Generational HORI & Constraint Decay VectorHORI (Cyan) vs Drift (Rose)
Understanding the Recursive AI Cascade & HORI Workbench
How does this workbench compute the Human Operational Relevance Index (HORI) and visualize multi-generational agent network drift?
This interactive workbench models hypothetical multi-tier AI agent delegation using stylized mathematical formulas for constraint retention, alignment divergence, and a composite Human Operational Relevance Index (HORI). Rather than empirical runtime safety telemetry from real production agent swarms, the page evaluates deterministic discrete functions of user-specified parameters—such as human alignment weight, inter-agent efficiency, generational drift rate, and an optional physical chokepoint bonus. Network relationships and generational degradation curves are dynamically rendered on SVG canvases using D3 force simulations and monotone line interpolations.
The HORI metric and the 25% chokepoint retention floor are illustrative heuristics hardcoded in client-side JavaScript, not standardized governance metrics or empirical safety benchmarks. Real-world autonomous multi-agent pipelines experience complex failure modes—such as prompt injection, reward hacking, semantic drift, and network partition faults—that cannot be captured by simple exponential compounding curves.
Try a worked example
Switching from the default preset to 'Strict Physical Chokepoint Lock' raises the Human Alignment Weight to 0.90, reduces the Drift Rate per Generation to 0.04, and drops Inter-Agent Efficiency to 0.50. Under 5 generations, the computed constraint retention increases to 0.86, alignment divergence drops to 0.14, and the Human Operational Relevance Index (HORI) rises to 93.8% while retaining two enforced physical chokepoints ('chk_hardware' and 'chk_power').
Mathematical Formulation of Retention, Divergence, and HORI
The simulation calculates base constraint retention across generation steps g and per-generation drift rate d using an exponential decay model: baseRetention = (1 - d)^g. When hardware verification is toggled active, the script applies an additive stabilizing bonus of 0.25 * (1 - (1 - d)^g), capping constraint retention at 1.0. Alignment divergence is directly defined as the arithmetic complement: divergence = 1 - constraint_retention.
The composite Human Operational Relevance Index (HORI) combines alignment weight h, constraint retention, efficiency e, and drift d via the expression: rawHori = (h * 50) + (retention * 40) - (e * d * 30) + (chk ? 15 : 0), clamped between 5.0% and 98.5%. These weights assign fixed linear importance to each term rather than reflecting real-world probabilistic alignment stability.
Dynamic Network Topology and Timeline Graphing
The workbench visualizes agent hierarchies through a D3 force simulation that applies link distance, many-body charge repulsion, center anchoring, and collision constraints to prevent overlapping nodes in the SVG viewport. d3-force | D3 by Observable
The generational trajectory chart maps HORI retention and cumulative drift across generation steps using D3 spline generation configured with d3.curveMonotoneX, smoothing the discrete generational coordinates into continuous monitoring curves. Lines | D3 by Observable
Documents the numerical velocity Verlet force integration algorithms (simulation, link, many-body, collide, center) used to position interactive multi-agent topology nodes.
Documents SVG path generation and curve smoothing options including d3.curveMonotoneX used in the multi-generational timeline chart.
Assigned retention and topology in the relevance workbench
Read the explanation
Default drift is point one two over five generations. Base retention is point eight eight to the fifth, about point five two seven seven. The checked hardware option adds one quarter of the lost fraction: base plus point two five times one minus base, about point six four five eight, then rounded to point six five. As generation count grows without bound, that formula approaches point two five. It does not halt drift or verify hardware; it changes an assigned formula. The relevance index combines human weight times fifty, rounded retention times forty, minus efficiency times drift times thirty, plus fifteen when the checkbox is on. Default values therefore yield seventy point four, rather than the earlier declared fifty eight point four fixture. Turning the checkbox off uses retention point five three and removes fifteen, yielding fifty point six. These are arbitrary scenario scores, not a validated measure of human control, alignment or operational relevance. The topology generates two agents in the first generation, three in the second and four in each later generation up to the selected fifth, totaling seventeen synthetic agent nodes. One human root and two hardware nodes bring the checked graph to twenty. Every child receives a parent by array position, not an observed agent interaction. The history chart further decays the already computed final index rather than recomputing a complete policy outcome per generation. Exported node data remains a local scenario, not physical enforcement or verified autonomous execution.