Prototype demonstration

Structural Integrity Screening (QDL)

This page presents a lightweight, implementation-oriented demonstration of QDL as an upstream structural screen for computational and theoretical models. The intent is to flag representational fragility under composition, iteration, and scale change before calibration or deployment.

Closure Checks Iterative Stability Operator Growth Mixing Flags Interpretable Reports

Demonstration components

The pseudo-code below sketches the screening workflow, while the diagram shows how the screen fits into a practical model lifecycle: proposal → structural screen → calibration → deployment (or redesign).

Minimal working pseudo-code (screening workflow)

Note: This is high-level pseudo-code intended to convey workflow and outputs. The released toolkit will be a small Python package with documented examples and notebook demonstrations. 

# QDL Structural Integrity Screening (minimal pseudo-code)
# Goal: flag structural fragility BEFORE calibration/deployment

function screen_model(model_spec, transforms, iterations=10):
    # model_spec: declared quantities, units/types, and allowed compositions
    # transforms: list of symbolic/computational operations used in the model

    report = new Report()

    # 1) Build a representation graph
    G = build_representation_graph(model_spec, transforms)
    # Nodes: quantities (observables, parameters, derived variables)
    # Edges: operations (compose, differentiate, integrate, normalize, etc.)

    # 2) Closure check: every derived quantity must map to an admissible class
    for q in G.derived_quantities:
        cls = classify(q)                 # e.g., ledger cell / admissibility class
        if not is_admissible(cls, model_spec.allowed_classes):
            report.add("Closure", "FAIL", q, "Derived quantity not admissible")
        else:
            report.add("Closure", "OK", q, "Admissible")

    # 3) Iterative stability: apply transforms repeatedly and detect drift
    state = G.initial_state
    seen_classes = multiset()
    for k in range(1, iterations+1):
        state = apply_transforms(state, transforms)
        classes_k = classify_all(state.quantities)
        seen_classes.add(classes_k)

        if introduces_new_classes(classes_k, model_spec.allowed_classes):
            report.add("Iterative Stability", "WARN", k,
                       "New representational classes appeared under iteration")

        if growth_unbounded(seen_classes):
            report.add("Operator Growth", "WARN", k,
                       "Class/term growth appears unbounded")

    # 4) Cross-type mixing: detect invalid combinations
    mixes = detect_heterogeneous_mixing(G)
    for m in mixes:
        report.add("Cross-Type Mixing", "WARN", m,
                   "Heterogeneous quantities combined")

    # 5) Summarize
    report.compute_overall_risk()
    return report


# Example usage (toy):
model_spec = {
  allowed_classes: ["AdmissibleCellA", "AdmissibleCellB"],
  quantities: ["x", "alpha", "f(x)", "g(x)"]
}
transforms = ["compose", "expand_series", "normalize", "iterate"]
report = screen_model(model_spec, transforms, iterations=20)
print(report)

Interpretation (PASS / WARN / FAIL)

PASS
Structural checks satisfied for the tested transformations and iteration depth.
WARN
Potential fragility detected (e.g., drift under iteration, growth patterns, or mixing flags).
FAIL
Non-closure or inadmissible representations detected; redesign or constrain before calibration.

Model pipeline → structural screen → deployment

┌──────────────────────────────┐
│  Model Proposal / Design      │
│  - variables                  │
│  - transformations            │
│  - assumptions                │
└───────────────┬──────────────┘
                │
                ▼
┌──────────────────────────────┐
│  Structural Screen (QDL)      │
│  - closure checks             │
│  - operator growth analysis   │
│  - iterative stability        │
│  - cross-type mixing flags    │
└───────────────┬──────────────┘
        PASS    │    FAIL / WARN
      ┌─────────┘        └──────────────┐
      ▼                                  ▼
┌──────────────────────────────┐   ┌──────────────────────────────┐
│  Empirical Calibration        │   │  Redesign / Constrain Model   │
│  - fit parameters             │   │  - revise representation      │
│  - validate on data           │   │  - remove unstable operators  │
└───────────────┬──────────────┘   └───────────────┬──────────────┘
                │                                  │
                ▼                                  └───────┐
┌──────────────────────────────┐                          │
│  Deployment / Use             │                          │
│  - scientific inference       │◄─────────────────────────┘
│  - decision support           │
│  - automation pipelines       │
└──────────────────────────────┘

Example output (static “Integrity Report”)

This is a representative example of the kind of concise, interpretable output the toolkit is designed to produce. It is intentionally domain-agnostic and meant to support rapid triage.

Structural Integrity Report (Example)
Run ID: DEMO-001 · Iterations: 20 · Scope: Toy model
Closure
PASS All derived quantities map to admissible representation classes.
Iterative Stability
WARN New representational classes appear after iteration depth ≥ 12 (structural drift).
Operator Growth
WARN Term/class growth increases monotonically with iteration; boundedness not established.
Cross-Type Mixing
PASS No heterogeneous mixing flags detected in the representation graph.
Overall Assessment
Proceed with calibration only after constraining iteration behavior. The model may fit data yet remain fragile under repeated reuse or scale extension.
Recommended Actions
  • Limit or regularize the expansion pathway that introduces new classes after iteration depth ≥ 12.
  • Establish a bounded operator/term-growth criterion (or adopt a pruning rule) prior to deployment.
  • Re-run screening after any change to transformation sequence, normalization, or parameterization.

Interpretation: a WARN does not mean the model is “wrong.” It means the representation may be fragile under reuse, iteration, or extrapolation, and should be constrained before being treated as stable infrastructure.

For collaboration or a pilot use case, contact [email protected].