============================================================ AGLA — GRAPHUS COMMUNIS ARTIS CLASS LAW Ars Generalis Applied — Root-Class Structural Object Version: 1.1.0-GRAPHUS-ROOT-CONTRACT-CANONICAL Status: CANONICAL / ROOT-CONTRACT / NON-RUNTIME / NO-EXECUTION-AUTHORITY Authority: AGLA / HUMAN CONTROL PLANE / HP-006-C Artifact ID: AGLA-GRAPHUS-COMMUNIS-ARTIS Class: AGLA / ROOT CLASS LAW / GRAPHUS COMMUNIS ARTIS Mutation Policy: VERSION-CONTROLLED ONLY Canonization Record: GRAPHUS_COMMUNIS_ARTIS_ROOT_CONTRACT_CANONIZATION_RECORD.md ============================================================ ## I. Declaration GRAPHUS COMMUNIS ARTIS is a root-class structural object. It is not TENET, not ROTA, not AREPO, not OPERA, not SATOR, and not a sixth member of the five-class stack order. It exposes a reusable graph grammar and a source-traceable topology from which contextual graph instances may be declared. This root contract is canonized by the human HP-006 Option C decision and its versioned root-only review record. Canonical status applies only to the graph object/instance grammar and authority boundary. It does not authorize execution and does not propagate canonical status to an edge set, test, instance, binding, visualization, or conformance result. ## II. Object and instance The root object declares: - the stable vertex-carrier vocabulary; - the versioned edge-set lifecycle and authority-status policy; - the distinction between topology, semantic assignment, traversal, and visualization; - the requirements every contextual instance must satisfy. A `GRAPHUS_INSTANCE` is a contextual contraction created by a registered ROTA, protocol, APPLICATIO, control record, or other admitted artifact. The instance selects a versioned edge set and assigns semantic carriers. It does not mutate the root object. `GRAPHUS OBJECT ≠ GRAPHUS INSTANCE` The object has global structural position. An instance has local, context-bounded position. ## III. Stable topology and contextual activation The source-declared common carrier set is: `{X, B, C, D, E, F, G, H, I, K}` `X` is the regime gate or anchor carrier. `B–K` are ordinal carriers. The letters do not carry one universal semantic content. Meaning is assigned by a declared regime or contextual carrier map. The first registered candidate edge set is `GRAPHUS-EDGESET-SCHOLASTICUS-1.0.0`, defined by the normative edge-set register. Its source is the human-supplied draft `LIBER GRAPHI COMMUNIS ARTIS`, which records the classroom graph and the normalization of a duplicated `E-H` declaration. That edge set has the independent state `CANDIDATE / SOURCE-DECLARED / CANONIZATION-PENDING / NON-RUNTIME / NO-AUTHORITY-EFFECT`. Root-contract canonization does not promote, validate, canonize, execute, or grant authority to it. Its source locator and tests 4/5 remain open; it must not be presented as runtime or canon. Every instance MUST declare `edge_set_ref` and `edge_set_authority_status` as independently addressable fields. A candidate edge set propagates `CANDIDATE / NON_RUNTIME / NO_AUTHORITY_EFFECT` to the instance and every binding or conformance result that consumes it. ASCII, geometry, node placement, proximity, and illustration MUST NOT be used to infer an edge. Ambiguity or mismatch MUST be returned to the human control plane; it MUST NOT be silently repaired. ## IV. Relative abstraction continuum The graph permits relative movement toward more general, medial, or more specified carriers. These are contextual relations, not universal, discrete ontological levels. Descriptions such as “first opening,” “medial,” and “terminal” are pedagogical heuristics. They do not make the graph a tree, impose one direction, or prohibit a source-authorized revisit. ## V. Holographic recurrence A node, edge, chamber, OPERA, composite OPERA, APPLICATIO, or other admitted carrier may invoke a child `GRAPHUS_INSTANCE`. The child: - records `parent_instance_ref`; - records the carrier or event that invoked it; - declares its own edge-set reference, edge-set authority status, and semantic assignment; - preserves a return trace to the parent; - does not overwrite parent state. This recurrence is holographic and contextual, not proof that every node contains the same semantics. ## VI. Graph, tree, and visualization GRAPHUS COMMUNIS ARTIS IS A GRAPH. It may contain cycles, revisits, alternative paths, cross-links, and context-dependent direction. A computational tree may be derived for a particular search, explanation, or execution plan, but the derived tree is a projection and MUST retain a reference to the graph instance and the rule that produced it. Topology is the declared vertex and edge structure. Visualization is a carrier of that structure. No visual arrangement is authoritative over the textual and machine-readable edge register. ## VII. GRAPHUS, ROTA, and OPERA GRAPHUS exposes admissible structural possibility. ROTA selects and orders a traversal regime over a graph instance. OPERA performs an authorized executable walk after AREPO admission. A visitation signature is an intended or observed ordered sequence of carriers. It is not automatically an executable walk. If consecutive members are not adjacent under the selected edge set, the signature requires a declared mediated path or fails admission. Revisits are lawful only when declared by the ROTA or OPERA contract. Each revisit MUST record the prior visit, the new visit, and a `state_delta`; an unreported repeated carrier is not evidence of progress. Focal OPERAE and composite OPERAE may both bind an instance. A composite OPERA MUST preserve child walk boundaries, invocation order, return edges, and provenance. ## VIII. Internal heuristic provenance Heuristics, weights, costs, directionality, and traversal preferences are not edges. Each must declare: - source or derivation; - scope; - confidence or maturity; - whether it is measured, source-derived, locally inferred, or hypothetical; - the ROTA or OPERA that may consume it. An internal heuristic MUST NOT silently alter the selected declared edge set. ## IX. Doctrinal and arithmetic foundation The operational invariants of GRAPHUS instances are supplied by: `00_TRANSVERSAL_ARTIFACTS/TENET/TENET_GRAPHUS_COMMUNIS_ARTIS.md` Generated, scored, reduced, or state-mutating instances also resolve: `16_STACK_ARITHMETICA/TENET_ARITHMETICA_DoctrinalInvariants.md` The first TENET governs graph-state and decision-articulation invariants. The second governs typed states, rules, reductions, and ordinal multi-OPERA modes. Both remain distinct from this root object law, and their current candidate status propagates. GRAPHUS may articulate candidate actions for one OPERA or a sequence of OPERAE when several user needs compete. It records options, constraints, trade-offs, admission, selection, state delta, and stop/continue decision. It does not execute the selected plan. Traversal is emulated by session self-binding and coherence pressure. Each effective step binds the prior state, proposed edge or rule, AREPO admission, active constraints, accepted delta, rejected alternatives, coherence result, and resulting state. The resulting state constrains the next step. This does not require a visual skill or an invocation-local graph file. A textual or machine-readable session trace is sufficient. Coherence pressure MUST NOT invent topology, rules, authority, or permission. ## X. Normative instance binding Every instance conforms to `GRAPHUS_COMMUNIS_ARTIS_INSTANCE_SPECIFICATION.md` and includes at least: - `instance_id`; - `graphus_class_ref`; - `edge_set_ref`; - `edge_set_authority_status`; - `context_ref`; - `carrier_assignments`; - `edge_policy`; - `traversal_owner`; - `visitation_signature`; - `executable_walk`; - `state_model`; - `quantitative_foundation_ref` when state generation or reduction occurs; - `decision_articulation` when alternatives are compared or selected; - `source_trace`; - `parent_instance_ref` and `invocation_ref` when nested. ## XI. LIBER and APPLICATIO LIBER may provide source substrate, examples, semantic assignments, and research provenance. LIBER does not execute and does not become a root law by resemblance. APPLICATIO is the stabilized applied contraction layer. An APPLICATIO may bind a graph instance, but it MUST identify its source LIBER, selected edge set, carrier assignments, ROTA, AREPO gate, and executable OPERA. The canonical spelling is `APPLICATIO`; `APLICATIO` is rejected. ## XII. Authority and failure The following are failures: - classifying GRAPHUS as TENET; - executing from this law or from an index summary; - omitting, inventing, or misrepresenting `edge_set_ref` or `edge_set_authority_status`; - deriving edges from an ASCII diagram; - collapsing carrier identity into semantic identity; - treating a visitation signature as a walk without adjacency checks; - concealing mediation, revisit, state delta, or nested-instance provenance; - treating a derived tree as the graph; - allowing heuristic or visualization metadata to mutate topology; - concealing the effective decision path or rejected lawful alternatives; - using graph reachability as permission to execute another OPERA; - narrating movement without an emulated and bound transition; - making traversal depend on a visual skill or invocation-local graph file; - allowing coherence pressure to invent an edge, rule, authority, or permission; - propagating root-contract canonization to an edge set, test, instance, binding, visualization, or conformance result; - claiming edge-set canon before an independent source-complete human review. ## XIII. Final law GRAPHUS COMMUNIS ARTIS is the reusable root-class graph object. Contextual instances bind versioned, source-traceable topology to declared carriers. ROTA owns traversal order; AREPO owns admission; OPERA owns execution; SATOR owns mediated presentation and trace disclosure. The graph remains distinct from every one of them. This canonical root contract is non-runtime; every selected edge set and dependent surface retains its own independently declared authority status.