Dimension-checked mesh, fields, equations, conditions and analyses.
Core-2 Physical Models
Status: normative preview; bounded native exact quantities, canonical affine meshes, model typing and one-dimensional conservative transfers implemented; physical source compilation and solvers unavailable
C2-PHYS-001 — Mathematical authority. A physical model defines a system of equations, geometry, materials, admissible conditions and observations. It is neither a callable nor a selected numerical solver. Fields denote mathematical unknowns; equation order does not imply assignment or execution order. Model construction is pure, finite and closed over versioned dependencies. A valid model is not a guarantee that a particular solver can solve it.
C2-PHYS-002 — Quantities. Dimensions are reduced rational exponent vectors in the order length, mass, time, electric current, temperature, amount and luminous intensity. Canonical quantities use SI base units. Addition, equality, conditions and interface matching require equal dimensions and tensor shape. Multiplication/division add/subtract exponent vectors; differentiation and integration account for the variable or measure’s dimensions. Transcendental arguments are dimensionless. Affine units such as Celsius convert explicitly to absolute quantities; an offset is not a multiplicative unit scale. Display units are presentation metadata and cannot change equations. Scalar, Vector and Tensor types bind a dimension; vector/tensor shape and coordinate frame are determined by a declared field space, not guessed from a solver backend.
C2-PHYS-003 — Canonical geometry. A mesh contains stable local IDs for nodes, edges, faces, cells, regions, boundaries and interfaces; coordinate quantities and frame; element type/order; ordered connectivity and orientation; and named membership sets. Standard element families are point, segment, triangle, quadrilateral, tetrahedron and hexahedron. Higher-order or other elements require a versioned element definition with basis and orientation laws. Reject missing references, repeated vertex IDs in an element, zero or negative oriented cell measure, incompatible dimensions and nonconforming interfaces without an explicit coupling law. Shared oriented faces must cancel between adjacent volume cells; a deliberate non-manifold junction requires a named physical interface law. Field location may be nodes, edges, faces, cells or regions and is part of its type. Vector orientation and frame transforms are explicit. Mesh records are sorted by stable ID within each entity kind, using the canonical owner/name/ordinal row order in C2-ART-006; connectivity order is preserved. Arbitrary mesh relabeling is not canonical graph isomorphism.
C2-PHYS-004 — Equation core. Model expressions admit pure constants,
parameters, field references, arithmetic, typed mathematical function calls,
derivatives, differential operators, integrals and relations. Assignment,
software I/O, allocation authority and mutable software references are invalid
inside equations. strong requires a dimensionally valid equality over its
declared domain. weak for v in Space binds a test function and requires a
dimensionally valid variational equality for every member of the declared
test space. Spaces specify rank, frame, continuity and boundary restrictions.
Weak and strong forms are alternatives unless an explicit equivalence claim
links them; a tool cannot silently replace one with the other. Constitutive
relations are checked equations or versioned pure model definitions, including
their validity ranges and regularity assumptions.
C2-PHYS-005 — Conditions and analyses. Initial, boundary, interface and source conditions identify their support and typed law. Constraint overlap with incompatible prescribed values is rejected. A missing required gauge, nullspace constraint, initial value or boundary condition prevents solver admission; structural checks do not claim to decide well-posedness of arbitrary PDEs. An analysis declares the solved fields, independent variables, domain, observations, numerical acceptance contract and applicable assumptions.
| Analysis | Required analysis facts |
|---|---|
| steady | fixed conditions, residual norms, nullspace/gauge treatment |
| transient | time interval, consistent initial conditions, event policy, error bounds |
| harmonic | frequency set, complex-field representation, linearity/linearization assumptions |
| eigenvalue | operator pair, constraints, requested spectrum, normalization and residual bounds |
| coupled | member analyses, exchanged fields, orientation, time/space mapping and coupling convergence |
Eigenvalue comparisons operate on declared modes/subspaces and account for sign/phase and multiplicity. Missing analysis facts are rejected rather than filled using unrecorded backend defaults.
C2-PHYS-006 — Observations and evidence. Observations identify support, field/component, frame, time or frequency, functional, units and uncertainty. Acceptance specifies absolute/relative norm bounds with reference scales, residuals and applicable conservation/stability requirements. NaN, infinity, unreported divergence and unit mismatch are failures. A small residual alone does not establish a small solution error. An inapplicable check requires an explicit applicability argument; it cannot be reported as a passed check. Constitutive uncertainty, measurement uncertainty and discretization error remain separately inspectable even when a contract combines them.
C2-PHYS-007 — Mesh refinement. The declared mesh remains model authority. A SolverPlan may generate another mesh only with parent identity, generation parameters, projection operators, orientation/frame transforms and bounded projection/discretization error. Comparisons are performed in the contract’s observation space. Replacing the declared geometry changes the model contract; refining a solver mesh changes the SolverPlan/implementation identities. Remeshing must preserve required interface and conservation laws or fail.
See libraries, SolverPlans and conformance.