Infinite Nodes and Connections

This page computes the proof that the system has no upper bound on nodes — ∞ by induction. Start by clicking on the main result ∞ = ∞ [1] to open it in the side panel, then use Focus in Graph to see the knowledge graph, or Focus in Layers to see the induction chain. Click Taints to see inconsistencies we're currently aware of — mostly documentation that hasn't caught up with the code yet.

The Integrity Cortex landing page shows ∞ for nodes and connections at enterprise scale. The infinity is not hyperbole — it is a mathematical property of the construction, proved by induction.

pltg

Load

(import (quote .src.unbounded ub))
ub.node-limit

Out

∞

The implied condition

The induction holds under a condition: the engine must handle all directive types. If any type lacked grounding support, the system would become invalid above that size. The condition is true [2] — the conjunction of evidence handling for facts/axioms/terms, transitive grounding for derives, and self-evaluating diffs.

Base case

A single-node system is valid when the condition holds: true. [3] A single fact loads, gets a grounding state via the quote verifier, and the system is consistent.

Inductive step

If a system with N nodes is valid (under the condition), then a system with N+1 nodes is also valid. The new node is one of the six directive types, and the engine handles all of them. The step is grounded in the README's own description of the ordinal hierarchy: *"Each layer of extension builds on everything below it."*

The axiom has no guard on ?n — it matches any successor. That absence of a guard IS the unboundedness. The induction fires and reduces to true: true [4] (base), true [3] (one node), true [5] (two nodes), true [6] (three nodes).

The ordinal hierarchy

The system grows by extension[7]. Each new ordinal — each new fact, term, or axiom — expands what can be proved[8]. This is the core idea from Turing's *Systems of Logic Based on Ordinals* (1939): a sequence of logics, each extending the previous by adding new axioms, can transcend the limitations of any single formal system.

Result

pltg

Result

ub.node-limit

Out

∞

Base case holds. Inductive step holds under the implied condition. The step has no guard. The ordinal hierarchy has no termination condition. Node limit: ∞. [9] Marketing claim: ∞ [10][1].

Checks

References

Lineage