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Add bridge switch / bridge-derived level graph; set up exhaustive test

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- Define bridge switch (E/O switch whose new same-parity edge is a bridge
  in its parity subgraph) and bridge-derived level graph in the paper.
  Note that bridge switches preserve bipartite parity subgraphs, so every
  bridge-derived level graph is automatically valid.
- Discover the E/O-switch relation is directed (irreversible when a switch
  produces a cross-parity edge); T*_9 reaches an ELG forward but no ELG
  reaches it, explaining why it is not derived. This rules out a simple
  switch-invariant characterization.
- Bridge orbits are far smaller than full E/O orbits (~10^4 vs ~10^8 for
  some labellings), making exhaustive search feasible. Each of the 4 open
  duals has ~150 valid parity partitions; exhaustive bridge-orbit search
  per partition can decide bridge-derivability conclusively.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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didericis
2026-05-22 00:09:19 -04:00
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papers/even_level_graph_generators/paper.log
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