Boundary: Drift Detection

Detect when a change expands d(S) — reopening a resolved boundary condition or widening an open one — and identify which domains in the partial order are affected.

Framework: Differential Closure Analysis

Every code change has a d(S) effect:

• Resolves d(S) — moves a boundary condition toward ∅ (seeding, typing, constraining)
• Preserves d(S) — no boundary conditions change (in-domain modification)
• Expands d(S) — reopens a resolved boundary or widens an open one (drift)

Drift is the third case. Because domains form a partial order, drift in Dm invalidates all dependent Dn.

Delta-Epsilon Characterization (Stochastic)

For any change δ, there exists an ε-neighborhood within which the change stays within its semantic domain. But ε is not a fixed threshold — it is a function of the noise floor η of the generation process:

ε_effective = ε_domain + η

|δ| < η           →  noise — acceptable sampling variance, not signal
η ≤ |δ| < ε_eff   →  review — may be noise or signal, apply d(S) test
|δ| ≥ ε_eff       →  drift — d(S) expanded, boundary crossed

Hamming distance measures how many independent coordinates differ. Small Hamming distance = local change. Large Hamming distance relative to semantic distance = likely boundary crossing. But Hamming distance must be interpreted against η: some coordinates have high noise floors (variable names) and others have near-zero (literal vs. reference).

See boundary-noise-model for characterizing η, domain confidence κ, and reproducibility equivalence.

When to Use This Skill

• Reviewing diffs for unintended d(S) expansion
• Auditing LLM-generated code for domain violations
• Validating refactors stayed within their domain
• Post-generation verification
• Monitoring the partial order: has a prerequisite domain reopened?

How to Detect Drift

Step 1: Name the intended domain

What domain was the change supposed to affect? At what layer in the partial order?

Step 2: Compute the change footprint

1. Files touched — modified, added, or deleted
2. Domains touched — which semantic domains do those files belong to?
3. Values changed — literals, references, or structures altered
4. Cross-references affected — anything referenced elsewhere?

Step 3: Filter noise from signal

Before classifying d(S) effect, separate noise from signal. For each difference in the footprint:

1. Could this difference appear between two correct implementations? If yes → likely noise (below η)
2. Does this difference change which boundary conditions are resolved? If yes → signal regardless of magnitude
3. Is this difference in a constrained dimension of ∂S? If yes → strict ε. If no → apply noise tolerance

Discard noise-floor variations (variable naming, formatting, import order, equivalent expressions). Retain signal variations for classification.

Step 4: Classify the d(S) effect

Footprint (signal only — noise filtered)	d(S) Effect	Assessment
All changes within intended domain, using existing references	Preserves	In-bounds
Changes resolve a boundary condition (literal → reference)	Resolves	Closure progress
Changes touch dependent domain via necessary coupling	Preserves	Boundary — verify minimality
Changes introduce new literals for seeded values	Expands	Drift — reopening a resolved domain
Changes touch unrelated domain	Expands	Escape — crossed a boundary
Changes touch prerequisite domain	Expands	Cascade — dependents invalidated

Step 5: Assess partial order impact

If drift occurred:

• Which domain boundary was crossed?
• Is it a prerequisite domain? If so, which dependent domains are now unreliable?
• Is the expansion necessary? (Schema changes necessarily affect consumers)
• Is it minimal? (Only required cross-domain effects)

Drift Patterns in Generated Code

Literal Duplication (reopening a resolved boundary)

The LLM emits a literal where a seed exists. d(S) was ∅; now it’s not.

Detection: New literal matching an existing seed value.

Interface Widening (expanding a boundary condition)

A function accepts more states than intended — | string, any, optional properties.

Detection: Type changes that increase representable states beyond ∂S.

Type Erasure (internal boundary collapse)

The implementation uses any, as unknown as, or untyped containers where a narrow type exists or could be derived. The public contract compiles, but the internal state space is unbounded — invalid states are representable within the implementation even though they can’t escape through the interface.

This is distinct from interface widening: the public boundary holds, but the implementation domain is open. d(S) appears to be ∅ at the interface but is ≠ ∅ inside.

Detection: Grep for any (excluding type declarations that re-export external types), as unknown as, and as any in implementation files. Each occurrence is a potential internal boundary collapse.

Severity: Medium-High. The interface prevents invalid states from escaping, but the implementation can silently accept malformed data, pass wrong fields to dependencies, or drift during future edits without compiler protection.

Style Contamination (bypassing domain boundaries)

Inline styles or local overrides that duplicate or contradict token-derived values.

Detection: New style definitions outside the established token system.

Prerequisite Violation (cascade drift)

A change in a lower domain (D1/D2) that wasn’t propagated to dependent domains.

Detection: Dependent domain code references values that changed upstream.

Output Format

CHANGE: <description>
INTENDED DOMAIN: <Dn — name and layer>
NOISE FILTERED: <variations classified as noise and excluded>
d(S) EFFECT: resolves | preserves | expands
DOMAINS TOUCHED: <list with layers>
TYPE ERASURE: <count of `any` / unsafe casts in implementation code>
DRIFT: none | boundary | escaped | cascade
CONFIDENCE (κ): high | moderate | low | unreliable
CASCADE IMPACT: <dependent domains invalidated, if any>
DETAILS: <what crossed where>
RECOMMENDATION: <accept | scope tighter | close reopened domain | fix forward from Dm | tighten context and regenerate>

Guidelines

• Not all differences are drift. Filter noise before classifying. Variations below the noise floor η are sampling variance, not signal. See boundary-noise-model for characterizing η.
• Not all cross-domain changes are drift. Necessary coupling preserves d(S). The test is whether the cross-domain effect is necessary and minimal.
• Reopening a resolved boundary is the most serious drift. d(S): ∅ → ≠∅ erases prior closure work. Highest priority.
• Cascade drift is the most damaging. Drift in a prerequisite domain invalidates every dependent. When detected, stop and fix forward from the affected prerequisite.
• Drift compounds. Each undetected expansion of d(S) accumulates. Detect early.
• Calibrate ε above the noise floor. ε_effective = ε_domain + η. Flagging noise as drift erodes trust in the detection system. See boundary-noise-model for calibration.
• LLM-generated code has higher η but needs tighter ε. The noise floor is wider (more syntactic variance) but the domain boundary must be stricter (LLMs don’t detect scope escape during generation). Separate the two thresholds.
• Most powerful over closed domains. Well-seeded, type-closed domains make drift mechanically detectable — the toolchain catches it.