{
    "model": {
        "rank": 6181,
        "code": "thing-q205034",
        "model_id": "vr.tr.perpendicularity",
        "name": "perpendicularity",
        "purpose": "Enable an AI agent to recognise a perpendicularity relation, evaluate its support and deviation, and determine whether to accept, constrain, correct or further inspect it.",
        "family": "Thing Registry",
        "category": "Cross-cutting context",
        "status": "research-draft",
        "kind": "thing",
        "plane": "XCT",
        "domain": "XCT.QLT",
        "industry": "",
        "version": "",
        "url": "/models/thing/q205034/",
        "tier": 2,
        "score": 62,
        "payload": {
            "layer": "wikidata",
            "aliases": [],
            "aliasCount": 0,
            "merged": 0,
            "knownIn": 62,
            "facets": null,
            "markers": [],
            "lexicalClass": "",
            "senseRank": null,
            "alsoRegisteredAs": null,
            "source": {
                "dataset": "wikidata",
                "item": "Q205034",
                "url": "https://www.wikidata.org/wiki/Q205034",
                "license": "CC0 1.0"
            }
        },
        "research": {
            "vercy": "1.0-draft",
            "publication": {
                "status": "research-draft",
                "adjudicationStatus": "unreviewed",
                "publishableCanonical": false,
                "generatedAt": "2026-09-07T11:59:43Z",
                "providers": [
                    "Codex",
                    "Grok"
                ],
                "missingProviders": [],
                "pass": 2,
                "cost": {
                    "grok": {
                        "usd": 0.01020816,
                        "turns": 1,
                        "seconds": 123.5,
                        "error": null
                    },
                    "codex": {
                        "seconds": 68.5,
                        "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.3\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a07bba-d3db-7af1-b1c4-39a2a1e82ed3\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: perpendicularity\nRegistry id: vr.tr.perpendicularity\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into this entry:"
                    }
                }
            },
            "metaModel": {
                "id": "THING-Q205034",
                "registryId": "vr.tr.perpendicularity",
                "name": "perpendicularity",
                "version": "0.1.0-research.1",
                "entryKind": "thing",
                "family": "Thing Registry",
                "domain": [
                    "XCT.REL"
                ],
                "status": "research-draft"
            },
            "canonicalUrl": "https://ver.cy/models/thing/q205034/",
            "model": {
                "registry_id": "vr.tr.perpendicularity",
                "name": "perpendicularity",
                "purpose": "Enable an AI agent to recognise a perpendicularity relation, evaluate its support and deviation, and determine whether to accept, constrain, correct or further inspect it.",
                "definition": "Perpendicularity is the geometric orientation of a line, axis or surface at a right angle to a reference line or plane; in product geometry specification it is an orientation tolerance whose zone (two parallel planes or a cylinder) is constrained at 90° to a datum system.",
                "scope_statement": "This model owns perpendicularity as a relation between specified geometric entities or local directions under a stated geometry, reference frame and evaluation rule, including exact, measured and required perpendicularity.",
                "in_scope": [
                    "The participating lines, directions, axes, planes, surfaces or local geometric elements.",
                    "The geometric context and criterion that give perpendicularity a definite meaning.",
                    "Exact right-angle relations and evidence supporting or contradicting them.",
                    "Measured departures from perpendicularity and their uncertainty.",
                    "Perpendicularity requirements, permissible deviation and resulting decisions."
                ],
                "out_of_scope": [
                    "Complete shape and dimensional descriptions of the participating objects.",
                    "Parallelism, collinearity and general angular relationships except as comparison cases.",
                    "Abstract orthogonality of functions, signals or other nongeometric entities.",
                    "Whole-system alignment, assembly fit and mechanical performance.",
                    "Instrument calibration and manufacturing processes beyond their effect on this relation."
                ],
                "distinguishing_features": [
                    "An exact perpendicularity assertion requires the applicable right-angle or equivalent geometric criterion; merely being nonparallel is insufficient.",
                    "A right angle visible in an image does not establish perpendicularity in the represented space unless the projection supports that inference.",
                    "For line-to-plane perpendicularity, the line must follow the plane's normal direction; being perpendicular to one selected in-plane line is insufficient.",
                    "For plane-to-plane perpendicularity, evaluate the planes' dihedral relation or their normals; perpendicular planes must not be confused with parallel planes whose normals are parallel.",
                    "A measured relation satisfying a tolerance is acceptable under that requirement but is not thereby established as mathematically exact."
                ],
                "characteristics": [
                    {
                        "name": "Participating geometric entities",
                        "kind": "relation",
                        "unit_or_values": "Identified pair of lines, directions, axes, planes, surfaces or local elements",
                        "why_it_matters": "Determines what is asserted to be perpendicular and which evaluation criterion applies."
                    },
                    {
                        "name": "Geometric context",
                        "kind": "category",
                        "unit_or_values": "Dimension, ambient space, metric or inner product, and coordinate conventions",
                        "why_it_matters": "Coordinates alone do not determine whether the relevant directions form a right angle."
                    },
                    {
                        "name": "Extent of assertion",
                        "kind": "category",
                        "unit_or_values": "Global; at a specified point; over a specified region; relative to a fitted feature",
                        "why_it_matters": "Separates whole-entity perpendicularity from a local or estimated relation."
                    },
                    {
                        "name": "Assertion role",
                        "kind": "category",
                        "unit_or_values": "Required; assumed; constructed; derived; observed",
                        "why_it_matters": "Separates intended geometry from established or measured geometry."
                    },
                    {
                        "name": "Evaluated angle",
                        "kind": "measurement",
                        "unit_or_values": "Degrees or radians, with the angle convention and geometric elements identified",
                        "why_it_matters": "Provides a quantitative basis for testing a right-angle relation without confusing direction, normal and dihedral angles."
                    },
                    {
                        "name": "Departure from perpendicularity",
                        "kind": "measurement",
                        "unit_or_values": "Angular deviation in degrees or radians, or a separately defined spatial deviation in length units",
                        "why_it_matters": "Quantifies the departure using the measure actually required by the application."
                    },
                    {
                        "name": "Evaluation uncertainty",
                        "kind": "measurement",
                        "unit_or_values": "Uncertainty interval or bound in the units of the evaluated quantity, with its interpretation",
                        "why_it_matters": "Determines whether available evidence can resolve the perpendicularity decision."
                    },
                    {
                        "name": "Perpendicularity assessment",
                        "kind": "state",
                        "unit_or_values": "Established exact; meets stated tolerance; fails stated tolerance; indeterminate; undefined",
                        "why_it_matters": "Supports an actionable conclusion while distinguishing exactness, acceptance and insufficient evidence."
                    }
                ],
                "affordances": [
                    "Test perpendicularity using the criterion appropriate to the participating geometry.",
                    "Identify missing references, undefined directions or incompatible coordinate representations before evaluating the relation.",
                    "Estimate departure from perpendicularity and determine whether uncertainty permits a decision.",
                    "Construct or impose a perpendicularity constraint on eligible geometric entities.",
                    "Determine an allowed adjustment toward perpendicularity while respecting fixed references and other constraints.",
                    "Request additional measurements or proof when the current evidence cannot settle the relation."
                ]
            },
            "sources": [
                {
                    "id": "iso-1101-2017",
                    "title": "ISO 1101:2017 Geometrical product specifications (GPS) - Geometrical tolerancing - Tolerances of form, orientation, location and run-out",
                    "url": "",
                    "what_it_supports": "Defines perpendicularity as an orientation tolerance, the associated symbols, and the planar and cylindrical tolerance zones used on technical drawings."
                },
                {
                    "id": "asme-y14-5-2018",
                    "title": "ASME Y14.5-2018 Dimensioning and Tolerancing",
                    "url": "",
                    "what_it_supports": "US product-definition rules for the perpendicularity characteristic, datum referencing, and how surface versus axis perpendicularity is applied."
                },
                {
                    "id": "iso-230-1",
                    "title": "ISO 230-1 Test code for machine tools - Geometric accuracy of machines operating under no-load or quasi-static conditions",
                    "url": "",
                    "what_it_supports": "How squareness/perpendicularity of machine-tool axes is measured in micrometres per metre of travel."
                },
                {
                    "id": "wikipedia-perpendicular",
                    "title": "Perpendicular",
                    "url": "https://en.wikipedia.org/wiki/Perpendicular",
                    "what_it_supports": "The Euclidean geometric relation (lines, a line and a plane, two planes) and its equivalence to a vanishing inner product of direction or normal vectors.",
                    "url_status": "live"
                }
            ],
            "structure": {
                "bundles": [
                    {
                        "id": "geometric-participants",
                        "name": "Geometric participants",
                        "description": "Identifies precisely what is perpendicular to what and where the assertion applies.",
                        "rationale": "Perpendicularity between directions, lines, planes and local surface elements requires different interpretations.",
                        "layers": [
                            {
                                "id": "participating-elements",
                                "name": "Participating elements",
                                "description": "Resolves the geometric entities underlying the relation.",
                                "findings": [
                                    {
                                        "id": "entity-pair-and-support",
                                        "name": "Entity pair and geometric support",
                                        "description": "Record the two participating elements and whether each is directly defined or extracted from a physical feature.",
                                        "questions": [
                                            {
                                                "text": "Which two lines, axes, directions, planes or local elements are asserted to be perpendicular?",
                                                "kind": "definition",
                                                "id": "entity-pair-and-support-q01"
                                            },
                                            {
                                                "text": "If an element represents a physical feature, how was its axis, direction or reference plane obtained?",
                                                "kind": "provenance",
                                                "id": "entity-pair-and-support-q02"
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "extent-and-incidence",
                                "name": "Extent and incidence",
                                "description": "Establishes the location, extent and intersection conditions of the assertion.",
                                "findings": [
                                    {
                                        "id": "locality-and-intersection",
                                        "name": "Locality and intersection",
                                        "description": "Distinguish a relation at a point or over a region from a global relation, and distinguish perpendicular entities from perpendicular directions.",
                                        "questions": [
                                            {
                                                "text": "Does the assertion apply to entire entities, fitted representatives or tangent elements at specified locations?",
                                                "kind": "boundary",
                                                "id": "locality-and-intersection-q01"
                                            },
                                            {
                                                "text": "Must the participating entities intersect under the intended definition, or is the assertion only about their directions?",
                                                "kind": "definition",
                                                "id": "locality-and-intersection-q02"
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "right-angle-criterion",
                        "name": "Right-angle criterion",
                        "description": "Defines the geometric meaning and valid test of perpendicularity.",
                        "rationale": "A perpendicularity judgement depends on the geometry and entity pairing, not merely on a coordinate pattern or visual appearance.",
                        "layers": [
                            {
                                "id": "geometry-and-representation",
                                "name": "Geometry and representation",
                                "description": "Establishes the space, metric and representation in which a right angle is evaluated.",
                                "findings": [
                                    {
                                        "id": "angle-defining-context",
                                        "name": "Angle-defining context",
                                        "description": "Record the dimensional and metric assumptions and reconcile the participants' coordinate frames.",
                                        "questions": [
                                            {
                                                "text": "What ambient space and metric or inner product define the angle between the relevant directions?",
                                                "kind": "definition",
                                                "id": "angle-defining-context-q01"
                                            },
                                            {
                                                "text": "Are both participants represented in a compatible frame, and does any image projection or transformation preserve the angle being tested?",
                                                "kind": "boundary",
                                                "id": "angle-defining-context-q02"
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "pair-specific-test",
                                "name": "Pair-specific test",
                                "description": "Selects a valid perpendicularity criterion for the identified entity types.",
                                "findings": [
                                    {
                                        "id": "criterion-and-degeneracy",
                                        "name": "Criterion and degeneracy",
                                        "description": "Identify the right-angle, direction-normal or normal-normal test and conditions under which it is undefined.",
                                        "questions": [
                                            {
                                                "text": "For this entity pair, should the agent test a right angle between directions, alignment with a plane normal, or a right angle between plane normals?",
                                                "kind": "definition",
                                                "id": "criterion-and-degeneracy-q01"
                                            },
                                            {
                                                "text": "Does a zero direction, undefined tangent, nonunique normal or inadequately determined plane prevent this test from having a geometric meaning?",
                                                "kind": "boundary",
                                                "id": "criterion-and-degeneracy-q02"
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "evidence-and-deviation",
                        "name": "Evidence and deviation",
                        "description": "Connects the assertion to proof, construction or measurement and quantifies any departure.",
                        "rationale": "Intended right angles, proved right angles and measurements near a right angle support different conclusions.",
                        "layers": [
                            {
                                "id": "assertion-support",
                                "name": "Assertion support",
                                "description": "Separates the role of the assertion from the evidence available for it.",
                                "findings": [
                                    {
                                        "id": "requirement-versus-established-relation",
                                        "name": "Requirement versus established relation",
                                        "description": "Record whether perpendicularity is requested, assumed, imposed by construction, derived or observed.",
                                        "questions": [
                                            {
                                                "text": "Is perpendicularity a design requirement, a working assumption, a construction constraint, a proved result or a measurement conclusion?",
                                                "kind": "definition",
                                                "id": "requirement-versus-established-relation-q01"
                                            },
                                            {
                                                "text": "Which derivation, construction record or observations support this assertion, and on what assumptions do they depend?",
                                                "kind": "provenance",
                                                "id": "requirement-versus-established-relation-q02"
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "departure-and-resolution",
                                "name": "Departure and resolution",
                                "description": "Determines the magnitude of departure and whether available evidence resolves it.",
                                "findings": [
                                    {
                                        "id": "measured-departure",
                                        "name": "Measured departure",
                                        "description": "Record the deviation measure, observation extent and uncertainty without treating an estimate as exact geometry.",
                                        "questions": [
                                            {
                                                "text": "What angular or spatial departure was evaluated, in which units, and over what length, area or sample of the feature?",
                                                "kind": "measurement",
                                                "id": "measured-departure-q01"
                                            },
                                            {
                                                "text": "How do measurement uncertainty, numerical precision and feature fitting affect the reported departure?",
                                                "kind": "measurement",
                                                "id": "measured-departure-q02"
                                            },
                                            {
                                                "text": "Could unsampled portions or local variation invalidate a conclusion drawn from the fitted direction or plane?",
                                                "kind": "boundary",
                                                "id": "measured-departure-q03"
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "acceptance-and-adjustment",
                        "name": "Acceptance and adjustment",
                        "description": "Relates perpendicularity evidence to an applicable requirement and permissible next actions.",
                        "rationale": "An agent needs a justified decision rule and adjustment constraints before accepting or changing the relation.",
                        "layers": [
                            {
                                "id": "requirement-and-decision",
                                "name": "Requirement and decision",
                                "description": "Makes exactness, tolerance and unresolved assessments explicit.",
                                "findings": [
                                    {
                                        "id": "applicable-acceptance-rule",
                                        "name": "Applicable acceptance rule",
                                        "description": "Record the governing perpendicularity requirement, its reference and the decision rule applied to the evidence.",
                                        "questions": [
                                            {
                                                "text": "Does the task require exact perpendicularity, an angular limit or a spatial tolerance relative to a specified reference?",
                                                "kind": "definition",
                                                "id": "applicable-acceptance-rule-q01"
                                            },
                                            {
                                                "text": "Where is that requirement defined, including any applicable datum, tolerance-zone interpretation or decision convention?",
                                                "kind": "provenance",
                                                "id": "applicable-acceptance-rule-q02"
                                            },
                                            {
                                                "text": "Given the evidence and uncertainty, is the relation established exact, acceptable, unacceptable, indeterminate or undefined?",
                                                "kind": "measurement",
                                                "id": "applicable-acceptance-rule-q03"
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "permitted-geometric-change",
                                "name": "Permitted geometric change",
                                "description": "Identifies how the relation may be established, corrected or investigated.",
                                "findings": [
                                    {
                                        "id": "adjustment-and-recheck",
                                        "name": "Adjustment and recheck",
                                        "description": "Determine which participant may change, which geometric constraints must remain satisfied and how the result will be verified.",
                                        "questions": [
                                            {
                                                "text": "Which participant is fixed, and what rotations, reorientations or feature changes are permitted while preserving required positions and other geometric relations?",
                                                "kind": "action",
                                                "id": "adjustment-and-recheck-q01"
                                            },
                                            {
                                                "text": "What construction, proof or measurement will verify perpendicularity after an adjustment or resolve the current indeterminate assessment?",
                                                "kind": "action",
                                                "id": "adjustment-and-recheck-q02"
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "evidence-and-external-alignment",
                        "name": "Evidence and external alignment",
                        "description": "What the world already says about this thing, gathered so the model can be checked against it.",
                        "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.",
                        "layers": [
                            {
                                "id": "reported-evidence",
                                "name": "Reported evidence",
                                "description": "Findings from the breadth pass, kept separate from the structural claims.",
                                "findings": [
                                    {
                                        "id": "evidence-kinds",
                                        "name": "Kinds and varieties",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            "Line-to-line perpendicularity in a plane",
                                            "Line-to-plane (axis-to-face) perpendicularity",
                                            "Plane-to-plane perpendicularity",
                                            "Surface perpendicularity as a GPS/GD&T planar tolerance zone",
                                            "Axis or median-line perpendicularity as a cylindrical tolerance zone",
                                            "Vector orthogonality in an inner-product space",
                                            "Construction and layout squareness (wall-to-floor, plumb-to-level)",
                                            "Machine-axis squareness in motion geometry"
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-kinds-q01",
                                                "text": "Which of these kinds and varieties hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    },
                                    {
                                        "id": "evidence-identifiers",
                                        "name": "Identifiers and schemes",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            {
                                                "scheme": "ISO 1101 / ASME Y14.5 characteristic symbol",
                                                "value_or_pattern": "⊥",
                                                "note": "Drawing symbol for the perpendicularity orientation tolerance."
                                            },
                                            {
                                                "scheme": "Unicode",
                                                "value_or_pattern": "U+27C2",
                                                "note": "PERPENDICULAR character ⟂, used for the geometric relation in text."
                                            }
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-identifiers-q01",
                                                "text": "Which of these identifiers and schemes hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    },
                                    {
                                        "id": "evidence-standards-and-regulation",
                                        "name": "Standards and regulation",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            "ISO 1101 Geometrical product specifications (GPS) - Geometrical tolerancing (International Organization for Standardization)",
                                            "ISO 5459 Geometrical product specifications (GPS) - Datums and datum systems (International Organization for Standardization)",
                                            "ASME Y14.5 Dimensioning and Tolerancing (American Society of Mechanical Engineers)",
                                            "ISO 230-1 Test code for machine tools - geometric accuracy, including squareness of axes (International Organization for Standardization)"
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-standards-and-regulation-q01",
                                                "text": "Which of these standards and regulation hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    },
                                    {
                                        "id": "evidence-real-world-use",
                                        "name": "Real-world use",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            "A bore axis specified square to a mounting flange so a shaft or fastener seats without edge load.",
                                            "CMM, granite-square and autocollimator checks of prismatic parts against a perpendicularity callout.",
                                            "Machine-tool acceptance: spindle or linear-axis squareness to a table or to another axis.",
                                            "Setting walls, columns and formwork square to a floor, grid or datum line on site."
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-real-world-use-q01",
                                                "text": "Which of these real-world use hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    },
                                    {
                                        "id": "evidence-measurements",
                                        "name": "Typical measurements",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            {
                                                "quantity": "Angular departure from 90°",
                                                "typical_range": "about 0.5 arcseconds (precision squares and autocollimators) to about 1° (rough construction)",
                                                "unit": "arcsecond or degree"
                                            },
                                            {
                                                "quantity": "Perpendicularity tolerance-zone width on a drawing",
                                                "typical_range": "commonly 0.02-0.5 on precision prismatic parts",
                                                "unit": "mm"
                                            },
                                            {
                                                "quantity": "Machine-tool axis squareness",
                                                "typical_range": "typically 5-30",
                                                "unit": "µm/m"
                                            }
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-measurements-q01",
                                                "text": "Which of these typical measurements hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    },
                                    {
                                        "id": "evidence-failure-modes-and-hazards",
                                        "name": "Failure modes and hazards",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            "A pin or hole that is not square to a face binds, galls, or loads on an edge instead of in bearing.",
                                            "A flange not perpendicular to a bore leaks at a gasket or misaligns a mating vessel or motor.",
                                            "Shaft-to-housing out-of-square edge-loads bearings and shortens life.",
                                            "Uncorrected CMM or machine-tool squareness error reports a good part as bad, or the reverse.",
                                            "Stacked 'square' plates accumulate angular error until an assembly will not close."
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-failure-modes-and-hazards-q01",
                                                "text": "Which of these failure modes and hazards hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    },
                                    {
                                        "id": "evidence-regional-variation",
                                        "name": "Regional variation",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            "US engineering drawings use ASME Y14.5 perpendicularity; ISO GPS (Europe and much of the rest of the world) uses the same symbol with different default datum and independence rules.",
                                            "Shop and site language often says 'square' or 'plumb and square' rather than 'perpendicular'; mathematics prefers 'orthogonal' for the inner-product condition."
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-regional-variation-q01",
                                                "text": "Which of these regional variation hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    },
                                    {
                                        "id": "evidence-neighbours",
                                        "name": "Neighbouring kinds and how to tell them apart",
                                        "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.",
                                        "evidence": [
                                            {
                                                "name": "Angularity",
                                                "difference": "Same orientation family, but the specified angle is not 90°; perpendicularity is the right-angle special case."
                                            },
                                            {
                                                "name": "Parallelism",
                                                "difference": "Orientation at constant separation (0° between directions) rather than a right angle; a feature can be parallel to one datum and perpendicular to another."
                                            },
                                            {
                                                "name": "Position",
                                                "difference": "Locates a feature relative to a datum system and can subsume perpendicularity; a pure perpendicularity control does not locate the feature."
                                            },
                                            {
                                                "name": "Flatness",
                                                "difference": "A form control with no datum; a surface can be flat and still lean relative to a reference."
                                            },
                                            {
                                                "name": "Orthogonality",
                                                "difference": "The inner-product condition (including function spaces and coordinate axes); perpendicularity in product geometry is the Euclidean 90° case of lines and planes."
                                            },
                                            {
                                                "name": "Squareness (shop metrology)",
                                                "difference": "Often the measured deviation of two machine or part axes in µm/m, not the drawing characteristic or its tolerance zone."
                                            }
                                        ],
                                        "questions": [
                                            {
                                                "id": "evidence-neighbours-q01",
                                                "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of perpendicularity this model covers, and on what evidence?",
                                                "kind": "provenance"
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    }
                ]
            },
            "openQuestions": [
                "Does the registry intend perpendicularity to include non-Euclidean local geometry, or only Euclidean geometric and physical relations?",
                "Should nonintersecting lines with perpendicular directions be included as perpendicular lines, or represented only through a relation between their directions?",
                "Which engineering perpendicularity conventions must this model support, and which datum, tolerance-zone and acceptance details belong in neighbouring models?",
                "How should perpendicularity between curved surfaces be represented when it holds only at selected points or along an intersection?",
                "Does an existing Vercy world model already own this concept or its geometric orthogonality meaning, requiring a registry link instead of a separate publication?"
            ],
            "statistics": {
                "bundles": 5,
                "layers": 9,
                "findings": 16,
                "questions": 26
            }
        },
        "draft": {
            "generator": "vr.draft.v3",
            "status": "draft-generated",
            "researched": false,
            "archetype": "abstract concept",
            "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.",
            "facetsInferred": true,
            "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.",
            "purpose": "Give an agent a durable, checkable way to recognise a perpendicularity, record what state it is in, and decide what may be done with it.",
            "whatItIs": "Enable an AI agent to recognise a perpendicularity relation, evaluate its support and deviation, and determine whether to accept, constrain, correct or further inspect it.",
            "characteristics": {
                "substance": "abstract",
                "origin": "conceptual",
                "agency": "inert"
            },
            "whatYouCanDoWithIt": [
                "observed and measured"
            ],
            "distinguishingFeatures": [
                "Described in 62 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is."
            ],
            "openQuestionsForResearch": [
                "Which of the bundles below does a real task actually need, and which are ceremony?",
                "What does this thing have that the facets do not capture at all?",
                "Which neighbouring kind is most often confused with a perpendicularity, and on what evidence are they told apart?"
            ],
            "whatItIsMadeOf": "an abstraction with no physical instance",
            "physicalCharacter": [
                "Does nothing on its own; everything it does, something else did to it.",
                "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing."
            ],
            "whatCanBeDoneWithIt": [
                "observe it, measure it, record its state"
            ],
            "howItIsRecognised": [
                "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about."
            ],
            "relatedModels": [],
            "standing": "Described in 62 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is.",
            "structure": {
                "bundles": [
                    {
                        "id": "identity-and-classification",
                        "name": "Identity, naming and classification",
                        "description": "How an agent tells one perpendicularity from another, and a perpendicularity from things that resemble it.",
                        "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.",
                        "layers": [
                            {
                                "id": "naming-and-identifiers",
                                "name": "Names and identifiers",
                                "description": "The names this thing goes by and the identifiers that survive translation and time.",
                                "findings": [
                                    {
                                        "id": "preferred-name-and-aliases",
                                        "name": "Preferred name, aliases and local names",
                                        "description": "Which name to use, which names mean the same thing, and which merely sound similar.",
                                        "questions": [
                                            {
                                                "id": "preferred-name-and-aliases-q01",
                                                "text": "What identifies and describes the name of a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "preferred-name-and-aliases-q02",
                                                "text": "Who or what asserted this about the name of a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "preferred-name-and-aliases-q03",
                                                "text": "What may an agent decide or do once the name of a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    },
                                    {
                                        "id": "stable-identifiers",
                                        "name": "Stable identifiers and external keys",
                                        "description": "Identifiers that keep pointing at this kind of thing across systems and languages.",
                                        "questions": [
                                            {
                                                "id": "stable-identifiers-q01",
                                                "text": "What identifies and describes an identifier for a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "stable-identifiers-q02",
                                                "text": "Who or what asserted this about an identifier for a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "stable-identifiers-q03",
                                                "text": "What may an agent decide or do once an identifier for a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "classification-and-granularity",
                                "name": "Classification and granularity",
                                "description": "Where a perpendicularity sits among kinds, and how finely a task needs to cut it.",
                                "findings": [
                                    {
                                        "id": "kind-and-parents",
                                        "name": "Kind, parents and neighbouring kinds",
                                        "description": "The classes this thing belongs to and the ones it is next to.",
                                        "questions": [
                                            {
                                                "id": "kind-and-parents-q01",
                                                "text": "What identifies and describes the kind of a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "kind-and-parents-q02",
                                                "text": "Who or what asserted this about the kind of a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "kind-and-parents-q03",
                                                "text": "What may an agent decide or do once the kind of a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    },
                                    {
                                        "id": "distinguishing-features",
                                        "name": "Distinguishing features",
                                        "description": "What separates a perpendicularity from the things most often confused with it.",
                                        "questions": [
                                            {
                                                "id": "distinguishing-features-q01",
                                                "text": "What identifies and describes what distinguishes a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "distinguishing-features-q02",
                                                "text": "Who or what asserted this about what distinguishes a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "distinguishing-features-q03",
                                                "text": "What may an agent decide or do once what distinguishes a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "state-and-lifecycle",
                        "name": "State and lifecycle",
                        "description": "The states a perpendicularity passes through and the events that move it between them.",
                        "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.",
                        "layers": [
                            {
                                "id": "lifecycle-stages",
                                "name": "Lifecycle stages",
                                "description": "From coming into existence to ceasing to be one of these.",
                                "findings": [
                                    {
                                        "id": "stages-and-transitions",
                                        "name": "Stages and transitions",
                                        "description": "The stages worth naming and what moves a perpendicularity between them.",
                                        "questions": [
                                            {
                                                "id": "stages-and-transitions-q01",
                                                "text": "What identifies and describes the lifecycle of a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "stages-and-transitions-q02",
                                                "text": "Who or what asserted this about the lifecycle of a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "stages-and-transitions-q03",
                                                "text": "What may an agent decide or do once the lifecycle of a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "observations-and-status",
                                "name": "Observations and current status",
                                "description": "What is observed about a perpendicularity, how often and by whom.",
                                "findings": [
                                    {
                                        "id": "observation-record",
                                        "name": "Observation record",
                                        "description": "How an observation of a perpendicularity is recorded so that it can be superseded rather than overwritten.",
                                        "questions": [
                                            {
                                                "id": "observation-record-q01",
                                                "text": "What identifies and describes an observation of a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "observation-record-q02",
                                                "text": "Who or what asserted this about an observation of a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "observation-record-q03",
                                                "text": "What may an agent decide or do once an observation of a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "definitions-in-contest",
                        "name": "Definitions and who holds them",
                        "description": "What perpendicularity is taken to mean, and by whom.",
                        "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.",
                        "layers": [
                            {
                                "id": "competing-definitions",
                                "name": "Competing definitions",
                                "description": "The main readings and the traditions behind them.",
                                "findings": [
                                    {
                                        "id": "definition-map",
                                        "name": "Definitions and their holders",
                                        "description": "Each definition with the school or body that holds it.",
                                        "questions": [
                                            {
                                                "id": "definition-map-q01",
                                                "text": "Which definitions of perpendicularity are in use, and which tradition or body holds each?",
                                                "kind": "definition"
                                            },
                                            {
                                                "id": "definition-map-q02",
                                                "text": "What turns on the difference between them in practice?",
                                                "kind": "boundary"
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "operationalisation",
                                "name": "Operationalisation",
                                "description": "How it is measured or applied when it has to be.",
                                "findings": [
                                    {
                                        "id": "operational-record",
                                        "name": "Measures and proxies",
                                        "description": "Instruments and indicators used to stand in for it.",
                                        "questions": [
                                            {
                                                "id": "operational-record-q01",
                                                "text": "How is perpendicularity operationalised or measured in practice, and by what instrument?",
                                                "kind": "measurement"
                                            },
                                            {
                                                "id": "operational-record-q02",
                                                "text": "What does that operationalisation leave out, and when does that matter?",
                                                "kind": "boundary"
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "instances-and-use",
                        "name": "Instances, use and consequence",
                        "description": "What counts as an instance of perpendicularity and what follows from calling something that.",
                        "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.",
                        "layers": [
                            {
                                "id": "instances",
                                "name": "What counts as an instance",
                                "description": "Clear cases, borderline cases and non-cases.",
                                "findings": [
                                    {
                                        "id": "instance-tests",
                                        "name": "Tests for an instance",
                                        "description": "What would settle whether something falls under it.",
                                        "questions": [
                                            {
                                                "id": "instance-tests-q01",
                                                "text": "What would settle whether something is an instance of perpendicularity?",
                                                "kind": "boundary"
                                            },
                                            {
                                                "id": "instance-tests-q02",
                                                "text": "Which borderline cases are argued about, and on what grounds?",
                                                "kind": "definition"
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "consequence",
                                "name": "Consequence of application",
                                "description": "Rights, duties or decisions that follow from the label.",
                                "findings": [
                                    {
                                        "id": "consequence-record",
                                        "name": "What the label licenses",
                                        "description": "What an agent may do once something is classified this way.",
                                        "questions": [
                                            {
                                                "id": "consequence-record-q01",
                                                "text": "What follows practically once something is treated as perpendicularity?",
                                                "kind": "action"
                                            },
                                            {
                                                "id": "consequence-record-q02",
                                                "text": "What must an agent not infer from the label alone?",
                                                "kind": "action"
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    },
                    {
                        "id": "provenance-and-evidence",
                        "name": "Provenance, evidence and time",
                        "description": "Where every claim about a perpendicularity came from and when it held.",
                        "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.",
                        "layers": [
                            {
                                "id": "source-and-authority",
                                "name": "Source and authority",
                                "description": "Who said it, on what evidence, and how strongly.",
                                "findings": [
                                    {
                                        "id": "claim-provenance",
                                        "name": "Claim provenance and confidence",
                                        "description": "The authority behind each claim about a perpendicularity and how confident it is.",
                                        "questions": [
                                            {
                                                "id": "claim-provenance-q01",
                                                "text": "What identifies and describes a claim about a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "claim-provenance-q02",
                                                "text": "Who or what asserted this about a claim about a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "claim-provenance-q03",
                                                "text": "What may an agent decide or do once a claim about a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    }
                                ]
                            },
                            {
                                "id": "time-and-versions",
                                "name": "Time, versions and supersession",
                                "description": "When a claim was true, when it was learnt, and what replaced it.",
                                "findings": [
                                    {
                                        "id": "validity-and-supersession",
                                        "name": "Validity period and supersession",
                                        "description": "How an old claim about a perpendicularity is retired without being erased.",
                                        "questions": [
                                            {
                                                "id": "validity-and-supersession-q01",
                                                "text": "What identifies and describes the validity of a claim about a perpendicularity, and in what units or vocabulary?",
                                                "kind": "definition",
                                                "answer_data": [
                                                    "identifiers",
                                                    "types and classes",
                                                    "values with units",
                                                    "explicit unknowns"
                                                ]
                                            },
                                            {
                                                "id": "validity-and-supersession-q02",
                                                "text": "Who or what asserted this about the validity of a claim about a perpendicularity, by which method, and when was it true?",
                                                "kind": "provenance",
                                                "answer_data": [
                                                    "authority",
                                                    "method",
                                                    "evidence",
                                                    "event time",
                                                    "knowledge time"
                                                ]
                                            },
                                            {
                                                "id": "validity-and-supersession-q03",
                                                "text": "What may an agent decide or do once the validity of a claim about a perpendicularity is known, and what must it refuse?",
                                                "kind": "action",
                                                "answer_data": [
                                                    "permitted actions",
                                                    "preconditions",
                                                    "refusals",
                                                    "escalation"
                                                ]
                                            }
                                        ]
                                    }
                                ]
                            }
                        ]
                    }
                ]
            },
            "statistics": {
                "bundles": 5,
                "layers": 10,
                "findings": 12,
                "questions": 32
            }
        }
    }
}