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Graph topology G* = (V, E*) Node i: P_iN = (x_iN, y_iN) r_i = radiusShortN role_i = functionalRole visual_i = visualRoleCandidate Aspect-corrected pair vector: dxPx = (x_jN - x_iN) * Canvas.W dyPx = (y_jN - y_iN) * Canvas.H dPx = sqrt(dxPx^2 + dyPx^2) dShortN = dPx / min(Canvas.W, Canvas.H) theta360 = (atan2(dyPx, dxPx) * 180/pi + 360) mod 360 theta180 = theta360 mod 180 Node degree: deg(i) = |N(i)| Angular gaps: Theta_i = sort(theta360 of selected neighbors) gap_k = wrappedDifference(Theta[k+1], Theta[k]) IMPORTANT: E* is topology only. Line geometry / routing / crossings are delegated to Compo 2.xx.

basePreferredDegree = profile(functionalRole) visual modifier: focus -> may raise preferred upper bound by +1 support -> no default change background -> may lower preferred upper bound by -1 UNRESOLVED -> no modifier roleRigidity: hard -> semantic minimum/maximum may become HARD_CONSTRAINT soft -> degree is scored, not forced if deg(i) > hardMax(functionalRole): remove lowest localTopologyScore incident intents first NOTE: visualRoleCandidate modifies preference only. It MUST NOT replace functionalRole.

effectiveDistance = dShortN // owner geometry derived here Eligibility(i,j): if i == j: REJECT if semanticPairForbidden(i,j): REJECT if both points are background and no style rule asks for network: DOWNRANK if distance exceeds profile hard limit: REJECT else: CREATE ConnectionIntentCandidate Distance preference alone MUST NOT create a connection. Nearest-neighbor-only is forbidden as a complete strategy.

PRIORITY 1. hard safety / semantic constraints 2. mandatory role relations 3. owner-provided line feasibility 4. global composition overrides 5. local topology 6. style variation 7. seeded randomization

function buildPointTopology(scene, points, seed): intents = [] for each unordered pair (a,b): if !semanticEligible(a,b): continue g = aspectCorrectedPairGeometry(a.positionN,b.positionN,scene.canvas) if !distanceEligible(g, a, b): continue intents.push({ from:a.id, to:b.id, geometry:g, roleCompatibilityScore:scoreRoleCompatibility(a,b), distancePreferenceScore:scoreDistance(g,a,b) }) intents = hardTopologyFilter(intents) selected = optimizeDegreeAndAngularSeparation(intents) lineEvidence = Compo2.evaluateConnectionIntents(selected, scene) // DEFERRED selected = applyOwnerProvidedLineEvidence(selected, lineEvidence) globalEvidence = CompositionCore.evaluateDeferred(selected, scene) selected = applyGlobalOverrides(selected, globalEvidence) return buildNodeTopology(selected)

{ "module_id": "Compo 1.07", "name": "point_as_connection_node", "scope": "point topology only; no rendered line routing", "consumes": [ "Compo0.Canvas", "Compo0.ProtectedZones[]", "Point.positionN", "Point.radiusShortN", "Point.visualWeightBase", "Point.visualWeightContextual?@fresh", "Point.functionalRole", "Point.visualRoleCandidate", "Point.subroles[]", "Point.roleRigidity", "Point.gridCandidates[]?", "StylePreset?", "Seed" ], "provides": [ "NodeTopology", "ConnectionIntentCandidate[]", "ConnectionIntentCandidate.centerDistanceShortN", "ConnectionIntentCandidate.directionAngle360Deg", "ConnectionIntentCandidate.directionAngle180Deg", "NodeTopology.localConnectivityScore" ], "owns_metrics": [ "point_topology.node_degree_fit", "point_topology.angular_separation_score", "point_topology.role_compatibility_score", "point_topology.distance_preference_score", "point_topology.local_edge_topology_score", "point_topology.local_connectivity_score" ], "functional_role_degree_profile": { "node": {"preferred":[2,5],"hardMax":7,"source":"INITIAL_HEURISTIC"}, "anchor": {"preferred":[1,3],"hardMax":5,"source":"INITIAL_HEURISTIC"}, "rhythm_member": {"preferred":[1,2],"hardMax":2,"source":"INITIAL_HEURISTIC"}, "marker": {"preferred":[0,1],"hardMax":2,"source":"INITIAL_HEURISTIC"}, "free": {"preferred":[0,2],"hardMax":3,"source":"INITIAL_HEURISTIC"} }, "defaults": { "hardMinAngularGapDeg": {"value":8,"source":"INITIAL_HEURISTIC"}, "distanceMetric": "short_side_normalized_aspect_corrected", "allowBundledConnections": {"value":false,"source":"STYLE_PRESET"} }, "deferred_inputs": { "point.conflict_score": "Compo 1.09", "point.local_contrast": "Compo 1.10", "line.route_feasibility": "Compo 2.xx", "line.crossing_score": "Compo 2.xx", "line.visual_weight": "Compo 2.xx", "global.balance_score": "future owner", "global.negative_space_score": "future owner", "global.hierarchy_score": "future owner", "global.eye_flow_score": "future owner" }, "forbidden_metric_ownership": [ "line.route_cleanliness_score", "line.crossing_score", "line.stroke_weight", "global.balance_score", "global.negative_space_score", "global.hierarchy_score", "global.eye_flow_score" ], "recompute_when": [ "point position changes", "functionalRole/visualRole changes", "effective point weight changes materially", "line owner rejects selected intent", "global solver overrides topology" ], "finality": "LOCAL_TOPOLOGY_PROPOSAL_ONLY" }