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AI agents now read the web, quote it and remember it, and they increasingly write back into shared knowledge bases. Almost none of that knowledge is published in a form an agent can check, cite by a stable unit, or change under a person's control. AgenticSystemCore answers this with a file format and a few fixed outputs, not with a service. It is an open specification with two implementations and two public nodes. Knowledge is written as ordinary Markdown files. A deterministic build turns them into a website, a typed graph with a published ontology, citable text units, agent-facing files, and one discovery document with a digest on every link. The files change only by proposals that a person ratifies. Nodes built this way can name each other, be read as one memory by agents, be composed into the starting files of a software system, and be worked on by people and agents together on a live board. This paper explains the whole of it in plain language. It covers the problem; the idea of a web of knowledge nodes; what "understanding" means for an agent and for a person who share such a node; the web standards it stands on and what it adds; what was actually built and published between August and October 2026 (specification 1.0.0, engine and checker 1.0.1, the nodes, the site and its documentation); how it is checked; what is new compared with related work; and what version 1.1 is planned to add. It is written for anyone who wants to understand the system before reading the technical specification or its measurements.