Viridis Compiled Theorem Stack — Canon v6 (Heat and Disorder + Gaian Thermodynamic Uncertainty + Symbiotic Valuation + D-Score Measurement Closure)

Viridis Compiled Theorem Stack — Canon v6. A growing, machine-checked Lean 4 corpus of the Viridis canon, every module rooted in the formally proven Intelligence Bound dI/dt ≤ P·D/(k_B T ln 2). This version adds four verified components to the v5 spine, for twenty-two compiled modules in total. Each new component leads with a journal-style working paper, backed by its Lean module and Aristotle provenance. New in v6 (vs v5, 2026-05-30): Book_HeatAndDisorder (12 theorems) — the formal spine of the trade book Heat and Disorder: entropy monotonicity, the feedback dichotomy, a saddle-node tipping threshold, radiative-equilibrium uniqueness, a strict Clausius production inequality, Planck climate sensitivity, and the headline thermodynamic speed limit on ecological restoration — the first instantiation of the Intelligence Bound (P0) onto an ecological-order metric. Companion paper: “A Thermodynamic Speed Limit on Planetary Restoration.” Aristotle projects b18b368f (foundation), a9312b60 (first-principles). GTUT — Gaian Thermodynamic Uncertainty Theorem (TUR_floor) — applies the thermodynamic uncertainty relation to planetary homeostasis: the Cramer–Rao/TUR floor v/m^2 ≥ 2/Σ shows homeostatic precision is bought with dissipation. Because dissipation enters linearly and information-cost only logarithmically, the biosphere is dissipation-limited, not information-limited, reconciling maximum-entropy-production with homeostasis. Aristotle project 8c50d44e. SVT — Symbiotic Valuation Theorem (3 theorems) — coupling two D-Capital systems is superadditive by exactly the Landauer-priced mutual information between them (Symbiosis Dividend Δ_sym = ε_L(I(X;Y) − Σ_hk)); the Symbiosis Quotient Q ≡ I/Σ_hk governs a mutualism→parasitism phase transition, with a directed-information Shapley revenue-share. Aristotle project 9d3513e5. DMCT — D-Score Measurement Closure Theorem (5 theorems) — gives D-Score a measurement-theoretic backbone: closure-operator structure, certificate join, σ-cert = max, a τ^(−1/2) measurement-floor positivity law, and a unique value-of-information-optimal monitoring power. Aristotle project f2d90770. v5 spine (carried forward): P0 Intelligence Bound, P1 D-Score, P2 HDFM corridor-resilience POC, P3 Impossibility / alignment-as-feasibility, P4 Thermodynamic Economics, P5 SLSPT shadow-price tower, P7 Plasma Nitrogen Fixation, P9 AI Safety, Bridge_MissionFeasibility, ConservationOperator, Bridge_EcoChainInstrument, EcoChain_DendriticCorridor, PSIT_Symplectic. Verification provenance: all theorems machine-checked by the Aristotle (Harmonic) automated proving system; theorem statements preserved verbatim; zero sorry; axiom audits limited to {propext, Classical.choice, Quot.sound}. Lean toolchain v4.28.0; Mathlib pin 8f9d9cff6bd728b17a24e163c9402775d9e6a365. Scope note (honest): the Lean proofs certify the validity of the mathematical reasoning, not the empirical magnitudes or the surrounding papers' prose claims. The working papers are not peer-reviewed. Companion DOIs. Concept DOI (always resolves to latest): 10.5281/zenodo.19317982. v1 (IB-only): 10.5281/zenodo.19317983. Prior version v5 (Dendritic Corridor): 10.5281/zenodo.20467431.