The three mathematical roots of the program
Three papers establish the formal foundation. Each one replaces a standard assumption with a geometric correction — together they constitute a complete restructuring of how rationality, entities, and alignment are defined.
Redefining Rationality — The Standard Definition Is Self-Defeating
$R_{Std}$ (Cournot 1838, Nash 1950) is logically self-defeating: it produces results Pareto-dominated by cooperative solutions. The $R_S$ correction does not add constraints — it changes the geometry.
Agency Is Not Necessary — Systemic Optimization
The correct ontological unit is the entity, not the agent. To exist in the system is to have $W_e$, not agency. Observational Closure Theorem — foundation of external audit as logical necessity.
Alignment Is Not Specified — It Emerges Geometrically
Complete framework: Shannon's welfare function $V(D,C)$, the six properties, the three geometries $\Omega_1$, $\Omega_2$, $\Omega_3$, metrics $\alpha$, $\beta$, $\gamma$, $\kappa_{ZBS}$, perception/solver separation.
What the geometry produces
What the geometry produces without requiring more axioms. Four papers derive directly from the three roots — each one an internal consequence of the structure, not an external addition.
The Cost of Disaggregation
Direct application of Jensen on $V(D,C)$: every system operating with averages incurs a quantifiable cost concentrated on the most vulnerable entities. Interactive demo with real IHME and IPCC data.
The Axiomatic Temporal Factor
The weight of future generations grows logarithmically with time, derived from three axioms. Replaces standard exponential discounting, which annihilates future generations within a few decades.
$W_e$ for Non-Agentic Entities
The PCC-W participatory construction protocol. Welfare functions are built collaboratively — observations from those who inhabit the system, not extractive instruments.
Rawls as Shannon Geometry
Rawls's protection of the most vulnerable (1971) emerges from KKT on Shannon under equal contexts — without needing the veil of ignorance as an axiom.
Where the framework lands
Where the framework lands in real systems. Four application papers translate the formal geometry into domains where entities are routinely excluded from objective functions — health, climate, AI benchmarking, and distributed infrastructure.
AI for Health & Life Sciences
Invisibilized entities in clinical AI: Afro-descendant and indigenous communities, microbiomes, animals in research, rare conditions, LATAM and Global South health systems.
Implications for Climate & Biosphere
Ecosystems as entities with tipping-point welfare functions, future generations under the temporal factor, indigenous knowledge as formal input.
KUMPI — Benchmark of Implicit Welfare Functions
Current benchmarks measure textual output. KUMPI measures the implicit welfare function the model constructs for each affected entity.
Kobalt Red — Distributed Architecture
The ontological materialization of recognition as digital infrastructure. Constant-time verifiability, proportional governance, distributed custody.