V0.1 Scope#

Must Implement#

V0.1 is the smallest vertical slice that proves the library’s central claim: numerical recovery and verification of a Lie symmetry from PDE data through a clean, reproducible pipeline.

Stable scope for V0.1:

  • uniform rectilinear grids only

  • synthetic PDE data only

  • polynomial generators only

  • verification-first development

Canonical contracts to freeze for this slice only:

  • FieldBatch

  • DerivativeBatch

  • ResidualBatch

  • ResidualEvaluator

  • GeneratorFamily

  • VerificationReport

Development order:

  1. freeze contracts

  2. synthetic data

  3. derivatives

  4. residuals

  5. generator fitting

  6. verification

Concrete V0.1 target:

  • synthetic heat equation only

  • one FieldBatch implementation

  • one derivative backend: spectral_fd (spectral in space, finite in time)

  • one analytic heat ResidualEvaluator

  • one polynomial generator fitter

  • one finite-transform verifier

  • one VerificationReport

  • one controlled benchmark task

Documentation rules for V0.1:

  • one authoritative spec for contracts and defaults

  • consistent ResidualEvaluator and ResidualBatch definitions everywhere

  • one default verification norm

  • one default epsilon sweep

  • clear statement that normalization is restricted for symmetry recovery

  • clear statement that nonuniform rectilinear grids are not part of stable derivative support

Explicitly Deferred#

The following are not part of V0.1 stable scope:

  • The Well adapter

  • broad interoperability work beyond the MVP path

  • NeuralOperator integration

  • operator symmetry

  • weak-form backend beyond an interface placeholder

  • broad benchmark zoo

  • nuisance baselines beyond one mandatory control

  • lazy or out-of-core semantics

  • full schema richness for unused objects

  • serialization of every artifact if it slows implementation of the first proven path

  • nonuniform rectilinear support in stable code

  • InvariantMap as a stable contract

  • InvariantLibrary as a stable contract

  • DiscoveryResult as a stable contract

  • downstream discovery tooling beyond what is needed later

  • duplicate or near-duplicate spec text across multiple docs

These items may exist conceptually or as experimental placeholders, but they are not release-defining for V0.1.

Release Gate#

V0.1 is releasable only if the heat-equation vertical slice works cleanly and reproducibly end to end.

Minimum gate:

  • recover spatial translation on the heat equation from synthetic data

  • pass the default epsilon sweep

  • pass held-out evaluation on at least 3 unseen initial conditions

  • remain stable under a defined small-noise condition

  • produce a VerificationReport with reproducible classification across runs

  • keep all work within the frozen V0.1 contracts

  • avoid broadening stable scope beyond the listed slice

If this path is not yet working, V0.1 is not complete. The next expansion after a successful release gate is Burgers as the second PDE, not broader adapters or downstream ecosystem tooling.