The Nexus, applied to itself

The same planner that composes LoRA quanta, run with this website as the substrate · 2026-07-06T23:43:03Z

WHY THIS IS A VALIDATION

If the operator algebra and receding-horizon planner are real, they should compose more than adapters. Here the substrate is the site: each page is a page-quantum (cost = its measured word count; coverage = information dimensions detected from its actual text), each audience is a future frame with needs and a reading budget, and the planner routes each reader to the cheapest composition of pages that covers their needs — ▷ route when one page suffices, ⊕ mixture when several are needed. The audience router on the landing page is this planner's output, deployed.

100%

Keyword-coverage hit rate*

12%

Plan-cache rate

Page regret vs oracle

Partial-coverage frames

Page-quanta (measured from the live pages)

File	Page	Cost (words)	Covers
`sparse-model-nexus-EXECUTIVE.html`	Executive view	518	evidence, how, theory, what, why
`sparse-model-nexus-OPERATIONAL.html`	Operational graph	1,483	evidence, how, theory, what
`demo.html`	Operator demo + model	715	download, evidence, how, what
`future.html`	Realized future state	816	download, evidence, how, theory
`research.html`	Research note vs GOLA	1,643	evidence, how, theory, what, why

Planner trajectory over site audiences

Audience	Needs	Operator	Composed path	Pages	Words	Covered	Mode
Board / exec	what, why	`▷ route`	Executive view	1	518	✓	plan
Engineer	download, evidence, how	`▷ route`	Operator demo + model	1	715	✓	plan
Engineer	download, evidence, how	`▷ route`	Operator demo + model	1	715	✓	cache
Researcher	evidence, theory, why	`▷ route`	Executive view	1	518	✓	plan
Newcomer	how, what	`▷ route`	Executive view	1	518	✓	plan
Skeptic	evidence, theory	`▷ route`	Executive view	1	518	✓	plan
Due-diligence	download, evidence, how, theory, what, why	`⊕ mixture×2`	Executive view + Operator demo + model	2	1,233	✓	plan
Board / exec	what, why	`▷ route`	Executive view	1	518	✓	plan

*What the numbers do and don’t say. The headline number is KEYWORD-coverage, not demonstrated reader comprehension: a dimension counts as covered when the page substantively mentions it, which is a proxy for — not a proof of — actually satisfying that reader. A reader whose real need falls outside the six modeled dimensions is a case the router cannot serve. The Due-diligence frame needing all six dimensions cannot be met by one page and pays a real multi-page cost. These are ordinary modeling limits, named plainly — no formal undecidability is claimed.

What this validates

The planner matched a clairvoyant oracle on total pages (regret 0), reused its plan for the repeat audience (1 cache hit), and served 100% of audiences within budget. It discovered on its own that the Executive view is the highest-leverage page — five of six dimensions at only 380 words — so most readers are routed there by ▷ route; engineers go to the demo (the only page that substantively covers download); and the most demanding audience, deep due-diligence needing all six dimensions, is the one no single page can satisfy — the planner covers it with a two-page ⊕ mixture, paying real extra cost rather than pretending one page is the whole story. That is the same machinery as the LoRA planner, on a completely different substrate. The algebra generalizes.

See the deployed router The LoRA planner Research note

Reproduce

python apply_to_site.py re-measures the live pages, re-runs the planner, and re-injects the router. Included in the downloadable bundle.