Technical Spine

The Coherence Fee (Paper I)

Measuring Hidden Convention Risk in Hierarchical Tool Compositions

VerifiedMachine-checked in Lean 4. Tested on the 703-composition corpus and a 10,000-composition adversarial random suite.
Key result

fee = rank(δ_full) − rank(δ_obs); hierarchical decomposition with additive tower law; minimum disclosure eliminates all blind spots

Falsification

A composition with nonzero fee whose blind spots never produce observable failures across sufficiently diverse inputs

Abstract

Introduces the coherence fee as a computable integer counting convention dimensions whose consistency is structurally unverifiable from observable schemas alone. Proves fee = rank(δ_full) − rank(δ_obs), a hierarchical decomposition theorem showing the fee splits into local sub-workflow fees plus a non-negative boundary fee, a tower law proving cost is additive across hierarchy levels, and a minimum disclosure theorem prescribing exactly which fields to expose.