# V0.2 Scope ## Summary `v0.2` is the smallest next release that expands PDELie in a disciplined way. It does **not** introduce a new major representation layer. It does **not** introduce a new numerical regime. It does **not** widen the ecosystem surface. Instead, it asks a narrower and more important question: > Do the current stable contracts and symmetry pipeline survive contact with a second PDE? The second PDE for `v0.2` is **1D Burgers**. For Milestone 1, the Burgers target is frozen as: - viscous 1D Burgers with fixed `nu` - uniform periodic grid on `x in [0, 2π)` - spatial translation as the first stable recovery / verification target - no new canonical stable objects - no new stable derivative backend --- ## Must Implement ### Stable scope for `v0.2` - uniform rectilinear grids only - synthetic PDE data only - polynomial generators only - verification-first development - Heat remains supported - Burgers is added as the second stable PDE ### Stable canonical objects for `v0.2` The stable contract set remains the current narrow slice unless a second-PDE requirement forces a minimal extension: - `FieldBatch` - `DerivativeBatch` - `ResidualBatch` - `ResidualEvaluator` - `GeneratorFamily` - `VerificationReport` No other canonical objects should become stable in `v0.2` unless absolutely necessary to support the second-PDE vertical slice. --- ## Concrete `v0.2` Target Add a second end-to-end stable path: `FieldBatch -> DerivativeBatch -> ResidualBatch -> GeneratorFamily -> VerificationReport` for synthetic 1D Burgers on a uniform periodic grid. ### Required components - one synthetic 1D Burgers dataset generator - one trusted Burgers residual evaluator - derivative support that works within the existing stable numerical assumptions - one broadened translation fitting path that works for Heat and Burgers under the current stable slice - one finite-transform verification path for the Burgers spatial-translation target - one controlled benchmark task comparing behavior on Heat and Burgers Milestone 1 may retain a minimal internal fitter fallback to the reference spatial-translation direction if the residual-based SVD drifts on Burgers, provided: - the public fitter / verifier API does not change - the fallback remains specific to the spatial-translation target - diagnostics state whether the fallback was used ### Required scientific result - recover and verify spatial translation on Burgers under the stable pipeline - maintain the existing Heat result without regressions --- ## Development Order 1. freeze `v0.2` scope 2. add synthetic 1D Burgers data 3. add Burgers residual evaluator 4. broaden the current translation fitting path just enough for the second PDE 5. add/adjust verification for the Burgers spatial-translation target 6. add cross-PDE tests and release-gate checks --- ## Explicitly Deferred The following are **not** part of stable `v0.2` scope: - weak-form derivatives as a stable backend - invariant-coordinate pipelines as a stable feature - `InvariantMap` as a stable contract - `InvariantLibrary` as a stable contract - `DiscoveryResult` as a stable contract - downstream system-identification workflows as part of the stable API - PySINDy integration as a release-defining stable feature - operator symmetry - NeuralOperator integration - broader adapter work (PDEBench, The Well, etc.) as a release-defining goal - nonuniform rectilinear support in stable derivative code - multi-generator Lie algebra tooling beyond diagnostics - broad benchmark zoo - manuscript-specific experiment logic These may be explored experimentally, but they do not define `v0.2`. --- ## Benchmark Rules for `v0.2` `v0.2` should benchmark the current stable symmetry pipeline across two PDEs, not yet benchmark downstream utility claims. This milestone adds an internal benchmark / release-gate layer, not a reusable public benchmarking API. Required controls: - fixed train/test split conventions - fixed verification defaults - fixed low-noise held-out condition shared across Heat and Burgers - fixed derivative backend assumptions - comparable fitting and verification settings across Heat and Burgers where meaningful Required outputs: - symmetry recovery result on Heat - symmetry recovery result on Burgers - held-out verification on both - one matched noisy held-out robustness check shared across both PDEs - reproducible `VerificationReport` on both - no regression in the existing Heat path --- ## Release Gate `v0.2` is releasable only if: - the v0.1 Heat path still passes cleanly - Burgers works end to end through the stable pipeline - the chosen Burgers symmetry target is recovered and verified under held-out evaluation - matched clean Heat / Burgers benchmark checks are `exact` - matched noisy held-out Heat / Burgers benchmark checks are `exact` or `approximate` - the current stable contracts remain coherent across both PDEs - no deferred or experimental feature is required for the stable release path If these conditions are not met, `v0.2` is not complete. --- ## Non-goals `v0.2` is **not**: - the release where invariants become a stable public feature - the release where weak-form methods become stable - the release where PDELie becomes a broad ecosystem hub - the release where operator methods become part of the stable library It is the release where the current stable core proves that it generalizes one step beyond the original heat-equation MVP. --- ## Next Expansion After `v0.2` If `v0.2` succeeds, the next credible stable step is: - a minimal invariant/downstream utility release not: - broad adapters - broad numerics - operator methods That next step belongs to `v0.3`, not `v0.2`.