Add roadmap: finite spectral graph theory and continuous-time quantum walks - #258
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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 Mathlib-native finite spectral graph theory and continuous-time quantum walks.
The roadmap fixes the column-state and sign conventions for
U_A(t) = exp(-itA), then decomposes the subject into finite Hermitian evolution, local spectral projectors, transfer and periodicity, arithmetic criteria, mixing, products, standard graph families, and finite spatial search.Scope and coordination
This PR owns continuous-time unitary dynamics. It consumes the equitable-reduction layer proposed in #257 and the general operator-theory work in #126. Discrete-time coined/Szegedy walks are intentionally split into a sibling roadmap.
It excludes open quantum systems, graphon evolution, hardware compilation, and unqualified quantum-advantage claims.
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), including formalized state-transfer, strong-cospectrality, quotient, hypercube, and mixing results. Tau Ceti should refactor the durable mathematics onto Mathlib matrices andSimpleGraphrather than importing Graphplay's private carriers.Validation
lake build TauCetiRoadmap.SpectralQuantumWalks.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.