What question did this study set out to answer?

The aim is to establish the Certification Complexity Theorem and its implications on certifying conservation claims.

June 22, 2026Open Access

The Certification Complexity Theorem: A Landauer Floor on the Cost of Certifying Conservation Claims

JHJustin HartUniversity of Providence A(Aristotle (Harmonic)Laboratoire Spécification et Vérification

Key Points

The aim is to establish the Certification Complexity Theorem and its implications on certifying conservation claims.
Proved core relationships within framework of Lean 4 environment.
Establishes cost bounds using mathematical formulations.
Pairs findings with Monitoring Water-Filling and D-Score Measurement Closure Theorems.
Established a certification ceiling positivity based on Landauer’s principles.
Demonstrated a positive certification floor for confidence intervals.
Provided a certified-bit budget relationship denoted by C ≤ E_cert·D/εL.

Abstract

Standalone record of the Viridis Canon — Monitoring series (S2, the Surveyor family). The core IB spine is unchanged (frozen at v9). Proves the Certification Complexity Theorem (CCT): the cost of certifying a conservation/measurement claim is itself bounded by the Intelligence Bound applied to the monitor. Lean 4 (Aristotle 062250b6, zero sorry, axioms ⊆ propext, Classical. choice, Quot. sound) certifies (T1) a Landauer-priced certification-ceiling positivity (the IB self-applied to the certifier), (T2) the certified-bit budget chain C ≤ Ecert·D/εL, and (T3) a strictly-positive certification floor εL·ln (1/φ) for confidence φ∈ (0, 1). Pairs with the Monitoring Water-Filling Theorem (MWT) and the D-Score Measurement Closure Theorem (DMCT). Working paper; not peer-reviewed.

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