Fragility Evidence Language (FEL) v0.1

Formal vocabulary for schedules, rollouts, objectives, interventions, and evidence in the Fragility Discovery Engine. FEL does not introduce new physics; it axiomatizes what the engine already computes so exports, benchmarks, and explain artifacts share one semantics.

Implementation: src/fragility_engine/fel/

Preprint: preprint/FEL_preprint_v0.1.md · Publishing guide: preprint/PUBLISHING.md

Related: MATH.md (formulas), ALGORITHMS.md (procedures)

0. Design goals

1. One meaning per operator — dominance, hypervolume, and attribution deltas are named once.

2. Two attribution roles — counterfactual bundles vs path/sweep edges use different delta signs on purpose.

3. Schema registry — JSON schema fields map to FEL constructors.

4. Deterministic replay — same world, schedule, and seed ⇒ same rollout (charter worlds).

Surface syntax (.fel files) is optional; v0.1 is the semantic core plus Python helpers.

1. Core types

Evaluation:

\[

R = \mathrm{eval}(W, G, \sigma)

\]

Laws (see §9): determinism on charter worlds; schedule decode is fixed; interventions produce paired rollouts (R₀, R₁).

2. Objectives and dominance

Attack-layer Pareto uses maximize severity, minimize attack cost:

\[

A \prec B \iff S(A) \ge S(B) \land c(A) \le c(B) \text{ with strict inequality on at least one axis}

\]

Python: fel.attack_pareto_dominates, adversary.pareto.pareto_indices.

Non-dominated set = attack Pareto front.

3. Hypervolume coordinates

Hypervolume is computed in minimization 2-D space:

\[

(\tilde{s}, \tilde{c}) = (-S, c)

\]

Reference point must lie above all points in both minimized coordinates (worse than the front). See MATH.md § Hypervolume.

Python: fel.to_min_objectives, benchmarks.hypervolume.hypervolume_2d_attack_pareto.

4. Interventions

An intervention I maps a baseline configuration to a variant and runs paired rollouts:

\[

R_0 = \mathrm{eval}(W, G, \sigma), \quad R_1 = \mathrm{eval}(W', G, \sigma) \text{ or } \mathrm{eval}(W, G', \sigma)

\]

Examples (explain layer): remove shock, epsilon sweep on a gate, inventory buffer shift, mutation chain prefix.

Intervention metadata is stored on bundles (intervention, pinned parameters).

5. Attribution operators

FEL defines two delta conventions; do not mix them on the same edge kind.

5.1 Δ⁻ Counterfactual (bundle attribution)

Used in counterfactual JSON bundles and attribution merges comparing baseline vs variant:

\[

\Delta^{-}(\phi_0, \phi_1) = \phi(R_0) - \phi(R_1)

\]

Reading: positive Δ⁻ on integral_instability ⇒ variant reduced instability vs baseline (variant is better on that metric).

Python: fel.delta_counterfactual, fields delta_integral_instability, delta_attack_cost on counterfactual exports.

5.2 Δ⁺ Path forward (sweep / mutation chain)

Used on consecutive nodes along a cumulative path (epsilon sweep, mutation chain):

\[

\Delta^{+}(\phi_i, \phi_{i+1}) = \phi(R_{i+1}) - \phi(R_i)

\]

Reading: positive Δ⁺ ⇒ metric increased when moving forward along the path (e.g. added mutation increased cost).

Python: fel.delta_path_forward, path trace edges[].delta_*.

5.3 When to use which

6. Evidence constructors

Registry in code: fel.SCHEMA_REGISTRY.

Merge (star): several counterfactual bundles with a shared baseline node; edges carry Δ⁻ from baseline to each variant.

Certificate: existential witness (W, G, σ) with metrics exceeding thresholds documented in the certificate payload.

7. Composite evaluation

Institutional composite:

\[

\{ R_i = \mathrm{eval}(W_i, G, \sigma) \}_{i=1}^{k}

\]

Same schedule G across worlds; aggregation (e.g. max severity, percentile costs) is documented per manifest. Not a single coupled multi-world simulation unless explicitly modeled in one W.

8. Surface syntax (informative)

Optional .fel notation for human-authored specs (not required for v0.1 tooling):

```fel

world network_charter_v1

seed 42

schedule G {

horizon 64

# shocks decoded from [0,1] columns

}

rollout R0 = eval(W, G, seed)

intervention remove_shock { index 3 }

rollout R1 = eval(W, G', seed)

delta_minus instability = R0.integral_instability - R1.integral_instability

delta_minus cost = R0.attack_cost - R1.attack_cost

evidence merge {

baseline R0

variant R1

intervention remove_shock

}

```

Parsers are future work; Python APIs and JSON schemas are normative for v0.1.

9. Laws (axioms)

1. Determinism: On pinned charter worlds, eval(W, G, σ) is reproducible.

2. Schedule domain: G entries ∈ [0,1]; decode to events is fixed by world template.

3. Attack Pareto order: §2; hypervolume uses §3 transform.

4. Δ⁻ on bundles: §5.1 for counterfactual and merge exports.

5. Δ⁺ on path edges: §5.2 for sweeps and mutation chains.

6. Composite independence: Multi-world composites are parallel evals, not hidden coupling.

7. Schema versioning: New fields bump schema IDs; FEL version fel-v0.1 tags convention docs.

Machine-readable: fel.fel_laws_summary().

10. Implementation map

Changelog

• fel-v0.1 — Initial semantic spec; dual delta operators; schema registry; Python fragility_engine.fel.