank.md
• lean-matroid-bag-gives-rank-connected-set.md
• high-tangle-order-gives-large-tangle-independent-set.md
• expansion-cut-to-syndrome-depth.md

On-Demand Support

These nodes remain useful and correct, but they are not part of the default active spine. Load them only when the current argument explicitly needs them.

• spectral-gap-to-regular-graph-expansion.md
• dual-distance-excludes-zero-coordinates.md
• tensor-product-preserves-no-zero-coordinates.md
• connected-basis-for-nonzero-coordinate-code.md
• tanner-to-contracted-expansion-transfer.md
• contracted-expansion-to-cross-cut-stabilizers.md
• 2d-local-clifford-syndrome-space-depth-tradeoff.md
• fixed-minor-free-hardware-syndrome-depth-barrier.md
• balanced-cut-rank-to-syndrome-depth.md
• cut-rank-is-interface-state-dimension.md
• exact-2-separation-is-2-sum.md
• nonminimal-exact-3-separation-is-3-sum.md
• maximal-partial-3-tree-displays-all-nonsequential-3-separations.md
• nonsequential-equivalence-class-without-special-gadgets-is-canonical-chain.md
• well-positioned-nonsequential-3-separation-has-safe-element.md
• internally-4-connected-forces-cut-rank-at-least-three.md
• k-flower-local-connectivity-classification.md
• normalized-sequential-orderings-have-bounded-end-variation.md
• tangle-order-equals-branchwidth.md
• large-tangle-yields-weakly-4-connected-minor.md
• large-k-connected-set-persists-in-weakly-4-connected-minor.md
• canonical-tree-distinguishes-all-matroid-tangles.md
• good-codes-have-logarithmic-branchwidth.md
• linked-branch-decomposition-exists-at-optimal-width.md
• branchwidth-and-matroid-treewidth-are-equivalent.md
• good-codes-have-logarithmic-matroid-treewidth.md
• every-matroid-admits-optimal-lean-tree-decomposition.md
• good-codes-have-weakly-4-connected-log-branchwidth-minor.md
• good-codes-have-some-linear-cut-rank.md
• good-code-parameters-do-not-imply-cut-rank.md
• good-ltc-does-not-imply-balanced-cut-rank.md
• smooth-ltc-cayley-characterization.md
• cayley-ltc-characterization-insufficient-for-balanced-cut-rank.md
• left-right-cayley-ltc-from-local-agreement-plus-expansion.md
• agreement-expander-lifts-local-testability.md
• ltc-sparse-cut-product-decomposition.md
• strong-ltc-constraint-graph-small-set-expander.md
• separator-profile-bounds-code-distance.md
• 2d-local-syndrome-tradeoff-tightness.md
• 2d-qec-overhead-from-logical-error-target.md
• code-realization-vc-treewidth-bound.md
• balanced-linear-cut-rank-from-trellis-width.md
• matroid-pathwidth-equals-code-trellis-width.md
• good-classical-codes-have-linear-matroid-pathwidth.md
• trellis-width-to-syndrome-depth-via-hardware-ordering.md
• hardware-cutwidth-to-syndrome-depth.md
• code-branchwidth-to-syndrome-depth-via-hardware-tree-decomposition.md
• qldpc-css-constituent-codes-not-good.md
• wolf-parameter-bound-insufficient-for-css-qldpc-constituents.md
• quantum-tanner-constituent-ltc.md

Alternate CD-Route Nodes

These nodes are still worth keeping because they stay closest to the conjectured congestion-dilation functional, but they are no longer the shortest path to the current theorem frontier.

• packet-routing-o-c-plus-d.md
• expander-cut-to-crossing-matching.md
• cross-cut-matching-service-bound.md
• 2d-grid-routing-tightness.md
• 2d-grid-bisection-width.md
• nonadaptive-2d-nearest-neighbor-lower-bound.md
• swap-only-2d-check-layer-cut-barrier.md

Boundary And Escape Nodes

These are important as scoping and falsification markers. They show which extra resources evade the barrier and therefore should be excluded when stating the conjecture precisely.

• nonlocality-cost-for-good-qldpc.md
• thin-planar-connectivity-escape.md
• bilayer-locc-2d-implementation-boundary.md
• hierarchical-memories-2d-threshold-escape.md
• edge-disjoint-path-teleportation-escape.md

Superseded Or Historical Corollaries

These remain mathematically correct, but they should not be loaded by default because stronger nodes now subsume their role.

• random-local-codes-generic-no-zero-coordinates.md
• quantum-tanner-random-model-parity-expander.md
• quantum-tanner-random-model-static-2d-barrier.md
• quantum-tanner-explicit-gap-reduction.md

Merge / Deletion Recommendation

• Do not merge or delete nodes yet.
• The graph is still internally consistent and the node boundaries remain mathematically meaningful.
• If future context pressure becomes severe, the first safe compression target is the Superseded Or Historical Corollaries section above, not the canonical spine.