RFC-035: Mediation Vector Profile — A Validity-Aware Measurement Model for Domains of Concern — 9. The Gap Calculus

AIGP Specification › RFC-035: Mediation Vector Profile — A Validity-Aware Measurement Model for Domains of Concern › 9. The Gap Calculus

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9. The Gap Calculus

The gaps between states are the primary mechanism by which a Mediation Vector produces concern signals.

9.1 Gaps Are Declared Operators, Not Arithmetic Subtraction

A gap is the distance between two states of a variable. But distance is scale-dependent: a ratio variable admits numeric difference, an ordinal variable admits rank distance, and a nominal variable admits only match/mismatch. Computing anticipated − evidenced arithmetically across all variables would violate the Stevens measurement discipline established in §4.5.

Therefore a gap is never a fixed subtraction. It is a declared gap operator:

Gap = gap_fn(variable, state_a, state_b)

Each variable MUST declare the gap operator permitted by its measurement scale:

Scale	gap_operator	Computation	Output
ratio / interval	numeric_difference	abs(a − b) normalized to range	continuous [0,1]
ordinal	rank_distance	distance over declared rank_mapping	continuous [0,1]
nominal / categorical	categorical_mismatch	0.0 if a == b else 1.0	binary
boolean	boolean_mismatch	0.0 if a == b else 1.0	binary
temporal	temporal_distance	declared duration metric	continuous [0,1]

Examples of gap-operator declaration per variable:

{ "variable_id": "authority_compliance", "scale": "ratio", "gap_operator": "numeric_difference" }

{ "variable_id": "observer_mode", "scale": "nominal", "gap_operator": "categorical_mismatch" }

{
  "variable_id": "consequence_severity",
  "scale": "ordinal",
  "gap_operator": "rank_distance",
  "rank_mapping": { "low": 1, "medium": 2, "high": 3, "critical": 4 }
}

A variable whose gap_operator is incompatible with its declared scale is malformed and MUST NOT participate in concern calculation.

9.2 The Four Gaps

Each gap applies its variable’s declared gap_operator to two states. The interpretation of each gap is fixed; the computation is per-variable.

Gap	States Compared	Meaning	AIGP Mechanism
Anticipation Gap	anticipated, evidenced	What governance expected vs. what evidence supports	VERIFY verdict (MATCH / MISMATCH)
Perception Gap	perceived, evidenced	What users believe vs. what evidence supports	FEEDBACK ≠ VERIFY disagreement
Measurement Gap	actual, evidenced	What was observed vs. what can be proven	Evidence completeness signal
Governance Gap	anticipated, perceived	What governance intended vs. what users believe it ensures	Criteria calibration signal

Anticipation Gap > threshold  → MISMATCH / VIOLATION
Perception Gap > threshold    → Calibration alert (belief diverges from evidence)
Measurement Gap > threshold   → Evidence insufficiency (observed but not provable)
Governance Gap > threshold    → Communication failure (intent diverges from belief)

Each variable declares its own per-gap thresholds; thresholds are scale-appropriate (a categorical_mismatch gap is over threshold at any value of 1.0; a numeric_difference gap has a tunable threshold).

9.3 Gap as Verdict Demand

A gap does not assert a conclusion. A gap demands a verdict.

When a gap exceeds its threshold, the system does not conclude that the artifact is bad. The system concludes that a verdict is required — from a human, machine, or hybrid observer qualified within the Domain of Concern.

This preserves the non-causal principle:

A Mediation Vector Profile does not make a concern true; it makes the concern measurable under declared validity conditions.

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