Add roadmap: equitable partitions and finite operator reduction - #257
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This was referenced Aug 17, 2026
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The README roadmap list and the two issue-template `area` dropdowns are regenerated from the roadmap directories by the sync bot after merge, and the root `TauCetiRoadmap.lean` no longer carries an import list, because `lakefile.toml` globs every module under `TauCetiRoadmap/`. Editing these four files by hand was never required, and made this branch conflict with every other open roadmap pull request. Restoring them to the merge base makes this branch mergeable again; the roadmap is still registered automatically once it merges. Pushed by a maintainer to clear a repository-wide merge conflict, see TauCetiProject#273 Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Summary
Adds a roadmap for equitable partitions as finite operator reductions, centered on Mathlib-native finite types, matrices, and linear maps.
The roadmap separates four notions that are easy to conflate:
A E - E Q;It then identifies graph, stochastic, and symmetry-orbit adapters as consumers of the common operator API.
Scope and coordination
This PR owns the reusable finite reduction layer. The continuous- and discrete-time quantum-walk roadmaps consume it rather than re-defining quotient operators. It is distinct from graph regularity, which concerns approximation by large combinatorial partitions, and from the structured block-operator roadmap, where block constancy is a stronger hypothesis.
The proposed declarations are design probes, not claims that the layer is already implemented.
Provenance
The decomposition is informed by the formal development in
emberian/graphplayat commit822204afe580a93206aa71adbe66b98f9e2beac8(MIT/Apache-2.0). Graphplay's private graph wrappers are not proposed for import; the roadmap calls for refactoring the durable mathematics onto Mathlib-native foundations.Validation
lake build TauCetiRoadmap.EquitableOperatorReduction.Suggestedlake build(8,781 jobs)git diff --checkPrepared with GPT-5.6 Codex under Ember's direction. Ember is reviewing the mathematics and ownership boundaries before marking this ready for review.