02 — Concepts Index

30 concepts. For each: what it is, the canonical source(s) to go and read, when it first appeared, how well developed it is, and — critically — whether a newcomer could follow the existing document. That last column is what tells you which pages can be published near-as-is and which need rewriting.

All paths are relative to the repo root of SGraph-AI__App__Send @ v0.33.62 and were verified to exist. Founder briefs live under team/humans/dinis_cruz/briefs/ — abbreviated below as briefs/.

Tier 1 — the core twenty-two

C1 · Meaning Through Connectivity (the root)

A node carries no inherent meaning. What a thing is emerges from the edges traceable from it, and confidence in that meaning is proportional to connectivity depth and to the authority of the nodes reached. Properties are "just words"; connections are meaning. The operational corollary: identical content can be different things if their edges differ, and the same node can be classified differently by different parties without either being wrong. Read: library/concepts/v0_4_0__thinking-in-graphs.md (Parts 1–2, 5) · briefs/06/28/ontology-and-definitions/v0.33.36__arch-brief__sg-send-node-type-formulas-classification-as-testable-path-pattern-not-judgment.md · briefs/06/26/digital-twins-and-world-models/v0.33.35__arch-brief__sg-send-digital-twins-twin-of-anything-dimensions-discipline-of-reality-simulation-testing.md First: 2026-02-05 · Maturity: well-developed — the most argued concept in the corpus · Newcomer-followable: YES

C2 · Confidence Is a Function of Connectivity

Every assertion sits on a computable confidence spectrum: no edges → few local edges → edges to typed definitions → edges to anchor nodes → edges to external references → rich multi-hop connectivity. Default posture is honest uncertainty — "We know X. We think Y. We cannot confirm Z." The remedy for low confidence is enrichment (add edges), never enforcement (add validation rules). Read: library/concepts/v0_4_0__thinking-in-graphs.md (Part 5, has an ASCII confidence ladder) · briefs/06/16/theses-and-reflections/v0.33.38__strategy-brief__confidence-through-evidence-blast-radius-graphs-mapping-the-gaps.md First: 2026-02-05, extended 16 Jun · Maturity: well-developed · Newcomer-followable: YES

C3 · Map the Gaps (Absence of Evidence Is Evidence)

An honest system lists not only the evidence it has but the evidence it lacks. Knowing you hold three of ten needed pieces is itself vital information — it quantifies confidence and makes the business case for connecting the missing dots. In a regulation graph this becomes a coverage measure: a provision whose hooks reach no twin is a provision not actually mapped. Read: briefs/06/16/theses-and-reflections/v0.33.38__strategy-brief__confidence-through-evidence-blast-radius-graphs-mapping-the-gaps.md First: 16 Jun 2026 · Maturity: well-developed · Newcomer-followable: YES (short and plain)

C4 · Compatibility Is Computed, Not Declared

Two things are compatible to the degree their subgraphs overlap when traced toward common reference points. Compatibility is a spectrum, is asymmetric, and is purpose-relative — two review processes may be compatible for "did someone look at this" and incompatible for "does this satisfy BaFin". No party has to agree to anything, change its process, or adopt a shared vocabulary. Read: library/concepts/v0_4_0__thinking-in-graphs.md (Part 2 — the five-team Review example) · library/concepts/v0_4_0__compatibility-through-connectivity.md First: 2026-02-05 · Maturity: well-developed · Newcomer-followable: YES — the five-team example (Tokyo / open source / Frankfurt / Lagos / São Paulo) is outstanding and needs no technical background. This is the site's best on-ramp.

C5 · Every Artifact Is a Graph → Cross-Graph Compatibility

Prose docs, diagrams, code, config and runtime traces are five languages describing one truth. Extract a graph from each and compare. The question stops being "does the code work?" and becomes "do all representations of this system agree on what it is?" Divergence is information, not failure. Read: library/concepts/v0_4_0__compatibility-through-connectivity.md (whole; Parts 2, 6, 7) First: 2026-02-05 · Maturity: well-developed (10 principles + decisions log) but never implemented · Newcomer-followable: YES

C6 · Anchor Nodes (Reference Without Authority)

An anchor node is well-connected, well-maintained, well-known — and has no special authority. Local nodes link to anchors at whatever granularity fits ("our document_findings step is similar to what schema.org calls reviewBody") rather than declaring "I am a schema:Review". The mapping is granular, honest, traversable, disputable, and can be added by a third party without touching the original node. Read: library/concepts/v0_4_0__thinking-in-graphs.md (Part 4) · library/concepts/v0_4_0__lexicon-architecture.md (lines 91–189 contain a 97-row ASCII ontology tree — redraw this as SVG; it is the site's signature diagram) · briefs/08/09/graphing-text/v0.33.57__arch-brief__sg-send-enrichment-and-shared-anchors-research-paid-once-wikidata-is-the-concept-layer.md First: 2026-02-05 · Maturity: well-developed conceptually; gestural on governance · Newcomer-followable: YES

C7 · Fractal Graphs / Graphs of Graphs / Ontologies of Ontologies

Self-similarity, scale invariance, composition, recursion — one node-and-edge grammar, one validator, one query engine, one provenance rule at every altitude, from a property to a paragraph to a person to a national estate. "Fractal is a precise claim, not a decoration." Read: briefs/07/12/architecture/v0.33.48__arch-brief__sg-send-fractal-semantic-graphs-agentic-operating-layer-deterministic-sovereign-open-source.md (the precise definition) · library/concepts/v0_4_0__thinking-in-graphs.md (Parts 3, 6 — the readable version) · briefs/06/18/agentic-permissions/v0.33.40__strategy-brief__graphs-of-graphs-ontology-of-ontologies-permissions-mapping-reality-not-complexity.md First: 23 Feb 2026 as "graphs of graphs of graphs" applied to signed paragraphs; formalised 12 Jul · Maturity: well-developed · Newcomer-followable: PARTLY — the 12 Jul definition is precise but wrapped in a ~400-word single-sentence abstract

C8 · Node Type Formulas (Classification as a Testable Path-Pattern)

What a node is is not decided by a human's judgment but by an explicit required pattern of typed, directed paths that a node either matches or does not. Vulnerability := a Fact (grounded below) that also has an upward path to a Risk. Judgment does not disappear — it moves out of the classifier's head and into the formula, where it is visible, versioned, inspectable and arguable. Read: briefs/06/28/ontology-and-definitions/v0.33.36__arch-brief__sg-send-node-type-formulas-classification-as-testable-path-pattern-not-judgment.md First: 28 Jun 2026 · Maturity: well-developed · Newcomer-followable: PARTLY (assumes C1)

C9 · Three Layers: Shared Facts / Per-Party Formulas / Declared Bridges

Layer 1 is a shared factual graph owned by nobody. Layer 2 is per-party formulas that classify those nodes — a CISO's, a CFO's, a regulator's. Layer 3 is declared bridges connecting formulas at specific points. Parties can disagree about meaning while still agreeing about facts, which is the only stable basis for working together. Merging ontologies is rejected explicitly, because merging erases the disagreement. Read: briefs/06/28/ontology-and-definitions/v0.33.36__arch-brief__sg-send-ontologies-of-ontologies-three-layers-formulas-bridges-multiple-definitions.md (1,275 words, one clean table) First: 28 Jun 2026 · Maturity: well-developed · Newcomer-followable: YES

C10 · Directed Edges with Distinct Inverses (and Why the Graph Doesn't Explode)

Every edge is directed and has a distinct, meaningfully-named inverse — owned_by/owns, gives_rise_to/arises_from. The inverse is not the same edge walked backwards. This asymmetry makes typed query paths narrow: at each hop fan-out collapses to edges matching type and direction, so traversals move monotonically toward natural peaks. Seed a query in a thousand places and the paths converge on a handful of peaks; result size is bounded by peaks, not fan-out. Read: briefs/06/26/semantic-graph-and-query-paths/v0.33.35__arch-brief__sg-send-directed-edges-inward-outward-query-paths-prevent-node-explosion.md — contains a 17-query, 5-tier path language with real notation (-edge->, <-edge-, *) First: 22 Jun, developed 26 Jun · Maturity: well-developed · Newcomer-followable: YES

C11 · Verb Edges, Never relates-to

Every edge is a verb, stated in both directions. relates-to is banned because it is meaningless — everything relates to everything. Granularity of the verb is what makes the query precise, and precise verbs are what let a path be read as a sentence. Read: briefs/06/10/network-intelligence/v0.33.16__arch-brief__sg-send-semantic-graph-visualisation-subgraph-flip-verb-edges.md (four-row edge/reverse table anyone can read) First: 10 Jun 2026 · Maturity: well-developed · Newcomer-followable: YES ⚠️ The repo violates its own rule: .issues/config/link-types.json ships a relates-to / relates-to pair, and one edge instance uses it. Narrate or fix — either way it is a teaching moment.

C12 · Paths That Read as Language

A path should read as a natural sentence in the language, culture and business context of the reader: this risk is created by this vulnerability, which impacts this system, which belongs to this entity, which has this stakeholder, who reports to this role… Because the path reads as language, the graph explains itself rather than requiring a key. Read: briefs/06/26/semantic-graph-and-query-paths/v0.33.35__arch-brief__sg-send-path-properties-read-as-language-ontology-of-ontologies-multigraph-creation-paths.md First: 26 Jun 2026 · Maturity: well-developed · Newcomer-followable: YES — arguably the single most accessible conceptual document in the corpus

C13 · The Blob Anti-Pattern, and the Wide-Then-Flip Method

The failure mode of semantic graphs is the blob: a hairball that shows nothing — and worse, triggers "a race to the bottom" where people remove relationships to keep the picture clean. Inverted here: rich nodes are good, enrich rather than prune, solve the blob at query time. Method: (1) a wide first pass captures the universe around a subject; (2) find the few relevant nodes; (3) flip and re-root the query at those nodes. Never render the whole graph; render the result of a query. Read: briefs/06/10/network-intelligence/v0.33.16__...subgraph-flip-verb-edges.md · briefs/08/02/vault-as-substrate/v0.33.55__arch-brief__sg-send-graph-canvas-repl-un-blinding-the-agent-mermaid-for-output-never-render-whole-graph.md First: 10 Jun 2026 · Maturity: well-developed · Newcomer-followable: YES — and the most persuasive concept for anyone who has seen a graph demo fail

C14 · Digital Twins as the Graph's Endpoint (the Discipline of Reality)

A twin can be made of anything — an organisation, an inbox, a person, a behaviour, the weather, even luck — because a twin is just a system with properties, behaviours, functions, inputs and outputs. Twins are where the graph stops modelling and continues into a real system. Two properties: whether an endpoint actually reaches reality is itself a measurable fact; and everything modelled must be real, so the graph never fills with hypothetical risks. Read: briefs/06/26/digital-twins-and-world-models/v0.33.35__arch-brief__sg-send-digital-twins-twin-of-anything-dimensions-discipline-of-reality-simulation-testing.md First: 25 Mar 2026 (as "digital twin of the website"), expanded 26 Jun · Maturity: well-developed · Newcomer-followable: YES

C15 · The Air Gap (What the Graph Cannot Reach, Named)

Where the graph cannot connect to a real system, the twin holds an explicit, tracked gap — "this needs to be manually updated once a week, but the point is we now know where that gap is." Any risk not connected to the register is an air gap. The operational sibling of C3: a named absence beats a hidden one. Read: briefs/06/26/digital-twins-and-world-models/v0.33.35__arch-brief__sg-send-digital-twins-integration-layer-real-world-tracked-air-gaps-agent-twin.md · briefs/06/26/risk-register-and-five-whys/v0.33.35__arch-brief__sg-send-risk-register-graph-of-graphs-facts-only-no-deny-cascade-cia-blast-radius.md First: 26 Jun 2026 · Maturity: partially argued · Newcomer-followable: NO — only ever a paragraph inside longer briefs. Gap G9: needs its own page. The Wardley air-gap map (see 04__visual-assets-and-infographics.md Set D) is its natural illustration.

C16 · The Grounding Ladder (Fact → Evidence → Measure → Vulnerability → Risk)

The worked instance of C8. Downward is grounding ("is it real?"), upward is implication ("what does it mean and why does it matter?"). A Fact becomes a Vulnerability the moment it acquires an upward path to a Risk. Measure is not the floor — the true floor is the last node where going deeper would neither improve observability nor change a decision. Explicitly framed as one formula among possible others. Read: briefs/06/28/ontology-and-definitions/v0.33.36__arch-brief__sg-send-grounding-ladder-fact-evidence-measure-vulnerability-risk-definitions.md First: 28 Jun 2026 · Maturity: well-developed · Newcomer-followable: YES for a risk-literate reader, partly otherwise

C17 · A Graph at Every Boundary (Meaning Is Lost at the Seams)

The AI-native argument. Conventional agentic stacks glue layers with JSON and prompt text; at every seam structure, grounding and provenance are flattened and re-guessed — which is where determinism, explainability, provenance, sovereignty and auditability die. Make a semantic graph the interface at every boundary and six properties fall out as consequences rather than features. The model lives at the edge and only proposes a graph; a deterministic validator executes it. Untrusted input is data and can never become instruction, so prompt injection fails at the validator, structurally. Read: briefs/07/12/architecture/v0.33.48__arch-brief__sg-send-fractal-semantic-graphs-agentic-operating-layer-deterministic-sovereign-open-source.md (with an honest-tensions table) First: 12 Jul 2026 · Maturity: well-developed · Newcomer-followable: NO — the abstract is one ~500-word sentence. The ideas are highly accessible; the document is not. This is the highest-value rewrite target on the site.

C18 · Messages Are Graph Transformations (Everything Is a Message)

Registers do not share a database; they talk. A message is not a notification about a change — it is the change: "the command, the action that is transforming the graph." Every mutation becomes an ordered message, making the system an eventually-consistent event stream whose by-product is a transaction log giving "a hell of a provenance, and also determinism, explainability, but also a lot of resilience." Because messages are structured, an LLM can produce and parse them — the same stream is the natural agent interface. Read: briefs/07/17/architecture-and-mvp/v0.33.49__arch-brief__sg-send-fractal-distributed-vault-architecture-registers-of-registers-messages-as-graph-transformations-transaction-log-pki-authorization.md First: 17 Jul 2026 · Maturity: well-developed, but flagged in-doc as needing its own brief (never written) · Newcomer-followable: PARTLY (interleaved with RiskMandate specifics)

C19 · Documents (and Skills, and Standards) Are Projections of Graphs

The graph is the truth; the document is a view of it, generated in the context of use. Today's artefacts — a skill file, a compliance standard, a consolidated legal text — are "static photographs of what they should be." The sharpest version: don't store the consolidated text at all — hold the base text plus amendment instructions as data and compute the consolidated version as a projection. Consolidation and per-organisation customisation then turn out to be one mechanism, not two. Read: briefs/06/04/v0.32.3__arch-brief__sg-send-skill-as-projection-of-graph-forking-ecosystem.md · briefs/07/31/canonical-act-build/v0.33.54__arch-brief__sg-send-canonical-ai-act-paragraph-as-file-amendment-as-native-graph-operation-view-from-any-provision.md · briefs/05/30/v0.31.9__arch-brief__sg-send-vault-per-standard-document-to-graph-artefacts.md First: referenced as already recurring on 4 Jun — the origin document is not in this repo · Maturity: well-developed in application, no home document for the general principle · Newcomer-followable: NO — always stated by analogy to itself. Gap G2.

C20 · Every Paragraph Is a Graph (Document → Graph Pipeline)

A document is not one blob but a hierarchy of paragraphs, points and definitions, each written for a reason and therefore yielding something extractable. Each provision carries its own subgraph, and those subgraphs present hooks the real world attaches to. A document's own definitions are the first and most valuable node layer, and three kinds of work follow: how they relate, where they contradict (the highest-value output, and the one nobody produces), and what the text uses but never defines (where interpretive risk concentrates). Read: briefs/07/28/regulation-graph-and-acceptability/v0.33.53__arch-brief__sg-send-every-paragraph-is-a-graph-eu-ai-act-definitions-as-nodes-twins-as-hooks-with-concepts-appendix.md — Appendix A is the single best existing concept summary in the whole corpus · briefs/07/31/canonical-act-build/v0.33.54__arch-brief__sg-send-document-ontology-positional-and-content-hashes-taxonomy-upward-ontology-outward-document-agnostic.md First: 23 Feb 2026 in embryo, doctrine 30 May, full 28 Jul · Maturity: well-developed · Newcomer-followable: PARTLY (body readable, abstract not)

C21 · Concepts, Not Words (Meaning Must Not Live in a Language)

The unit of meaning is a concept, language-independent, carrying one preferred label per language plus alternates, related by broader/narrower/related. A term is how one language expresses it. Once meaning lives in a concept, translation stops being word-to-word and a whole class of failures disappears by construction. The unexpected corollary the founder discovered: a bad Portuguese rendering diagnosed a bad English word — naming a concept forces a decision the source language let you avoid. And where two languages' induced graphs diverge, that divergence is either an error or a genuine lexical gap — and it is a finding. Read: briefs/08/06/voice-debrief/v0.33.56__arch-brief__sg-send-concepts-not-words-skos-is-the-model-divergence-is-the-finding.md — opens with a plain terminology table (concept / term / taxonomy / ontology / semantic field / concept scheme) which is exactly what a newcomer needs First: 31 Jul via EuroVoc, named 6 Aug · Maturity: well-developed · Newcomer-followable: YES

C22 · Decompilation, Not Compilation (the Author Is the Oracle)

Lifting text into a graph runs concrete → abstract, which in compiler terms is decompilation — ambiguous, and impossible to do reliably without help. The point is not absolute truth but the author's own meaning confirmed by the author, so lifting needs an oracle, and the author is the only party who holds the answer. Therefore a reader saying "that is not what I meant" is not a failure of extraction — it is the elicitation working. Every node at every altitude carries a source map back to the span it came from. Rendering is answered by altitude, not by subsetting. Read: briefs/08/09/graphing-text/v0.33.57__strategy-brief__sg-send-refactoring-meaning-decompilation-not-compilation-author-is-the-arbiter.md First: 9 Aug 2026 — the newest major concept · Maturity: well-developed · Newcomer-followable: PARTLY

Tier 2 — the "then more" eight

The teaching order — this IS the site's information architecture

Ordered so each step is motivated by the previous one and no step requires a forward reference. Steps 1–5 are "initial concepts"; 6–12 "then more"; 13–18 "then more".

Argue the IA from the corpus itself using quote 35 (city walls → roads → buildings → people). Progressive disclosure is altitude, which makes the navigation a demonstration of C13/C22 rather than merely a choice.

This document is released under the Creative Commons Attribution 4.0 International licence (CC BY 4.0).

== briefs/03__worked-examples-index.md