Viridis Compiled Theorem Stack — Canon v10.1.0 (The Keystone Wave: Universal Water-Filling Meta-Theorem + Geodesic Saturation Theorem folded into the spine)

The Viridis Canon — Lean-Checked Conditional Mathematics for the Intelligence Bound. A machine-checked formal corpus underpinning the Viridis research program on the thermodynamics of intelligence and its application to planetary conservation. Its spine is the Intelligence Bound — a Landauer/erasure-grounded limit on the rate of intelligence creation — formalized in Lean 4 and extended through a stack of modules spanning information theory (the D-Score biodiversity metric), graph-theoretic landscape optimality (HDFM / dendritic corridors), thermodynamic economics, alignment-as-feasibility (Goodhart impossibility), the speed-limit shadow-price tower, and the recovered post-Wolpert erasure-side footing. Every theorem's type is machine-verified in Lean 4 (pinned toolchain; axioms audited to propext, Classical. choice, Quot. sound). The canon deliberately distinguishes proof validity from physical and empirical validity: it is conditional mathematics with explicit assumptions, not a claim that those assumptions describe nature. Headline results are graded by formal strength in CLAIMSMATRIX. md via the labels in THEOREMSTATUSTAXONOMY. md (Derived / Conditional / Definition-expansion / Bridge-assumption / Empirical-hypothesis / Conjecture / Exploratory), with separate formal and interpretive status. Empirical validation is reserved for the companion papers and field studies. Concept DOI 10. 5281/zenodo. 19317982 always resolves to the latest version. Source mirror: github. com/jdhart81/viridis-canon. Co-authored with Aristotle (Harmonic). This version (v10. 1. 0). "The Keystone Wave" — folds two Intelligence-Bound core-extensions into the verified spine: the Universal Water-Filling Meta-Theorem (UWMT, "the Keystone"; unifies the nine-member shadow-price/water-filling family into one variational object with two control knobs — curvature and temperature — where the multiplier λ is simultaneously the water level, the economic shadow price, and the thermodynamic free energy; 8 named results) and the Geodesic Saturation Theorem (GST, "the Sage"; characterizes the Intelligence Bound's own equality/saturation condition dI/dt= (P−F) ·c, saturating iff the forcing F=0 — a constant-speed Fisher–Rao geodesic, "wu wei" made literal; 6 named results). GST names UWMT as its multichannel shadow, forming a coherent milestone wave. Both modules are 0 sorry with axioms ⊆ propext, Classical. choice, Quot. sound, added to SPINEMANIFEST. txt, lakefile defaultTargets, and AxiomAudit. lean. Spine freeze-break authorized by J. D. Hart (pre-authorized 2026-06-29 for UWMT specifically; confirmed and extended 2026-07-06 after applying the five-gate Spine Admission Test to the full nightly-forge backlog). Five sibling backlog results (MINT, SRT, IET, SCT, GNT) were evaluated against the same test, did not clear the domain-defining gate, and are published the same day as their own series/standalone records rather than merged into the spine. See CHANGELOGᵥ10. 1. 0. md.