Viridis Research → Viridis OS

Scientific kernels, explicit contracts.

Each package states what it computes, what it assumes, and what its evidence establishes. Publication, proof, runnable code and production adoption are separate states.

Explore the decision workspace Existing reference workbench Inspect package JSON Package schema

Workspace registry 2026.09.08-preview.1: unsigned preview only. These new packages have not been approved for production adoption.

applicability and constraint framework

The Intelligence Bound

Assess the foundational information and thermodynamic constraint framework without inventing a mapping to field conditions.

Package intelligence-bound · 1.0.0-preview.1

Formal proof

public ci passed exact source

The conditional P0 statement and compiled transitive axiom allowlist passed the cited public CI. This implementation run inspected receipts; it did not rerun Lean.

Implementation

conditional assessment implemented

Structured applicability, missing inputs and source references; numerical constraint result is null.

Empirical validation

not recorded

No field mapping or validation supplied for this workflow.

Release approval

local review preview

This package composition is available for local unsigned scenario evaluation. Production release has not been authorized.

Relationship to the Intelligence Bound

root: This exact formal framework is the architectural root; every decision records its applicability. A formal statement is not itself a field calibration.

Statement, assumptions and executable contract

İ(τ) ≤ min(ρ(τ) B, P / (k_B T ln 2))

μ is a probability measure; Ω and State are measurable spaces.
observationBandwidth μ O ≠ ⊤.
predictiveRichness μ X O τ ≤ 1; it is not established from ecosystem descriptions.
0 < kB and 0 < T, with nonnegative P and τ.
SatisfiesLandauerLimit μ X O τ P T kB, defined as P ≥ intelligenceCreationRate μ X O τ × ofReal(kB × T × ln 2). This physical applicability is assumed, not derived from microphysics in P0.
Justify actual X/O/μ/τ, physical regime, observation-channel quantities and mapping from available measurements; missing for generic conservation choices.

Executable inputs
Input	Units	Required	Supported values
mapping	categorical	Yes	unknown \| not_applicable \| proposed
explanation	text	Yes	Basis required for proposed mapping or exclusion; absent measurements remain missing

Implementation SHA-256 af3f345b36e7efb9c072c1d490d49f5b499fbbda05004fca72affb033f554968

What the proof covers—and what remains outside it

The conditional P0 statement and compiled transitive axiom allowlist passed the cited public CI. This implementation run inspected receipts; it did not rerun Lean.

Toolchain: leanprover/lean4:v4.24.0; Mathlib f897ebcf72cd16f89ab4577d0c826cd14afaafc7

intelligence_bound

For every public P0 declaration, Lean.collectAxioms recursively gathers dependency axioms and rejects anything outside the allowlist; CI requires audit PASSED and no compiler sorry warnings.

Ecological intelligence or a site score
Numerical satisfaction of this constraint in the current workflow
Field truth, conservation optimality or AI alignment

Sources and licenses

Exact repaired P0 formal source · Apache-2.0
Intelligence Bound Canon v10.2.0 archive · CC-BY-4.0
Transitive P0 axiom audit · Apache-2.0
Exact-source P0 public CI · Public build receipt
Implementation and release boundary · Proprietary application documentation

scenario resource allocation

Thermodynamic retrofit water-filling

Compare divisible conservation intervention scenarios within an explicitly declared one-budget USD objective.

Package thermodynamic-economic-allocation · 1.0.0-preview.1

Formal proof

six algebraic targets certified

Published exact-hash Comparator Lean and Nanoda receipt covers six listed algebraic claims.

Implementation

existing reference algorithm reused

Existing application bisection algorithm separated for shared use; package binds exact implementation bytes. Runtime checks and local cross-language comparisons are distinct from proof.

Empirical validation

user supplied unvalidated

The model does not measure ecological effects or independently establish USD values.

Release approval

local review preview

This package composition is available for local unsigned scenario evaluation. Production release has not been authorized.

Relationship to the Intelligence Bound

constraint compatibility: Generic real-algebra allocation proof does not import P0. Zenodo isDerivedFrom metadata indicates source attribution, not mathematical derivation. USD and physical burden are declared inputs. Root assessment is an orchestration dependency, not a theorem import.

Statement, assumptions and executable contract

Maximize Σ[(Gᵢ − Eᵢ)yᵢ − ½ηᵢyᵢ²] subject to 0 ≤ yᵢ ≤ 1 and Σcᵢyᵢ ≤ B. Reference allocation: yᵢ = clip((Gᵢ − Eᵢ − λcᵢ)/ηᵢ, 0, 1).

One explicitly declared time period and common USD convention
Each intervention is divisible; an indivisible land acquisition is outside this model
Fixed supplied coefficients and positive capital/friction terms
Independent additive interventions: no overlapping hectares, exclusivity or unmodeled network effects
Quadratic transition friction is an explicitly accepted model
Declared USD objective is justified separately; it is not an ecological effect estimate

Executable inputs
Input	Units	Required	Supported values
budget_usd	USD	Yes	finite, ≥0; workspace upper limit 1e12
assets	named array of declared coefficients	Yes	1–25 in reference; two in conservation workspace
capital_cost_usd, transition_friction_usd	USD	Yes	>0; workspace minimum 0.01
gross_avoided_value_usd, embodied_transition_cost_usd	USD	Yes	finite, ≥0
declared_evidence_ready, declared_price_authorized	boolean	Yes	false in this unsigned scenario workspace; no real allocation authority

Implementation SHA-256 3f81dd0d78bfde887da87c5a48fd58d7d927269e8aaf214e2edf7e8efdaade37

What the proof covers—and what remains outside it

Published exact-hash Comparator Lean and Nanoda receipt covers six listed algebraic claims.

Toolchain: leanprover/lean4:v4.28.0; Mathlib 8f9d9cff6bd728b17a24e163c9402775d9e6a365

clippedAllocation_nonnegative
clippedAllocation_le_one
interior_stationarity
coordinate_improvement_identity
embodied_burden_lowers_benefit
retrofit_allocation_nonvacuous

Read published dual Lean/Nanoda target-verification receipt; no independent rebuild of transitive Mathlib closure this turn. Proof covers six named targets, not Python/TypeScript correctness.

thermodynamic integral
full finite-dimensional KKT existence/uniqueness
floating-point bisection implementation correctness
ecological or monetary coefficient validity
real-world decision authority
field outcomes
general replacement optimality

Sources and licenses

The Thermodynamic Retrofit Water-Filling Note · CC-BY-4.0
Run-139 six algebraic claims · Apache-2.0 repository; archive CC-BY-4.0
Published Comparator certificate · CC-BY-4.0
Published numerical verification · CC-BY-4.0
Implementation and release boundary · Proprietary application documentation
Exact repaired P0 formal source · Apache-2.0

Existing individual reference kernels

The existing workbench remains available. These individual computations have their own scope and maturity; they are not automatically admitted into the new composed workspace.

Kernel and role	Source	Current interface state
Mutualist — natural-capital risk-premium pricing Deterministic theorem-backed computation; empirical input validity is external.	Published record	blocked product warrant required
Restoration — nucleation planting design (Θ go/no-go + n*) Deterministic theorem-backed computation; empirical input validity is external.	Published record	ready unsigned preview Open reference computation
Afforestation — cubic optimal-seeding law + site-prep lever Deterministic theorem-backed computation; empirical input validity is external.	Published record	ready unsigned preview Open reference computation
Harmonization — thermodynamic shadow-price coordination Deterministic theorem-backed computation; empirical input validity is external.	Published record	ready unsigned preview Open reference computation
Carbon Continuity — wildfire recovery threshold diagnostic Deterministic theorem-backed computation; empirical input validity is external.	Published record	ready unsigned preview Open reference computation
Tempo — stewardship cadence Deterministic theorem-backed computation; empirical input validity is external.	Published record	preview only canon record reconciliation required Open reference computation
Shared-channel coverage audit Whitened quadratic dissipation model with a fixed orthogonal-projector channel; not empirical task calibration.	Published record	preview only canon classification reconciliation required Open reference computation
Forbidden-proxy information capacity audit Finite-variable mutual-information ceiling; leakage budget and measured information remain externally justified inputs.	Published record	preview only canon classification reconciliation required Open reference computation
Moment-robust precautionary capacity certificate One-period two-moment marginal certificate; support, dependence, and estimation uncertainty require separate treatment.	Published record	preview only canon classification reconciliation required Open reference computation
Bilateral-benefit reciprocity corridor Two-party one-period linear payoff screen with known positive coefficients and a normative symmetric Nash rule.	Published record	preview only canon classification reconciliation required Open reference computation
Anytime monitoring change certificate Single frozen Bernoulli likelihood-ratio process; iid null and fixed model are load-bearing.	Published record	preview only canon classification reconciliation required Open reference computation
Seed-source bottleneck certificate Continuous one-period frozen binary-eligibility network; no field establishment, legality, procurement, or cost claim.	Published record	preview only canon classification reconciliation required Open reference computation
Directional switching hysteresis certificate Two-state scalar-evidence myopic model with fixed directional penalties and retain-on-tie choice.	Published record	preview only canon classification reconciliation required Open reference computation
Inverse-square shadow-price and capacity planner Positive supplied coefficients only; shadow cost, budget tolerance, and P*D/C capacity are model outputs, not field costs or ecological calibration.	Published record	ready unsigned preview Open reference computation
Multi-ring alignment capacity audit Finite supplied factors in [0,1]; the result audits multiplicative alignment loss and does not validate ring definitions or measurements.	Published record	ready unsigned preview Open reference computation
Symbiotic reciprocity and surplus audit Two-partner supplied-flow screen; mutualistic/parasitic labels apply only inside the declared model and do not establish consent, benefit sharing, or ecological causality.	Published record	ready unsigned preview Open reference computation
Decision-information capacity audit Predictive-richness data ceiling; the thermodynamic minimum is applied only when the caller explicitly declares maintenance or erasure work subject to the Landauer premise.	Published record	ready unsigned preview Open reference computation
Ecological-thermodynamic capital allocation Run-139 one-period, divisible-retrofit, fixed-coefficient, quadratic-friction, single-budget scenario. All burden values, prices, costs, and authority flags are user-supplied and remain empirically unvalidated.	Published record	ready unsigned preview Open reference computation

Located research awaiting a supported package

These sources were inspected at the pinned Canon revision. Their presence does not make them interchangeable with existing implementations or ready for this workflow.

Formal P1 D-Score defines I(X;Y)/H(X). The application’s weighted ecological score is a different construction; no demonstrated calibration makes it a proxy for the Intelligence Bound.

D-Score · kernel candidate

Formal P1 shares Shannon entropy and mutual-information definitions. The application weighted ecological index is a different computation; no proven equality or empirical calibration maps it to I(X;Y)/H(X) or the IB budget.

Public Canon catalog reports external_validation:not-recorded. Runtime disposition: backlog no wrapper.

Exact source

Stewardship Setpoint · kernel candidate

Adds logistic renewable-stock dynamics and H<=Omega*D as model premises. Source treats D as disequilibrium stock; this is not derived from corrected erasure-side Intelligence Bound.

Public Canon catalog reports external_validation:not-recorded. Runtime disposition: backlog no wrapper.

Exact source

Universal Waterfilling · kernel candidate

Concave budget allocation is compatible with a separately declared resource constraint; generic real algebra does not derive from P0.

Public Canon catalog reports external_validation:not-recorded. Runtime disposition: backlog no wrapper.

Exact source

Harmonic Early Warning · not eligible

Stipulated positive power-law models and floor-plus-slack detector cost. No universal ecological warning rule or first-principles detector floor derived.