Multiphysics model libraries and foundational digital/physical bridges.
Core-2 Libraries and Mixed-Signal Bridges
Status: normative preview; library contracts specified, implementations deferred
C2-LIB-001 — Model libraries. Libraries are ordinary versioned model dependencies over the generic equation core. Every export declares quantities, fields, constitutive laws, valid parameter ranges, required conditions, observations and evidence obligations. Imports bind exact content identity. No domain-specific equation syntax, implicit unit coercion or hidden solver selection is introduced by an import.
| Library contract | Required initial model definitions | Characteristic evidence |
|---|---|---|
| electromagnetics/1 | electrostatics, conduction, Maxwell fields and material response | charge continuity, Gauss constraints, energy balance, gauge handling |
| thermal/1 | heat conduction, heat capacity, boundary heat exchange | energy balance, flux orientation, transient stability |
| mechanics/1 | displacement, strain, stress, momentum and elastic constitutive laws | rigid modes, force balance, energy and frame consistency |
| fluids/1 | mass/momentum transport, pressure, viscosity and boundary flux | continuity, admissible density, pressure nullspace and flux balance |
| semiconductor/1 | Poisson, carrier drift/diffusion, generation/recombination and contacts | charge/carrier conservation, positivity and contact conditions |
These contracts establish required definitions and their test obligations; this edition does not claim executable libraries have been supplied. Extension to nonlinear, turbulent, quantum or other models uses additional versioned definitions with their own assumptions and evidence.
C2-BRIDGE-001 — Foundational operations. A digital/physical bridge names its input/output dimensions and frames, direction, state, loading law, initialization, timing and uncertainty contract. The following foundational operations have inspectable equations or transfer laws:
| Operation | Contract facts |
|---|---|
| sample | aperture, sample times, interpolation, jitter and aliasing assumptions |
| drive | output law, finite impedance, load, slew and saturation |
| threshold | comparison thresholds, equality rule, hysteresis and initial state |
| quantize | range, code width, rounding, saturation/error policy and uncertainty |
| hold | interpolation/hold law, retention interval and discontinuities |
| couple | effort/flow orientation, field projection and conservation law |
ADC composes sampling and quantization; DAC composes code interpretation, hold and drive; a comparator composes threshold and timing/uncertainty laws. Wrappers may hide syntax but may not hide the foundation model or its identity. An ideal sampler or source is permitted only as an explicit idealization with declared limits. An X/Z value cannot be translated to a unique voltage without an admitted bridge policy. An observed metastable interval cannot be erased by converting it to a deterministic digital bit.
C2-BRIDGE-002 — Coupled evolution. Each co-simulation plan identifies one time unit and synchronization schedule, event direction, interpolation, rollback support and convergence test. At a synchronization time, continuous state is advanced to the event, samples are evaluated, digital updates settle, new drives are applied, and algebraic coupling is solved before observations are committed. Repeated equal-time exchanges use bounded microsteps and a declared fixed-point criterion. Zeno behavior, oscillating algebraic loops, step-size exhaustion and non-convergence return explicit failures. A backend without rollback may only admit schedules that do not require rollback. Co-simulation cannot repeat physical device actions while replaying a virtual step; hardware-in-the-loop uses irreversible recorded observations instead.
C2-BRIDGE-003 — Clock and region bridges. Pure combinational bridges preserve values and explicitly identify both regions. CDC bridges additionally carry the obligations in C2-CLOCK-003. Standard bridge definitions are content- bound elaborated components/models; they receive no intrinsic exemption from driver, hazard, uncertainty or capability checks. Their contracts expose latency, throughput, capacity, loss and failure semantics where applicable.