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.

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.

Decomposition-Concentration Package¶

This package is no longer part of the default active frontier. It already contains the exact single-bag conditional reduction and the exact adjacent-bag demotion, but no sourced theorem concentrating optimal lean/linked decompositions into dense original-matroid connected mass. Reopen it only if a run introduces a genuinely new subtree-union or cluster-merger invariant.

Boundary Package: Explicit Quotient-Block Witness Program¶

This package is now secondary boundary evidence, not part of the default active frontier. Load it only when a run explicitly needs to check whether a proposed selector-style invariant is already falsified by the current explicit low-cut data.

Route-D Computational Frontier Evidence¶

The coordinate-toggle finite branch is unresolved and should be treated as appendix/computational frontier evidence, not as the default active proof path. Reopen this package only with resumable large-scale column generation, a complete tail-conditioned sorter operation class, or an external valued-CSP/multimorphism theorem.

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.

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.

Superseded Or Historical Corollaries¶

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

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.